the task of keyword extraction is to automatically identify a set of terms that best describe the document .automatic keyword extraction establishes foundation for various natural language processing applications : information retrieval , automatic indexing and classification of documents , automatic summarization , high - level semantic description , etc .state - of - the - art keyword extraction approaches are based on statistical methods which require learning from hand - annotated data sets . in the last decade focus of researchhas shifted toward unsupervised methods , mainly toward network or graph enabled keyword extraction . in a networkbased keyword extraction the document representation may vary from very simple ( words are nodes and their co - occurrence is represented with links ) , or can incorporate very sophisticated linguistic knowledge like syntactic or semantic relations .typically , the source ( document , text , data ) for keyword extraction is modelled with one network . this way , both the statistical properties ( frequencies ) as well as the structure of source textare represented by unique formal representation , hence complex network .  network ( or graph , since the number of words in isolated documents is limited ) enabled keyword extraction exploits different measures for the task of identification and ranking of the most representative features of the source - the keywords .the keyword extraction powered by network measures can be on the node , network or subnetwork level .measures on the node level are : degree , strength , centrality ; on the network level : coreness , clustering coefficient , pagerank motivated ranking score or hits motivated hub and authority score ; on the subnetwork level : communities .majority of the research was motivated with various centrality measures : degree , betweenness , closeness and eigenvector centrality .our research aims at proposing an unsupervised method for keyword extraction in croatian language .since , croatian is a highly flective slavic language , usually source text needs a substantial preprocessing ( lemmatization morphological normalization , stopwords removal , part - of - speech ( pos ) annotation , morphosyntactic descriptions ( msd)tagging , etc . ), we design our approach with light or no linguistic knowledge . a new network measure - the node selectivity , originally proposed by masucci androdgers  ( which that can distinguish a real from a shuffled network ) , is applied to automatic keyword extraction .selectivity is defined as the average weight distribution on the links of the single node . in our previous work , the node selectivity measure performed in favour of differentiation between original and shuffled croatian texts , and for differentiation of blog and literature text genres . to the best of our knowledge ,the node selectivity measure was not applied to keyword extraction task before .section 2 presents an overview of related work on automatic keyword extraction . in section 3we present definition of the measures for the network structure analysis . in section 4we present the construction of co - occurrence networks from used text collection . in section 5 are the results of keyword extraction , and in the final section , we elaborate the obtained results and make conclusions regarding future work .lahiri et al . extract keywords and keyphrases form co - occurrence networks of words and from noun phrases collocations networks .eleven measures ( degree , strength , neighbourhood size , coreness , clustering coefficient , structural diversity index , page rank , hits hub and authority score , betweenness , closeness and eigenvector centrality ) are used for keyword extraction from directed / undirected and weighted networks . obtained results on 4 data sets are suggesting that centrality measures outperform the baseline term frequency / inverse document frequency ( tf - idf ) model , and simpler measures like degree and strength outperform computationally more expensive centrality measures like coreness and betweenness .boudin compare various centrality measures for graph - based keyphrase extraction .experiments on standard datasets of english and french show that simple degree centrality achieve results comparable to the widely used textrank algorithm ; and that closeness centrality obtains the best results on short documents .undirected and weighted co - occurrence networks are constructed from syntactically ( only nouns and adjectives ) parsed and lemmatized text using co - occurrence window .degree , closeness , betweenness and eigenvector centrality are compared to pagerank proposed by mihalcea in as a baseline .degree centrality achieve similar performance as much complex textrank and closeness centrality outperforms textrank on short documents ( scientific papers abstracts ) .litvak and last compare supervised and unsupervised approach for keywords identification in the task of extractive summarization .approaches are based on the graph - based syntactic representation of text and web documents .the results of the hits algorithm on a set of summarized documents performed comparable to supervised methods ( naive bayes , j48 , support vector machines ) .authors are suggesting that simple degree - based rankings from the first iteration of hits , rather than running it to its convergence should be considered .grineva et al . use community detection techniques for key terms extraction on wikipedia s texts , modelled as a graph of semantic relationships between terms .the results showed that the terms related to the main topics of the document tend to form a community , thematically cohesive groups of terms .community detection allows effectively processing of multiple topics in document and efficiently filters out noise .the results achieved on weighted and directed networks from semantically linked , morphologically expanded and disambiguated n - grams from article s titles .additionally , for the purpose of the noise stability , they repeated the experiment on different multi - topic web pages ( news , blogs , forums , social networks , product reviews ) which confirmed the community detection outperforms td - idf model .palshikar propose a hybrid structural and statistical approach to extract keywords from a single document .the undirected co - occurrence network , using a dissimilarity measure between two words , calculated from the frequency of their co - occurrence in the preprocessed and lemmatized document , as the edge weight was shown to be appropriate for centrality measures based approach for keyword extraction .mihalcea and tarau report a seminal research which introduced state - of - the - art textrank model .textrank is derived from pagerank and introduced to graph based text processing , keyword and sentence extraction .abstracts are modelled as undirected or directed and weighted co - occurrence networks using the co - occurrence window of variable sizes ( 2 .. 10 ) .lexical units are preprocessed : stopwords removed , words restricted with pos syntactic filters ( open class words , nouns and adjectives , nouns ) .the pagerank motivated score of importance of the node derived from importance of the neighboring nodes is used for keyword extraction . obtained textrank performancecompares favorably with the supervised machine learning n - gram based approach .matsou et al . in an early research which represents a document by a undirected and unweighted co - occurrence network , and study small - world properties of text . based on the network topology ,the authors proposed an indexing system called keyworld , which extracts important terms ( pair of words ) by measuring their contribution to small world properties .the contribution of the node is based on closeness centrality calculated as the difference in small world properties of the network with temporarily elimination of a node combined with inverse document frequency ( idf ) .erkan and radev introduce a stochastic graph - based method for computing relative importance of textual units on the problem of text summarization by extracting the most important sentences .lexrank , calculates sentence importance based on the concept of eigenvector centrality in a graph representation of sentences .a connectivity matrix based on intra - sentence cosine similarity is used as the adjacency matrix of the graph representation of sentences .lexrank is shown to be quite insensitive to the noise in the data .mihalcea in presents extension to earlier work , where the textrank algorithm is applied for text summarization task powered by sentence extraction . on this task textrankperformed at par with the supervised and unsupervised summarization methods , which motivated the new branch of research based on the graph - based extracting and ranking algorithms .tsatsaronis et al . present semanticrank , a network based ranking algorithm for keyword and sentence extraction from text .semantic relation is based on calculated knowledge - based measure of semantic relatedness between linguistic units ( keywords or sentences ) .the keyword extraction from the inspec abstracts results reported favorable performance of semanticrank over state - of - the - art counteparts - weighted and unweighted variations of pagerank and hits .huang et al . propose an automatic keyphrase extraction algorithm using unsupervised method based on conectedness and beetweenness centrality .the keyphrase extraction for croatian language has been addressed in both supervised and unsupervised settings .ahel et al . use a naive bayes classifier combined with tf - idf ( term frequency / inverse document frequen - cy ) , use part - of - speech ( pos ) and morphosyntactic description ( msd ) tags filtering followed by tf - idf ranking , and use distributional semantics to build topically related word clusters , from which they extract keywords and expand them to keyphrases .bekavac et al . propose a genetic programming approach for keyphrases extraction for croatian language on the same data set .gpkex can evolve simple and interpretable keyphrase scoring measures that perform comparably to other machine learning methods for croatian .reported research on extraction of croatian keywords use data set composed of croatian news articles from the croatian news agency ( hina ) , with hand annotated keywords by human experts .in the network , is the number of nodes and is the number of links . in weighted language networksevery link connecting two nodes and has an associated weight that is a positive integer number .  