Histopathological Image Analysis: A Review <s> B. Spatially Related Features <s> The reproducible classification of poorly differentiated abnormal epithelium specimens is still a diagnostic problem. The computer-aided method described here improves the differentiation between benign and malignant epithelium specimens. Hematoxylin and eosin-stained sections of normal squamous epithelium, dysplasia, carcinoma in situ, and carcinoma were scanned in a TV microscope system and analyzed by means of image processing methods on a DEC 5000/200 workstation. From the 15-20 microns thick histological sections, 3-5 focus positions in steps of 1-4 microns were scanned. The segmentation of the cell nuclei was performed automatically by color analysis and geometric operations. For each nucleus the best focus level was selected and at this level the center of the cell was calculated. Graph theoretical methods were applied to analyze the morphometry of the epithelium specimens. The minimal spanning tree was computed in the three-dimensional (3D) space of the sections with the selected centers of the nuclei as vertices. The best feature found for discrimination of the specimens is the average length of all edges in a tree. In the two-dimensional (2D) analysis we had to accept an error probability of about 20% in differentiation of dysplasia and carcinoma. In contrast to this we differentiated normal squamous epithelium, dysplasia, and carcinoma with a correct classification rate of 100% in the 3D analysis. <s> BIB001 </s> Histopathological Image Analysis: A Review <s> B. Spatially Related Features <s> Networks of coupled dynamical systems have been used to model biological oscillators1,2,3,4, Josephson junction arrays5,6, excitable media7, neural networks8,9,10, spatial games11, genetic control networks12 and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes. Here we explore simple models of networks that can be tuned through this middle ground: regular networks ‘rewired’ to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them ‘small-world’ networks, by analogy with the small-world phenomenon13,14 (popularly known as six degrees of separation15). The neural network of the worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular lattices. <s> BIB002 </s> Histopathological Image Analysis: A Review <s> B. Spatially Related Features <s> Despite the apparent randomness of the Internet, we discover some surprisingly simple power-laws of the Internet topology. These power-laws hold for three snapshots of the Internet, between November 1997 and December 1998, despite a 45% growth of its size during that period. We show that our power-laws fit the real data very well resulting in correlation coefficients of 96% or higher.Our observations provide a novel perspective of the structure of the Internet. The power-laws describe concisely skewed distributions of graph properties such as the node outdegree. In addition, these power-laws can be used to estimate important parameters such as the average neighborhood size, and facilitate the design and the performance analysis of protocols. Furthermore, we can use them to generate and select realistic topologies for simulation purposes. <s> BIB003 </s> Histopathological Image Analysis: A Review <s> B. Spatially Related Features <s> An ambitious goal of contemporary biological research is the elucidation of the structure and functions of networks that constitute cells and organisms. In biological systems, networks appear in many different disguises, ranging from protein interactions to metabolic networks. The emergence of these networks is driven by self-organizing processes that are governed by simple but generic laws. While unraveling the complex and interwoven systems of different interacting units, it has become clear that the topology of networks of different biological origin share the same characteristics on the large scale. In this chapter, we survey the most prominent characteristics of biological networks, focusing on the emergence of the scale-free architecture and the hierarchical arrangement of modules. <s> BIB004 </s> Histopathological Image Analysis: A Review <s> B. Spatially Related Features <s> The main goal of this dissertation is the development and discussion of techniques for higher-level image analysis, i.e., object-level analysis, of breast cancer imagery. Established cytologic (cell) criteria can be contradictory, and even histologic (tissue) criteria (considered the gold standard for diagnosis) are subject to varied interpretation. There is thus a need to quantitatively define characteristics of breast cancer to bettor coordinate clinical care of women presenting breast masses. We propose here an approach for such quantitative analysis, Quantitative Object- and spatial Arrangement-Level Analysis (QOALA), using expert (pathologist) input to guide the classification process. ::: The main contributions in this work are four-fold. First, quantitatively analyze the utility of multispectral imagery for classification and segmentation tasks in histopathology imagery. Second, we develop object-level segmentations for several histologic classes, as a quantitative object-level segmentation metric. Third, we extract a comprehensive set of both object- and spatial-level features which are used in a feature selection framework for classification of objects and imagery. Fourth, we extend the concepts of object-level features to higher-level image objects, analyze the utility of these high-level objects for image classification, and introduce the concept of a probabilistic graph-based model of imagery. ::: Overall, QOALA yields very good object- and image-level classification performances. More specifically, the object-level features as implemented in QOALA are versatile and general enough to elicit important information from even imperfectly segmented objects. Additionally, the use of non-nuclear features, namely features of cytoplasm and stoma have good classification performance, often exceeding that of nuclei. Higher-level features display a potential to increase both object- and image-level classification performance. <s> BIB005
Graphs are efficient data structures to represent spatial data and an effective way to represent structural information by defining a large set of topological features. Formally, a simple graph is an undirected and unweighted graph without self-loops, with and being the node and edge set of graph , respectively. Application of graph theory to other problem domains is impressive. Real-world graphs of varying types and scales have been extensively investigated in technological BIB003 , social BIB002 and biological systems BIB004 . In spite of their different domains, such self-organizing structures unexpectedly exhibit common classes of descriptive spatial (topological) features. These features are quantified by definition of computable metrics. The use of spatial-relation features for quantifying cellular arrangement was proposed in the early 1990s BIB001 , but did not find application to clinical imagery until recently. Graphs have now been constructed for modeling different tissue states and to distinguish one state from another by computing metrics on these graphs and classifying their values. Overall, however, the use of spatial arrangement of histological entities (generally at low resolutions) is relatively new, especially in comparison to the wealth of research on nuclear features (at higher resolutions) that has occurred during the same timeframe. A compilation of all the spatial-relation features published in the literature is summarized in Table II . Definitions for all graph structures and features can be found in BIB005 . The total number of spatial-relation features extracted is approximately 150 for all graph structures. Graph theoretical metrics that can be defined and computed on a cell-graph induce a rich set of descriptive features that can be used for tissue classification. These features provide structural information to describe the tissue organization such as: i) the distribution of local information around a single cell cluster (e.g., degree, clustering coefficient); ii) the distribution of global information around a single cell cluster (e.g., eccentricity, closeness, between-ness); iii) the global connectivity information of a graph (e.g., ratio of the giant connected component over the graph size, percentage of the isolated and end data points in the graph); iv) the properties extracted from the spectral graph theory (e.g., spectral radius, eigen exponent, number of connected components, sum of the eigenvalues in the spectrum). Refer to Table II for a list of commonly extracted graph features.