for every two connected nodes and the number of links lying on the shortest path between themis denoted as .for every two connected nodes and the number of shortest paths from node to node is denoted as , while the number of those paths that pass through node is denoted as .the node degree is defined as the number of edges incident upon a node .the in - degree and out - degree of node is defined as the number of its in and out neighbours .degree centrality of the node is the degree of that node normalised by dividing by the maximum possible degree n-1 :    analogue , the in / out - degree centralities are defined as in / out degree of a node :    closeness centrality is defined as the inverse of farness , i.e. the sum of the shortest distances between a node and all the other nodes .the normalised closeness centrality of a node is given by :    betweenness centrality quantifies the number of times a node acts as a bridge along the shortest path between two other nodes . in the directed network ,the normalised betweenness centrality of a node is given by :    the strength of the node is a sum of weights of all links incident with the node :    in the directed network , the in / out - strength of the node is defined as the number of its incoming and outgoing links , that is :    the selectivity of the node is a fraction of the node weight and node degree :    in the directed network , the in / out selectivity of the node is defined as :   the network based keyword extraction we use the data set composed of croatian news articles .the dataset contains 1020 news articles from the croatian news agency ( hina ) , with hand annotated keywords by human experts .the set is divided : 960 annotated documents for learning of supervised methods , and 60 documents for testing .the test set of 60 documents is annotated by 8 different experts , where the inter - annotator agreement in terms of f2 scores ( see section 6 ) are in average 46% ( between 29.3% and 66.1% ) .we selected the first 30 texts from the hina collection for our preliminary experiment .the texts required some preprocessing : parsing only textual part and title part excluding annotations , cleaning of diacritics and symbols ( w instead vv , ! instead l , etc . ) and lemmatization .non - standard word forms numbers , dates , acronyms , abbreviations etc .remain in text , since the method is preferably resistant to the noise presented in the data source .the selected 30 texts varied in the length : from very short 60 tokens up to 800 tokens ( 318 tokens in average ) .text can be represented as a complex network of linked words : each individual word is a node and interactions amongst words are links .co - occurrence networks exploit simple neighbour relation , two words are linked if they are adjacent in the sentence .the weight of the link is proportional to the overall co - occurrence frequencies of the corresponding word pairs within a corpus . for each document in hinadataset we construct one directed and weighted co - occurence network , 30 in total .network construction and analysis was implemented with the python programming language using the networkx software package developed for the creation , manipulation , and study of the structure , dynamics , and functions of complex networks .selectivity is a local ( node level ) network measures . in weighted and directed co - occurrence networks one can consider the in- and out- links for obtaining in / out selectivity of the node ( eq.8 ) .  in the first part of our experiment we compute in / out selectivity for all nodes in all 30 networks .the nodes are ranked according to the highest in / out selectivity values above threshold value . preserving the same threshold value ( 1 ) in all documents resulted in different number of nodes ( one word long keyword candidates ) extracted per each network . obtained set of one word long keyword candidatesis noted as set1 .then , for every filtered node we detect neighbouring nodes : for the in - selecti - vity we isolate one neighbour node with the highest outgoing weight ; for the out - selectivity we isolate one neighbour node with the highest ingoing weight .the result of in / out selectivity extraction is a set of ranked words - tuples - set2 .words - tuples are two words long sequences of keyword candidates . from obtained tuples we filtered out those containing stopwords in order to compare with the manually annotated evaluation set .for the keyword extraction task the strategy `` more is better '' can be utilized , since there is no objective judgement on keywords .hence , it is preferable to extract more keywords which makes trade off between precision and recall of the methods . the second polemic issue of keyword extraction task is : shorter keywords are more general vs. longer which are more accurate .motivated by this open arguments , and by the approach of other authors , we decided to follow the same principle : to extract as many as possible keyword candidates and evaluate them on the basis of recall ( ) and score , beside the standard precision ( ) and score . score is a harmonic mean of precision and recall : . measure gives two times as much importance to recall as to precision : .evaluation is the final part of the experiment based on the intersection of the obtained sets set1 and set2 of keyword candidates with the union of all 8 annotators keywords .the results in terms of precision and recall are in figures 1 and 2 respectively , and in terms of and scores in figures 3 and 4 respectively .obtained average score for the set 1 is 24,63% , and average score is 21,19% .expansion of obtained candidates to set2 increased average score to 25,9% and score to 24,47% .all supervised and unsupervised methods reported on keyphrases extraction from hina dataset incorporate linguistic knowledge ( pos , msd , .. ) of croatian .miji at al . initially extracted the list of keyword candidates as a comprehensive list of all words without stopwords ) which was expanded in a longer n - gram sequences up to length 4 . in keyphrase extraction system developed for a large - scale croatian news production system the tf - idf ranking model was used to extract n - grams of up to length four , which were lemmatized , and pos and msd filtered . for evaluationthe manually annotated key phrases from 60 documents were used .the evaluation set was reduced to keywords suggested only by 3 top annotators ( have the highest inter - annotator agreement among all 8 annotators ) .the results indicate that the performance is comparable to that of the human annotators .ahel at al .supervised for the one word long keywords reported precision of 22% and recall of 3.4% .we designed our method purely from statistical and structural information encompassed in the source text which is reflected into the structure of the network .our method achieved on a set1 average recall of 19,53% and precision of 39,1% .expansion to the words - tuples in set2 increased average recall to 23,87% and decreased precision to 32,23% .obtained results are comparable to and , but with slightly different evaluation set up .the preliminary results are promising and have potential to improve in several directions which is elaborated at the end of the next section .additional remark regarding results , is that beside keyword candidates our method captures personal names and entities , which were not marked as keyphrases and lowered the score .capturing names and entities can be of high relevance for the tasks like name - entity recognition , text summarization , etc .keyword annotation is an extremely subjective task as even human experts have difficulties to agree upon keyphrases ( inter - agreement around 40% ) .croatian is highly morphologically rich language , which puts another magnitude of challenge on the task , since annotators are freely choosing morphological word form as tag , which seems appropriate at the moment .additionally , there was no predefined set of index or keywords list , so annotators could make up their own , even worse in some cases it seemed appropriate to annotate with keywords , which were not present in the original article ( out - of - vocabulray words ) . in the number of out - of - vocabulary keywords on the whole hina datasetis estimated to high 57% . since our methodis derived from purely text statistics , it is not capable to capture all possible subjective variations of annotators .preliminary report on selectivity based keyword extraction for croatian news describes an unsupervised method which extracts nodes from complex network as keyword candidates .we build our approach with a new network measure - the node selectivity ( defined as the average weight distribution on the links of the single node ) , motivated by the research of the graph - based centrality approaches .the node selectivity value is used for extraction nad ranking of keyword candidates .furthermore , we expand extracted nodes to words - tuples with the highest in / out selectivity values .selectivity - based extraction does not require linguistic knowledge while it is purely derived from statistical and structural information encompassed in the source text which is reflected into the structure of the network .obtained average score for the set of extracted keyword candidates is 24,63% , and average score is 21,19% .expansion of obtained candidates to words - tuples increased average score to 25,9% and score to 24,47% , which is comparable to the results on the same dataset achieved by supervised and unsupervised methods .our results imply that the structure of the network can be applied on croatian keyword extraction task with many possible improvements .this should be thoroughly examined in the future work , which will cover : a ) evaluation - consider all flective word forms ; consider different matching strategies - exact , fuzzy , partof match ; b ) text types - consider texts of different length , genre and topics ; c ) multitopic - compare isolate document extraction vs. multitopic extraction ( one network constructed for the whole collection ) ; d ) other languages - test on standard english ( and other ) datasets ; e ) compare with other centrality motivated extraction approaches ; f ) longer keywords candidate sets - construct keyword sequences up to length 3 ; g ) entity extraction - test weather entities can be extracted from complex networks .d. margan , s. martini - ipi , and a. metrovi .preliminary report on the structure of croatian linguistic co - occurrence networks .5th international conference on information technologies and information society ( itis ) , slovenia , 89 - 96 ( 2013 )  d. margan , s. martini - ipi and a. metrovi .network differences between normal and shuffled texts : case of croatian .studies in computational intelligence , complex networks v. vol.549 .italy , pp .275 - 283 .( 2014 )                    r. ahel , b. dalbelo - bai and j. najder .automatic keyphrase extraction from croatian newspaper articles .the future of information sciences , digital resources and knowledge sharing , pp.207 - 218 , ( 2009 )

Abstract: preliminary report on network based keyword extraction for croatian is an unsupervised method for keyword extraction from the complex network . we build our approach with a new network measure - the node selectivity , motivated by the research of the graph based centrality approaches . the node selectivity is defined as the average weight distribution on the links of the single node . we extract nodes ( keyword candidates ) based on the selectivity value . furthermore , we expand extracted nodes to word - tuples ranked with the highest in / out selectivity values . selectivity based extraction does not require linguistic knowledge while it is purely derived from statistical and structural information encompassed in the source text which is reflected into the structure of the network . obtained sets are evaluated on a manually annotated keywords : for the set of extracted keyword candidates average score is 24,63% , and average score is 21,19% ; for the exacted words - tuples candidates average score is 25,9% and average score is 24,47% .   extraction , complex networks , croatian texts , selectivity


first milestone towards custom implant development is the accurate extraction of the target anatomical structure from medical image data .the tremendous evolution of ct imaging led to the widespread of this technique to all medical fields . from the engineering standpoint , ctimaging can be used for the development of patient - specific biomechanical and finite element models , as well as in the development of custom implants .currently , ct imaging is the modality of choice for imaging the human skeletal system .the ability to enhance the radiological contrast between hard and soft - tissue facilitates image segmentation , and the production of accurate representations of bone .the accurate segmentation of bone is the only way to guarantee the overall fit to the patient s anatomy , which may be paramount for success of the implant . nevertheless , the degree of patient fit necessary to minimize the biological impact of the implant is still unknown . on the one hand ,too much implant fit to the target anatomy may preclude implant insertion and may cause severe damages to the host bone . on the other hand , the absence of implantfit may cause interfacial micromotions that prevent bone ingrowth and implant osseointegration .  during image acquisitionthe ct scanner acts as a low - pass filter , and there is a degradation in image quality due to the limited frequency response of the imaging system .the sharp transitions between adjacent structures found in reality become diffuse in the final image . in was concluded that ct imaging produced large domain overestimations for structures with a cortical thickness below 2.0 mm .the amount of spatial image blur is often modelled in the image space by the system s point spread function ( psf ) .in addition , the inner and the outer cortical surfaces of bone could only be accurately determined for thickness greater than the full width at half maximum ( fwhm ) of the psf . for objects with a thickness smaller than the fwhm of the psf , domain overestimations up to 40% of the original size were obtained in .similarly , in it was observed that for small diameter spheres imaged with ct the apparent diameter was in fact the fhwm of the psf .therefore , the fwhm seems to provide a measure of the maximum spatial frequency that can be accurately encoded by a given ct machine , rather than other acquisition settings .  another limiting factorto image accuracy may be the reconstruction ( field of view ) fov .in high - resolution reconstructions the psf if often the limiting factor , however for larger fov if the pixel size is larger than the fwhm , the psf is spread to occupy a single pixel in the reconstructed image .image reconstruction with large voxel sizes has a higher impact on bone thickness overestimation than smaller sizes , and that large voxel sizes were also detrimental for the representation of thinner and highly curved structures .although relevant , the limitation of the image acquisition process may be minimal considering other error sources .in fact , the image reconstruction in ct imaging is known to have a very high accuracy , and to be almost free of geometrical magnification .image segmentation is often affected by high inter and intra - expert variability , and the image processing and segmentation chain may contribute up to 70% of the average error found in the final reconstruction .  in the literaturea plethora of studies have addressed bone segmentation , however few have evaluated the accuracy of the segmentation outcome . in an early study analysed the ct attenuation profile normal to the bone s surface , and concluded that a single threshold was insufficient to accurately define the femur s cortical shell . the relative thresholds of 45% and 50% of the maximum hu profile value were proposed to segment properly the diaphyseal and metaphyseal regions of the femur , respectively .more recently , , and reported the accurate segmentation of cortical bone from ct imaging with single thresholding , adaptive thresholding , and multiple thresholding . exploiting the concept of relative thresholding , in a levenberg - marquardt segmentation algorithm to quantify femoral cortical thickness with sub - millimetre accuracywas proposed .an ideal high - resolution attenuation model was fitted to the hu attenuation profile normal to the bone s surface and then thresholded with the 50% relative threshold .a similar approach was used in to segment bones from the craniofacial skeleton .the production of sub - pixel accuracy estimates of both inner and outer surfaces of the bone were reported .  in practice, the application of the aforementioned techniques may possess some limitations .single thresholding are very sensitive to image inhomogenities , noise , and threshold selection . with adaptive thresholdingthere is no guarantee that a closed contour will be obtained , and may provide incorrect estimates of the bone surface especially in regions with thin cortical shells .relatively to model fitting techniques , the application of adaptive / relative thresholds to each boundary pixel is extremely time consuming and unpractical .in addition , the normal direction is highly affected by the discrete nature of the image .the surface of the bone has to be sampled and each surface point needs to be processed independently , which produces highly irregular contours .it also produces unreliable estimates of the bone surface if the observed attenuation profile deviates from the ideal attenuation profile , which is common near the articulating surfaces of bones .  in this work a different approach to accurate bone segmentationis proposed .the proposed protocol allows the segmentation of bony structures with sub - pixel accuracy , and intrinsically guarantees the smoothness of the extracted contours .the proposed segmentation protocol is validated through the comparison between the segmentation outcome and a geometrically well - defined gold standard . for validation purposesa synthetic bone was used as the gold standard .the remainder of this paper is organized as follows : in section [ secii ] the segmentation protocol , the definition of the segmentation gold standard , and the means for quantifying the accuracy of the ct machine are described ; in section [ seciii ] one presents a methodology to estimate the psf of the ct machine ; in section [ seciv ] the impact of the domain discretization ( voxel vs. average error ) in the model accuracy is shortly analysed ; section [ secv ] and section [ secvi ] refer to the description and discussion of the results obtained with the proposed segmentation pipeline ; and ultimately in section [ secvii ] one presents the conclusions of the present work .due to the degree of variability in the human anatomy and image artifacts , segmentation methods designed specifically to each application often produce better results than general purpose algorithms . nevertheless , some degree of standardization is desirable , particularly when the segmentation is part of product development pipeline .therefore , in this work one proposes a two - step segmentation protocol for reliably and accurately extract hard tissue structures from image data . to evaluate the accuracy of the newly proposed segmentation protocol a phantom study was carried out . one composite replica of the human femur ( fig .[ fig : ch03fig01 ] ) commercially available at the sawbones was imaged with a ct machine .the image acquisition process was carried with a fourth - generation ct scanner toshiba  at the cuf hospital , porto ( portugal ) .  during image acquisition and reconstruction two types of scan settingswere used .three geometrically simpler phantom objects were added to the acquisition process . in practice , these geometrically simpler phantoms may be important to characterize the image acquisition process , especially the limiting resolution of the ct scanner .the tested objects were a calibrated hollow cylinder with an outer diameter of mm , a brass alloy wire with 0.10 mm of diameter , and a ceramic box with dimensions mm ( fig .[ fig : ch03fig01 ] ( b ) , ( c ) and ( d ) ) . the compact nature of these phantom objects allow them to be imaged simultaneously with the patient , and may avoiding the need to have a dedicated phantom to assess the spatial resolution of the ct scanner . the ability to quantify the system s limiting resolution was evaluate against the catphan 528 , which is a commercially available phantom often used for quality control .the catphan 528 was imaged to quantify the true in - plane resolution of the ct machine , against which the performance of each phantom could be compared .the summary of image acquisition protocols and image reconstruction resolutions for the phantom femur , the catphan 528 , and the three other phantoms is presented in table [ tab : ch03tab01 ] .[ tab : ch03tab01 ]  regarding the segmentation protocol , a pre - segmentation of the image must be provided . in this step the technique(s ) more suitable to provide an initial segmentation of the bone may be applied .the output of image pre - segmentation should contain a set of regions of interest ( rois ) ( for instance , the segmentation of the composite femur and the phantom object(s ) ) , and may also have some additional spatial constraints , such as the ct table .the pre - segmentation aims to provide some high - level information about the desired domain , as well as some spatial relationships between any existing adjacent structures .this allows us to handle segmentation variability prior to segmentation refinement . in the second step ( which will be referred as refinement step ) , a fully automatic segmentation refinement composed by several sub - stpng is performed in order to optimize the initial partition .[ fig : ch03fig02 ] schematically depicts the proposed segmentation protocol .the refinement protocol comprises image deconvolution , which is applied in order to minimize the partial volume effect caused by the psf during image acquisition .next , the image is cropped around the roi according to the pre - segmented data , and up - sampled with cubic spline interpolation ( [ e : ch03eq01 ] ) :    [c]{l?s }     \ieeestrut     \frac{2}{3 } - \frac{1}{2}\left| x \right|^2 \left ( { 2 - \left| x \right| } \right),\ \ 0 \le \left| x \right| < 1 \\     \frac{1}{6}\left ( { 2 - \left| x \right| } \right)^3 , \                \ 1 \le \left| x \right| < 2 \\0,\                                         \ 2 \le \left| x \right|     \ieeestrut   \end{ieeeeqnarraybox } \right.\ ] ]  where defines the finite support of the basis function . in concluded that cubic spline interpolation provides the best interpolation strategy for image processing applications , both in terms of computation effort and image induced artifacts .segmentation refinement is performed over the interpolated roi .the final segmentation obtained using the chan - vese level - set method , with the additional spatial constraints imposed in the pre - segmentation step ( [ e : ch03eq02 ] ) :  rcl [ e : ch03eq02 ] & = & div ( ) - _ 1 ( i - _ 1 ) ^2 + _ 2 ( i - _ 2 ) ^2 + & & + _ 2 _ k = 1;k i^n s_k  where is the level - set corresponding to the pre - segmented region , , and are the average intensity inside and outside the curve , and the final summation assigns the average intensity of the background to all the remaining pre - segmented sub - regions multiplied by a user defined cost .the chan - vese acwe level - set method is less sensitive to curve initialization and noise than other level - set methods , which allows a less restrictive pre - segmentation and a lesser dependency between the pre - segmentation and the final segmentation .segmentation refinement was performed independently for each region , instead of applying a multi - phase level - set method ( see for instance ) .this reduces the computational complexity and memory requirements of the segmentation refinement , by applying image interpolation in smaller region at each iteration .two refinement outputs were considered ( fig .[ fig : ch03fig02 ] ) .the new segmentation can be directly exported to the cad modelling software via point cloud or downscaled to the original image resolution for further surface or finite element mesh generation . to test the robustness against image noise , the segmentation refinement was tested over datasets # 1 to # 5 corrupted with additive white gaussian noise ( awgn ) .it is known from image acquisition theory that any image obtained from an imaging system is not perfect and is only an approximation to the real ( ideal ) image .the real image is never available due to the intrinsic nature of the acquisition process .however , an estimate of its true distribution may be obtained considering the output image and some prior knowledge about the system s behaviour . in 2d image acquisition theory ,the imaging system is commonly considered as being linear and spatially invariant , and the output image may be correlated with the input image according to ( [ e : ch03eq03 ] ) :  c [ e : ch03eq03 ] g ( x , y ) = i ( x , y ) h ( x , y ) + n ( x , y )  where denotes the 2d convolution , denotes the system blurring effect of the system s psf , and is an addictive noise term .the deconvolution problem is intrinsically limited by the knowledge about the psf and the noisy processes related with the acquisition itself .image restoration in this work is accomplished by applying a standard iterative blind deconvolution algorithm .the matlab function_ deconvblind _ is used for the purpose of image restoration .the _ deconvblind _ uses the lucy - richardson algorithm to obtain the new estimates of the original scene and the psf and can be defined as ( [ e : ch03eq04 ] ) :  llrllr [ e : ch03eq04 ] i_k + 1 ( x , y ) & = & + & i_k ( x , y ) + h_k + 1 ( x , y ) & = & + & h_k ( x , y )  where and are the complex conjugates of and , respectively , and where , and is the acquired image and the image noise n(x , y ) is neglected .the blind deconvolution is not dependent on the knowledge of the system s spatial blurring .however , we found that robust results may be obtained if an accurate initial guess of the system s psf is provided .the psf is determined by the overall behaviour of the image acquisition system .the noise term is typically a stochastic process that may be originated by a multitude of processes .noise can be efficiently suppressed by non - linear filtering , for instance applying anisotropic diffusion proposed in .it also avoids edge bias , which is very common with linear filtering .  in practice ,the psf of a given imaging system is frequently approximated by a normalized gaussian function as stated by the central slice theorem , such that ( [ e : ch03eq05 ] ) :  c [ e : ch03eq05 ] h ( x , y , z ) = e^ ( + + )  where , , and denote the standard deviation in each orthogonal direction .two assumptions are commonly found in literature for the psf namely : ( i ) the psf is assumed to be uniformly invariant in the slice plane ; and ( ii ) the cross - plane psf is generally also assumed to be invariant in the axial direction . in practice , the psf is not completely isotropic and shift invariant , however this approximation can be safely made for most ct scanners , as well as for several other medical acquisition modalities . for simplicity onewill only consider the estimation of the in - plane blur , and hence ( [ e : ch03eq05 ] ) can be reduced to its 2d counterpart .there are several approaches to determine the psf of an imaging system proposed in the literature .the phantom objects investigated in this work allow the measurement of psf directly by simulating an impulse signal , or by computing the edge spread function ( esf ) along the cylinder and the ceramic box .the esf can be computed simply by differentiating the edge response to radiopaque objects . in the esfa gaussian function was fitted to the gradient of the attenuation profile normal to each object surface .for profile de - noising , wavelet thresholding was applied to the 1d signals as proposed in .curve fitting was performed over a narrow band around the gradient maximum , in order to remove the influence of the adjacent structures .a similar approach was applied in to completely characterize the psf using a single image .the final estimate of the psf was defined as the average of all psf estimates along the sampled phantom edges .[ fig : ch03fig04 ] depicts the psf of the toshiba  ct scanner obtained directly from the catphan 528 and wire phantom , as well as the estimates obtained through the esf .64 ct scanner with the catphan 528 , the mm wire phantom , and the calibrated hollow cylinder and ceramic box phantoms , width=88 ]the system s psf may not be the only factor affecting the resolution of the ct scan .image reconstruction with large slice thicknesses is commonly associated with larger model inaccuracies . nevertheless , in a recent study it was demonstrated that alongside with the slice thickness , the fov also influences the spatial resolution of the scan and the amount of partial volume averaging .the size of the voxel may be more critical than other potential error sources , such as the surface meshing parameters . in impact of the voxel size and meshing parameters in the representation of a human lumbar motion segment was analysed .it was concluded that the resolution of the ct scan ( voxel size and slice thickness ) was the major source of geometrical inaccuracies of the reconstructed model .therefore , the effect of domain discretization ( slice thickness and voxel size ) can not be neglected when assessing the achievable model accuracy from a given set of ct images . to understand the effect of pixel size in domain accuracy ,the gold - standard model for composite femur was discretized with different isotropic voxels sizes , namely ( mm ) .[ fig : ch03fig06 ] shows the average and maximum domain error as a function of the voxel size .the average error due to the domain discretization varied between mm and mm , whereas the maximum deviation was mm and mm for a voxel size of mm and mm , respectively . as expected , the results show that as the domain sampling increases both the absolute average and the maximum error decrease ( fig .[ fig : ch03fig06 ] ( a ) ) .the largest domain deviations are found in small localized sharp features or surface irregularities along the reference model , which are lost or smoothed due to the domain sampling . for a voxel size consistent with the size of the fwhm of the psf ( mm ) , theoretically an average error of mm and a maximum deviation of mmare expected to occur due to the domain discretization .  in fig .[ fig : ch03fig06 ] ( b ) the average and maximum errors are normalized against the sampling size .the normalized average error decreases from 28% to 5.6% of the sampling size , while the maximum error decreases from 92.1% to 56.1% for domain samplings between 5.0 mm and 1.5 mm .however , for edge lengths equal and below 1.0 mm the maximum error shows a growth tendency , reaching 76.0% of the domain sampling for 0.2 mm .the normalized average error decreases and becomes almost constant for smaller sampling sizes , whereas the maximum normalized error increases initially for larger sampling sizes and increases as the sampling size becomes smaller .these provide an evidence that domain deviations may exist regardless of the sampling size used , and that the average deviations converge to a fixed percentage of the sampling size .two outputs may be produced after segmentation refinement ( fig . [fig : ch03fig02 ] ) , a high - resolution point cloud model obtained directly from the interpolated image , and a down - scaled version of the high - resolution segmentation . the surface mesh model obtained from the point cloudwill be referred as point cloud ( pc ) model . since image refinement is performed independently in each image , the pc model is produce directly from a set of equally spaced contours by tiling the cloud points .the surface mesh of the down - scaled version was generated in simpleware scanip , with standard pre - smoothing and mesh refinement settings , and will be referred simply as scanip mesh ( sm ) model .the segmentation pipeline was tested in noise - free and noisy images , corrupted with awgn with a standard deviation of hu .[ fig : ch03fig07 ] shows the sub - stpng of the segmentation refinement process when applied to both noise - free and noisy images . the hausdorff distance ( hd ) and the mean symmetric distance ( msd ) were applied to evaluate each segmentation outcome .[ fig : ch03fig08 ] shows the final pc model obtained from the segmentation of dataset # 1 and the comparison with the nikon metris  gold standard , whereas fig .[ fig : ch03fig09 ] depicts the down - scaled segmentation within simpleware scanip overlapped with reference surface .a close agreement between both pc and sm , and the gold standard is observed for both models .the agreement between the pc and sm model and the gold standard for all noise - free and noisy datasets regarding the distance measures are summarized in table [ tab : ch03tab02 ] and table [ tab : ch03tab03 ] , respectively .[ tab : ch03tab02 ]  [ tab : ch03tab03 ]  the average error between the gold - standard surface mesh obtained with nikon metris  and the pc model for ds # 1 was mm ( fig .[ fig : ch03fig08 ] ) , whereas for the sm model the average error was mm ( fig . [fig : ch03fig09 ] ) . for the dataset # 2the average error of the sm was mm , for the dataset # 3 the average error was mm , mm for the dataset # 4 , and mm for dataset # 5 .comparing the results of table [ tab : ch03tab02 ] and table [ tab : ch03tab03 ] , the surface meshes generated directly from the high - resolution point cloud allow the production of more accurate models for all datasets .the reduction on the average error ranges from 51% for dataset # 1 to 26% for dataset # 5 ( mm ) for noise - free images .similar values were observed for the noisy datasets , and therefore the algorithm shows robustness against image noise .  in the pc surfacemeshes are triangulated from the 3d points , and model smoothness is directly defined by the smoothness of the level - set contour .contrariwise , in the sm models the final accuracy is not only dependent on the segmentation accuracy , but also on the settings used for surface mesh generation .the results show that surface mesh tiling allows the accurate definition of the femoral outer surface not only in high - resolution scans , but also in scans with more _ clinical _ settings such as with dataset # 3 .surface meshing directly from the point cloud data effectively avoids the straircase artifacts commonly observed with larger slice thicknesses , and greatly improves the accuracy of the final model .  in section [ seciv ] for a domain sampling consistent with the fwhman average error of mm was expected .predictably image segmentation is an additional source of model errors . nevertheless , the average error obtained for dataset # 1 is in close agreement with the theoretical discretization error .the results show that the whole chain of image deconvolution , interpolation and segmentation only adds an error of approximately 0.36% to the theoretical average error .a fwhm of 0.88 mm causes obvious limitations in some datasets , and the spatial limitations imposed by the psf superimpose to the pixels size .[ fig : ch03fig11 ] compares graphically the theoretical average and maximum deviation from the gold standard due to domain discretization considering the fwhm of the psf , and the average and maximum error of all pc models .domain discretization contributes in a greater extent to the final deviation from the ground - truth , when compared with the segmentation refinement chain .[ fig : ch03fig12 ] shows volume deviation for each final model .the maximum volume deviation was found for the noise free dataset # 5 .the pc models underestimate the roi in datasets # 1 , # 3 and # 4 , more precisely -0.31% , -0.55% and -0.01% , respectively , and overestimate it in 0.55% in dataset # 2 , and in 1.27% in dataset # 5 . for the down - scaled model volume overestimation ranges from 1.52% in dataset # 1 to 8.09% in dataset # 5 for noise free images , and from 1.73% to 7.70% for dataset # 1 to # 5 , respectively .interestingly , for dataset # 5 the average error and volume deviation decrease with the addition of gaussian noise . , the point cloud - based model and sm model for noisy and noise - free images , width=88 ]during image acquisition the ct scanner acts as a low - pass filter , eliminating all the high - spatial frequencies . the sharp transitions between different anatomical regions become unclear , and sometimes barely recognizable .the edge blurring effect often leads to the overestimation of the roi , and the recovery of the original scene is intrinsically limited by our knowledge about the system s psf .the ability to precisely determine the psf is of paramount importance if one aims to extract geometrically accurate models from medical images .  in this workwe have tested three different phantom objects and their ability to estimate the system s psf against the catphan 528 , which is the phantom routinely used for quality control .the phantom objects aim to estimate the psf either directly from the system s response to an impulse signal , or indirectly through the estimation of the esf .relatively good estimates were obtained with all phantoms .however , the brass wire with 0.10 mm of diameter provided the most accurate estimate of the psf with a standard deviation error of only 2.9% when compared with the psf obtained with the catphan 528 .similar values for the toshiba  system were obtained in .unlike direct measurements , the estimation of the psf through the analysis of the system s response to strong edges implies additional signal processing stpng .gaussian filtering has been associated with edge bias by several authors .in addition , the esf may be affected by the presence of image noise during the calculation of the gradient of the attenuation profile .noise must be eliminated prior to the calculation of the gradient . in this context , proposed an additional blurring correction step to eliminate the gaussian smoothing effect from the estimate of the mtf estimate . instead of correcting the result , wavelet thresholding can be used to avoid linear signal filtering .our results show that although less accurate than the wire phantom , the estimate of the psf through the esf and wavelet denoising produces quite good approximations to the real ct spatial blurring function .the wavelet thresholding provides the means to effectively reduce the noise level along the attenuation profile , and to accurately estimate of the esf without the need for any compensation procedure .  in practice ,the accurate quantification of the system s psf allow us to accurately recover the original image using more standard image deconvolution algorithms .in fact , the accurate estimate of this quantity proved to be quite important to obtain accurate segmentations from image data . in it was concluded that reversing the blurring degradation prior to segmentation is essential for the construction of accurate fe models from medical imaging .regarding image segmentation , a two - step segmentation pipeline was proposed .the segmentation outcomes were validated through a phantom study , where the final models were compared against a gold standard surface mesh .the gold - standard representation of the phantom object was acquired with a coordinate measuring machine nikon metris  with a digital line scanner , which guarantees 28 of spatial accuracy .  in the results obtained the maximum average deviation from the gold standard was 0.172 mm for dataset # 5 , whereas the maximum deviation was 2.691 mm for all sets of images considered in the analysis .these results show that the accurate estimation of the system s psf , conjugated with image interpolation and level - set segmentation provide quite good segmentations of the target geometry .in addition , results provide clear evidences that surface meshes computed from a high - resolution 3d point cloud provide a more accurate representation of the bone than the standard surface meshing from the voxelized data .the point cloud data allows the production of surface models that are both smooth and relatively independent from the surface meshing .surface triangulation from adjacent contours ( or surface tiling ) also avoids staircase artifacts due to large section variation between consecutive slices caused by large slice thicknesses .the advantage of using surface tiling is observable when comparing the results obtained in datasets # 2 and # 3 .the average errors obtained with dataset # 2 and # 3 differ only in 0.003 mm .nevertheless , the largest maximum deviation observed in the pcm models may also be a consequence of surface mesh tiling , as can be observed in fig .[ fig : ch03fig08 ] .the results show that segmentation accuracy is more dependent on the reconstruction fov than on the slice thickness .this observation in in agreement with observations found in other phantom studies . using the high - resolution point cloud to generate the surface meshes may allow the acquisition of image data with more clinical settings , reducing the exposure of the patient to the radiation without a significant loss in model accuracy .in addition and unlike previous works , our results also show that bone segmentation through the level - set method is accurate and possesses numerous advantages against other segmentation methods .the level - set method is robust to noise , it guarantees contour smoothness , is topologically flexible , and allows a straightforward incorporation of user - defined spatial constraints .  considering the errors associated with domain discretization , the errors produced by the segmentation pipeline varied from 0.41% to 8.94% of the final error .these errors are in the same order of magnitude as the discretization itself . in section iv for a domain sampling consistent with the systems psf the normalized average error is approximately 8.3% of the sampling or ( mm ) .domain discretization may also explain the average errors obtained with dataset # 1 to # 4 , which are very similar despite of the voxel size , and the considerable increase in the average error observed for dataset # 5 . in dataset# 1 and # 4 the system s psf is the main limitation to the spatial accuracy of the model , whereas in dataset # 5 the main limitation is the voxel size itself .the average error obtained from dataset # 1 shows that the whole chain of image deconvolution , image up - scaling through cubic spline interpolation , and subsequent segmentation , there is almost no information degradation or distortion due to the image processing pipeline .our observations also corroborate previous observations in that the domain discretization contributes in a larger extent to the final error of the surface mesh model .the segmentation in two stpng proposed in this work is very similar to the other methods proposed in the literature . for comparison purposes ,the main results obtained by different authors in the literature are summarized in table [ tab : ch03tab05 ] .three studies that have an average error smaller than the maximum average error obtained with the proposed segmentation refinement protocol , namely the optimized 600 hu threshold proposed in , the levenberg - marquardt - based algorithm proposed in , and the gradient descent algorithm proposed in . nevertheless , in the average error varied from -0.20 mm to 0.20 mm in the eight femurs considered , which is larger than the maximum average error obtained with our algorithm for all datasets . the high standard deviation ( 0.77 mm )shows that the algorithm proposed in mainly oscillate around the true surface of the cortical bone . in slightly less oscilating results were obtained . however , for a comparable spatial resolution ( dataset # 4 ) , the results in this work have a smaller average error of 0.080 mm ( with 68.2% of the surface points within the interval of -0.004 to 0.164 mm ) for noise free data , and with an average error of 0.103 mm ( with 68.2% of the surface points within the interval of 0.020 to 0.185 mm ) for noisy data .  [tab : ch03tab05 ]  the practical implications of an average deviation from the gold standard of 0.172 mm in custom implant modelling are still unclear . in an early study, found that implant - bone surface gaps of 0.35 mm or more were not bridged by cortical bone , and that this value is close to the critical gap width for which direct lamellar bone apposition occurs onto unloaded implants .in an animal study , found that there was no bone integration at the interface of roughened titanium rods with 0.30 mm of diametrical gaps at the bone - implant interface .the average error obtained may have minor practical implications in the performance of the custom implants developed from the 3d models for both orthopaedic and trauma applications.in an inward offset of 0.50 mm to the contours obtained with the 600 hu contour was proposed to avoid custom femoral stem over dimensioning .endosteal contour shrinkage is needed due to the large standard deviation ( 0.52 mm ) around the average error ( table [ tab : ch03tab05 ] ) .traditional surgical techniques may play a more relevant role in the implant outcome than the geometrical accuracy obtained during implant modelling ( see for instance ) .the main limitations of the present study are directly linked with the limitations often associated with every phantom study .phantom studies are flexible to parameterize and allow the simulation of different acquisition and reconstruction protocols , noise levels , among others . in this type of studiesthe ground truth may be accurately characterized , and does not change under different environmental conditions .nevertheless , phantom studies may not be realistic enough to model the complexity of the real data .the ct images used in this analysis have good contrast and are almost noise free .such images are very difficult or even impossible to obtain in practice .the acwe are very robust to noise but sensitive to image contrast , therefore in real data the performance of the present algorithm may be slightly degraded .furthermore , although the use of acwe enables some degree of flexibility in the pre - segmentation step .there is still however some dependency on the curve initialization .image under - segmentation seems to be more problematic than over - segmentation , hence in ambiguous pixels it is better to over - segment the domain rather than excluding the pixels .the elimination of such a dependency and the extension of the protocol to the third dimension , in order to obtain a 3d point cloud instead of the current 2d contours are natural evolutions to the current algorithm , and will be considered in future work .these may facilitate the pre - segmentation step and may help to overcome the limitations of surface mesh tiling near bone ends , and allow the production of more accurate models near articulating surfaces .in this work a two - step segmentation pipeline is proposed for accurate bone segmentation from ct image data .the proposed methodology handles segmentation variability by allowing a first free pre - segmentation step , where the user can employ the necessary means to obtain a good approximation to the target segmentation .the second step is standardized and fully automatic and encompasses image restoration , cropping , interpolation , and level - set segmentation .the proposed methodology produces accurate estimates of the target geometries with a maximum average deviation of 0.172 mm .our results show that surface meshes extracted directly from the high - resolution point cloud reflect more accurately the target roi . for these meshes the final model accuracyis mostly affected by the image acquisition and reconstruction , rather than by the image segmentation and surface meshing processes .in addition , the ct machine psf can be accurately determined using a brass alloy wire phantom with 0.10 mm of diameter .the direct measures provide slightly more accurate estimates of the system s point spread function , when compared with indirect measures based on the edge spread function .the first author would like to acknowledge fct fundao para a cincia e tecnologia ( portugal ) for the phd grant sfrh / bde/51143/2010 .the authors also would like to acknowledge hospital cuf , porto ( portugal ) , clnica dr .campos costa , porto ( portugal ) , and isq instituto de soldadura e qualidade for all technical support provided during this work .s. d. stulberg , b. n. stulberg , and r. l. wixson , `` the rationale , design characteristics , and preliminary results of a primary custom total hip prosthesis , '' _ clinical orthopaedics and related research _ ,249 , pp . 7996 , 1989 .j. a. mandell , d. r. carter , s. b. goodman , d. j. schurman , and g. s. beaupr , `` a conical - collared intramedullary stem can improve stress transfer and limit micromotion , '' _ clinical biomechanics _19 , no . 7 , pp . 695703 , 2004 .s. prevrhal , k. engelke , and w. a. kalender , `` accuracy limits for the determination of cortical width and density : the influence of object size and ct imaging parameters , '' _ physics in medicine and biology _ , vol .44 , no . 3 , p. 751, 1999 .y. kang , k. engelke , and w. a. kalender , `` a new accurate and precise 3-d segmentation method for skeletal structures in volumetric ct data , '' _ medical imaging , ieee transactions on _ , vol . 22 , no . 5 , pp . 586598 , 2003 .m. ohkubo , s. wada , m. kunii , t. matsumoto , and k. nishizawa , `` imaging of small spherical structures in ct : simulation study using measured point spread function , '' _ medical & biological engineering & computing _ , vol .46 , no . 3 , pp .273282 , 2008 .a. maloul , j. fialkov , and c. whyne , `` the impact of voxel size - based inaccuracies on the mechanical behavior of thin bone structures , '' _ annals of biomedical engineering _ , vol .39 , no . 3 , pp .10921100 , 2011 .  c. f. hildebolt , m. w. vannier , and r. h. knapp , `` validation study of skull three - dimensional computerized tomography measurements , '' _ american journal of physical anthropology _ , vol .82 , no . 3 , pp .283294 , 1990 .p. rothuizen , l. van erning , and r. huiskes , `` the accuracy of criteria for automatic 3-d graphics reconstruction of bone from computer tomography , '' in _ biomechanics : basic and applied research_.1em plus 0.5em minus 0.4emspringer , 1987 , pp . 109114 .a. aamodt , k. a. kvistad , e. andersen , j. lund - larsen , j. eine , p. benum , and o. s. husby , `` determination of the hounsfield value for ct - based design of custom femoral stems , '' _ journal of bone & joint surgery , british volume _81 , no . 1 ,pp . 143147 , 1999 .k. rathnayaka , t. sahama , m. a. schuetz , and b. schmutz , `` effects of ct image segmentation methods on the accuracy of long bone 3d reconstructions , '' _ medical engineering & physics _ , vol . 33 , no . 2 , pp .226233 , 2011 .a. pakdel , n. robert , j. fialkov , a. maloul , and c. whyne , `` generalized method for computation of true thickness and x - ray intensity information in highly blurred sub - millimeter bone features in clinical ct images , '' _ physics in medicine and biology _ , vol .57 , no .23 , p. 8099, 2012 .w. yao , p. abolmaesumi , m. greenspan , and r. e. ellis , `` an estimation / correction algorithm for detecting bone edges in ct images , '' _ medical imaging , ieee transactions on _ , vol .24 , no . 8 , pp . 9971010 , 2005 .w. verbeek and l. j. van vliet , `` on the location error of curved edges in low - pass filtered 2-d and 3-d images , '' _ pattern analysis and machine intelligence , ieee transactions on _ , vol .16 , no . 7 , pp . 726733 , 1994 .h. bouma , a. vilanova , l. j. van vliet , and f. a. gerritsen , `` correction for the dislocation of curved surfaces caused by the psf in 2d and 3d ct images , '' _ ieee transactions on pattern analysis and machine intelligence _ , vol .27 , no . 9 , pp .15011507 , 2005 .s. dore and y. goussard , `` experimental determination of ct point spread function anisotropy and shift - variance , '' in _ engineering in medicine and biology society , 1997 .proceedings of the 19th annual international conference of the ieee _2.1em plus 0.5em minus 0.4emieee , 1997 , pp .788791 .i. cunningham and a. fenster , `` a method for modulation transfer function determination from edge profiles with correction for finite - element differentiation , '' _ medical physics _14 , no . 4 , pp . 533537 , 1987 .n. joshi , r. szeliski , and d. kriegman , `` psf estimation using sharp edge prediction , '' in _ computer vision and pattern recognition , 2008 .cvpr 2008 .ieee conference on_.1em plus 0.5em minus 0.4emieee , 2008 , pp .y. sato , h. tanaka , t. nishii , k. nakanishi , n. sugano , t. kubota , h. nakamura , h. yoshikawa , t. ochi , and s. tamura , `` limits on the accuracy of 3-d thickness measurement in magnetic resonance images - effects of voxel anisotropy , '' _ medical imaging , ieee transactions on _ , vol .22 , no . 9 , pp . 10761088 , 2003 .t. k. goto , s. nishida , y. nakamura , k. tokumori , y. nakamura , k. kobayashi , y. yoshida , and k. yoshiura , `` the accuracy of 3-dimensional magnetic resonance 3d vibe images of the mandible : an in vitro comparison of magnetic resonance imaging and computed tomography , '' _ oral surgery , oral medicine , oral pathology , oral radiology , and endodontology _ , vol .103 , no . 4 , pp . 550559 , 2007 .m. i. meurer , k. p. souza , a. von wangenheim , d. d. abdala , l. f. de souza nobre , e. meurer , and j. v. l. da silva , `` influence of tomographic slice thickness and field of view variation on the reproduction of thin bone structures for rapid prototyping purposes an in vitro study , '' _ open journal of radiology _, vol . 3 , p. 12, 2013 .s. cortez , j. claro , and j. alves , `` 3d reconstruction of a spinal motion segment from 2d medical images : objective quantification of the geometric accuracy of the fe mesh generation procedure , '' in _ bioengineering ( enbeng ) , 2013 ieee 3rd portuguese meeting in_.1em plus 0.5em minus 0.4emieee , 2013 , pp .p. young , t. beresford - west , s. coward , b. notarberardino , b. walker , and a. abdul - aziz , `` an efficient approach to converting three - dimensional image data into highly accurate computational models , '' _ philosophical transactions of the royal society a : mathematical , physical and engineering sciences _ , vol .1878 , pp .31553173 , 2008 .b. verbist , r. joemai , w. teeuwisse , w. veldkamp , j. geleijns , and j. frijns , `` evaluation of 4 multisection ct systems in postoperative imaging of a cochlear implant : a human cadaver and phantom study , '' _ american journal of neuroradiology _ , vol .29 , no . 7 , pp . 13821388 , 2008 .k. oka , t. murase , h. moritomo , a. goto , k. sugamoto , and h. yoshikawa , `` accuracy analysis of three - dimensional bone surface models of the forearm constructed from multidetector computed tomography data , '' _ the international journal of medical robotics and computer assisted surgery _ , vol . 5 , no . 4 , pp .452457 , 2009 .x. liang , i. lambrichts , y. sun , k. denis , b. hassan , l. li , r. pauwels , and r. jacobs , `` a comparative evaluation of cone beam computed tomography ( cbct ) and multi - slice ct ( msct ) .part ii : on 3d model accuracy , '' _european journal of radiology _75 , no . 2 , pp . 270274 , 2010 .l. carlsson , t. rstlund , b. albrektsson , and t. albrektsson , `` implant fixation improved by close fit cylindrical implant - bone interface studied in rabbits , '' _ acta orthopaedica _59 , no . 3 , pp .272275 , 1988 .u. pazzaglia , f. brossa , g. zatti , r. chiesa , and l. andrini , `` the relevance of hydroxyapatite and spongious titanium coatings in fixation of cementless stems , '' _ archives of orthopaedic and trauma surgery _ , vol .117 , no . 4 - 5 ,pp . 279285 , 1998 .  h. a. paul , w. l. bargar , b. mittlestadt , b. musits , r. h. taylor , p. kazanzides , j. zuhars , b. williamson , and w. hanson , `` development of a surgical robot for cementless total hip arthroplasty , '' _ clinical orthopaedics and related research _5766 , 1992 .

Abstract: in this work it is proposed a medical image segmentation pipeline for accurate bone segmentation from ct imaging . it is a two - step methodology , with a pre - segmentation step and a segmentation refinement step . first , the user performs a rough segmenting of the desired region of interest . next , a fully automatic refinement step is applied to the pre - segmented data . the automatic segmentation refinement is composed by several sub - stpng , namely image deconvolution , image cropping and interpolation . the user - defined pre - segmentation is then refined over the deconvolved , cropped , and up - sampled version of the image . the algorithm is applied in the segmentation of ct images of a composite femur bone , reconstructed with different reconstruction protocols . segmentation outcomes are validated against a gold standard model obtained with coordinate measuring machine nikon metris lk v20 with a digital line scanner lc60-d that guarantees an accuracy of 28 . high sub - pixel accuracy models were obtained for all tested datasets . the algorithm is able to produce high quality segmentation of the composite femur regardless of the surface meshing strategy used .  biomedical image processing , deconvolution , image segmentation , level set , spatial resolution .


data transmission in the internet network can be described as a self - adaptive system to the different congestion events that regularly occur at its numerous nodes . a connection , a tcp flow , in this network adapts its throughput according to the congestion it encounters on its path : packets are sent as long as no loss is detected and throughput grows linearly during that time . on the contrary when a loss occurs , the throughput is sharply reduced by a multiplicative factor .this scheme is known as an additive increase and multiplicative decrease algorithm ( aimd ) .globally , the tcp protocol can be seen as a bandwidth allocation algorithm on the internet . from a mathematical modelling perspective , the description is somewhat more difficult .while the representation of the evolution of the throughput of a single tcp flow has been the object of various rigorous works , there are few rigorous studies for modelling the evolution of a large set of tcp connections in a quite large network .a possible mathematical formulation which has been used is via an optimization problem : given classes of connections , when there are connections of class , their total throughput achieved is given by so that the vector is a solution of the following optimization problem where is the set of admissible throughputs which takes into account the capacity constraints of the network .the functions are defined as _ utility _ functions , and various expressions have been proposed for them .see kelly  , massouli  and massouli and roberts  . with this representation , the tcp protocol is seen as an adaptive algorithm maximizing some criterion at the level of the network .a different point of view has been proposed in graham and robert  .it starts on the local dynamics of the aimd algorithm used by tcp and , through a scaling procedure , the global behavior of the network can then be described rigorously .it is assumed that there are classes of _ permanent _ connections going through different nodes and with different characteristics .the loss rate of a connection using a given node , , is described as a function of the congestion at this node .the quantity is defined as the ( possibly weighted ) sum of the throughputs of _ all _ the connections that use node .the interaction of the connections in the network is therefore expressed via the loss rate at each node .it has been shown in graham and robert  that under a mean - field scaling , the evolution of a class connection , , can be asymptotically described as the unique solution of an unusual stochastic differential equation .furthermore , it has also been proved that the equilibrium distribution of the throughputs of the different classes of connections is in a one to one correspondence with the solution of a fixed point equation of dimension ( the number of nodes ) .  under `` reasonable '' conditions, there should be only one solution of and consequently a unique stable equilibrium of the network .otherwise this would imply that the state of the network could oscillate between several stable states .although this is mentioned here and there in the literature , this has not been firmly established in the context of an ip network .it has been shown that multi - stability may occur in loss networks , see gibbens  and marbukh  or in the context of a wireless network with admission control , see antunes  .raghunathan and kumar  presents experiments that suggest that a phenomenon of bi - stability may occur in a context similar to the one considered in this paper but for wireless networks .it turns out that it is not easy to check in practice whether the fixed point equation has a unique solution or not .the purpose of this paper is to investigate in detail this question for several topologies .the paper is organized as follows .section [ secone ] reviews the main definitions and results used in the paper .in addition , a simple criterion for the existence of a fixed - point solution is given .section [ sectree ] presents a uniqueness result for a tree topology under the assumptions that all connections use the root .section [ seclinear ] considers a linear network .section [ torus ] studies several scenarios for ring topologies and a uniqueness result is proved for connections going through one , two , or all the nodes . two main approaches are used to prove uniqueness : monotonicity properties of the network and contraction arguments .a general conjecture that we make is that when the loss rates are increasing in the level of congestion , this should be sufficient to imply the uniqueness of the equilibrium in a general network ( together with regularity properties perhaps ) .in this section , a somewhat simplified version of the stochastic model of interacting tcp flows of graham and robert  is presented .ott  presents a fluid model of a single connection . via scalings with respect to the loss rate , dumas proves various limit theorems for the resulting processes .the limiting picture of dumas  for the evolution of the throughput of single long connection is as follows .if the instantaneous throughput at time of the connection is , this process has the markov property and its infinitesimal generator is given by for a -function from to .for , the quantity should be thought as the instantaneous throughput of the connection at time .the markov process increases linearly at rate .the constant is related to the distance between the source and the destination .it increases proportionally to the round trip time , typically for some constants and .given , the process jumps from to ( is usually ) at rate .the expression represents the loss rate of the connection .of course , the quantities , and depend on the parameters of the connection .the density of the invariant distribution of this markov process is given in the following proposition .it has been analyzed in ott  at the fluid level and by dumas  , see also guillemin  .the transient behavior has been investigated in chafai  .[ oneprop ] the function with , is the density of the invariant distribution of the markov process whose infinitesimal generator is given by equation .furthermore , its expected value is given by    the network has nodes and accommodates classes of permanent connections . for ,the number of class connections is , and one sets an _ allocation matrix _ with positive coefficients describes the use of nodes by the connections .in particular the route of a class  connection goes through node only if . in practice ,the class of a connection is determined by the sequence set of nodes it is using .  if is the throughput of the class connection , , the quantity is the weighted throughput at node of this connection .a simple example would be to take or depending on whether a class  connection uses node or not .the total weighted throughput of node by the various connections is given by the quantity represents the level of utilization / congestion of node .in particular , the loss rate of a connection going through node  will depend on this variable .  for ,the corresponding parameters and of equation  for a class connection are given by a non - negative number and a function , so that when the resource vector of the network is and if the state of a class connection is :  * its state increases linearly at rate .for example where is the round trip time between the source and the destination of a class connection . *a loss for this connection occurs at rate and in this case its state jumps from to .the function depends only on the utilization of all nodes used by class connections .in particular , if a class connection goes through the nodes , , , , one has a more specific ( and natural ) choice for would be where is the loss rate at node when its congestion level is , and is the loss rate in a non - congested network .another example is when the loss rate depends only on the sum of the utilizations of the nodes used by class  , i.e. ,    if denotes the throughput of the class connection , , then the vector , t\geq 0)\ ] ] has the markov property .as it stands , this markov process is quite difficult to analyze . for this reason , a mean field scalingis used to get a more quantitative representation of the interaction of the flows .more specifically , it is assumed that the total number of connections goes to infinity and that the total number of class connections is of the order , where .  for each ,one takes a class connection at random , let be its index , .the process represents the throughput of a `` typical '' class connection .it is shown in graham and robert  that , as goes to infinity and under mild assumptions , the process  ] , where the processes , for , are independent and , for , the process is the solution of the following stochastic differential equation , with and , for , where are i.i.d . poisson point processes on with lebesgue characteristic measure .because of the role of the deterministic function in these equations , the markov property holds for this process but it is not _ time - homogeneous_. the analogue of the infinitesimal generator is given by the homogeneity holds when the function is equal to a constant , which will be the case at equilibrium. in this case a class connection behaves like a single isolated connection with parameters and .the following theorem gives a characterization of the invariant distributions for the process .[ thinv ] the invariant distributions for solutions of equation  are in one - to - one correspondence with the solutions of the fixed point equation where if is such a solution , the corresponding invariant distribution has the density on , where and is defined in proposition [ oneprop ] .the above theorem shows that if the fixed point equation  has several solutions , then the limiting process has several invariant distributions .similarly , if equation  has no solution then , in particular , can not converge to an equilibrium .these possibilities have been suggested in the internet literature through simulations , like the cyclic behavior of some nodes in the case of congestion .  under mild and natural assumptions , such as the loss rate being non - decreasing with respect to the utilization in the nodes ,we show that for some specific topologies there exists a unique fixed point .we believe that such a uniqueness result will hold , in fact , for any network in general ( under suitable regularity properties on the functions , ) . before proceeding to the examples , we first present an existence result that holds for a general network .   in this section the existence of a solution to the fixed - point equation ( [ fp ] )is proved for a quite general framework .if is a solution of equation  and , , then the vector satisfies the relation , i.e. , , , and as well proposition below gives a simple criterion for the existence of a fixed point .[ prop : fp_exist ] if the functions , , are continuous and non - decreasing , and if there exists a vector such that the relations hold coordinate by coordinate , then there exists at least one solution for the fixed point equation  and therefore also for equation .define the sequence , . from and , it follows that and .since the function is non - increasing , one gets that the relation holds .hence , there are such that with . since and , by continuity we also have that and .define the set .note that , hence is bounded . in addition , for , since the function is non - increasing .one can therefore apply brouwer fixed point theorem to restricted to the compact convex set , and conclude that contains at least one fixed point of the function .the proposition is proved .the conditions of proposition [ prop : fp_exist ] trivially hold when is non - decreasing and for all , since then , and . in particular ,when the function is given by ( [ eq : delta ] ) , is a sufficient condition for the existence of a fixed point .we consider a finite tree network .a connection starts in the root and then follows the tree structure until it leaves the network at some node .the set of routes is therefore indexed by the set of nodes , i.e. , a connection following route  starts in the root and leaves the tree in node .the tree can be classically represented as a subset of with the constraint that if , then , for , the element is a node of the tree as well .in addition , node  is the child of generation ( level ) and the ancestor of for this generation .one writes in this situation and when , i.e. , when is a daughter of .the quantity } ] , there exists a unique solution })\geq 0 ] is continuous and non - increasing .for such an , for , relation  can then be written as },u_{h ' } ) + \sum_{g\in { \cal t } ,  { h'}\vdash g }  f_g(u_{[\emptyset , p(h')]},u_{h'}).\ ] ] since and , with  a leaf , are non - increasing and continuous , there exists a unique solution })\geq 0 ] , })$ ] is the unique solution of },u_g )  + \sum_{g'\in { \cal t } ,  { g}\vdash g ' } f_{g'}(u_{[\emptyset , p(g)]},u_g).\ ] ] equation  at the root then writes and this equation has a unique solution .now , one defines recursively ( by increasing level of nodes ) } ) , \ \g\in{\cal t}.\ ] ] then clearly satisfies relation  and is the unique solution .in this section we consider a linear network with nodes and classes of connections .class connections , , use node  only , while class 0 connections use all nodes . assume if class uses node , and 0 otherwise .equation ( [ fp ] ) is in this case with .if the functions , , are continuous and non - decreasing , then there exists a unique solution for the fixed point equation .let , , which is continuous and non - decreasing . hence , ( [ eq : lin ] ) can be rewritten as for some constant , see equation .in addition , define the function , , which is continuous and non - increasing .> from ( [ eq : uj ] ) we obtain the relation since is non - decreasing and is non - increasing , the fixed point equation has a unique solution .hence , the relation ( [ eq : uj ] ) has a unique fixed point , which is given by .in this section , the topology of the network is based on a ring .several situations are considered for the paths of the connections .it is assumed that there are nodes and classes of connections and class uses two nodes : node and .assume if class uses node , and 0 otherwise .equation  is in this case for , the above equation can be rewritten as follows      consequently , possibly up to an exchange of and , one can assume that there exists such that and .define and .hence , and . without loss of generality, it can be assumed that the classes are ordered such that . since the function is non - increasing , and we have that either i.e. , and/or . because then , necessarily , .hence since is non - increasing , one has and consequently .> from , we obtain , which , using the same steps as before , implies . in particular , by induction it can be concluded that where the indices , and are considered as modulo .this implies that , for all , and hence , i.e. , for .we can conclude that the fixed point is unique .the proof consists in showing that ( [ eq : lin_y ] ) has a unique solution . by the implicit function theorem, there exists a unique such that , and this function is positive and continuous differentiable . taking the partial derivative to on both sides of this identity , one gets that with .hence , \right|_{s = s(y ) }  { \leq } 0.\ ] ] a similar expression holds for and one can conclude that \right|_{s = s(y)}.\notag\end{aligned}\ ] ] if , then by relation , one gets that , for some constant , see equation , which holds only if .hence , .since is continuous and positive , and , one obtains that there exists an such that for all .similarly , there exists an such that .this gives the following upper bound , where we used that is non - decreasing , lipschitz continuous ( with constant ) and differentiable .> from equation ) one now obtains that there exists a constant such that hence , the mapping with for is a contraction , and has a unique fixed point , i.e. , equation  has a unique solution .consider now a ring with nodes and classes .class uses two nodes : nodes and , .class uses one node : node , .we assume that if and only if class  uses node  , and zero otherwise .we focus on functions that satisfy ( [ eq : lossr ] ) . equation  is in this context for and , , the above equation can be rewritten as follows , for ,   if the functions , , , are lipschitz , continuously differentiable , non - decreasing , and satisfy ( [ eq : lossr ] ) , then there exists a unique solution for the fixed point equation .  by the implicit function theorem , for each , there exists a unique satisfying the relation , and this function is non - increasing and continuous differentiable .one now has to solve the equation > from the fact that , it can be easily checked that the right - hand side of equation ( [ eq : torusb_yj ] ) is non - increasing in .define the function since , the derivative of this function is with so is non - increasing in .hence , there exists a unique such that satisfies equation , and this function is positive and continuous differentiable ( by the implicit function theorem ) .in particular , , for all , with > from this one can derive that \right/\\ \left [ \rule{0mm}{4mm}1-  \phi_j'(f_j(y))(2+x_{0j}'(y_{j-1}+x_j(y_{j-1},y_{j+1}))\right.\\\left.\rule{0mm}{4 mm } + x_{0,j+1}'(x_j(y_{j-1},y_{j+1})+y_{j+1 } ) ) \right ] \leq 0,\end{gathered}\ ] ] and a similar expression holds for as in the proof of proposition [ bell ] , an upper bound on can be obtained .this implies that there exists a constant such that hence , the mapping with is a contraction , and has a unique fixed point .one concludes that there exists a unique solution and , , of .if the functions , , are continuous , non - decreasing , satisfy ( [ eq : lossr ] ) , and satisfy the assumptions of proposition [ prop : fp_exist ] , then there exists a unique solution for the fixed point equation .if the relation holds for all , then since the function is non - increasing , one gets that summing over all , we obtain which implies that .however , hence , we obtain a contradiction .vincent dumas , fabrice guillemin , and philippe robert , _ a markovian analysis of additive - increase multiplicative - decrease ( aimd ) algorithms _ , advances in applied probability * 34 * ( 2002 ) , no . 1 , 85111 .kelly , a.k .maulloo , and d.k.h .tan , _ rate control in communication networks : shadow prices , proportional fairness and stability _ , journal of the operational research society * 49 * ( 1998 ) , 237252 .laurent massouli and james roberts , _ bandwidth sharing : objectives and algorithms _ , infocom 99 .eighteenth annual joint conference of the ieee computer and communications societies , 1999 , pp .

Abstract: the equilibrium distributions of a markovian model describing the interaction of several classes of permanent connections in a network are analyzed . it has been introduced by graham and robert  . for this model each of the connections has a self - adaptive behavior in that its transmission rate along its route depends on the level of congestion of the nodes on its route . it has been shown in  that the invariant distributions are determined by the solutions of a fixed point equation in a finite dimensional space . in this paper , several examples of these fixed point equations are studied . the topologies investigated are rings , trees and a linear network , with various sets of routes through the nodes .