Vectorizing hand-drawn sketches is a challenging task, which is of paramount importance for creating CAD vectorized versions for the fashion and creative workflows. This paper proposes a complete framework that automatically transforms noisy and complex hand-drawn sketches with different stroke types in a precise, reliable and highly-simplified vectorized model. The proposed framework includes a novel line extraction algorithm based on a multi-resolution application of Pearson's cross correlation and a new unbiased thinning algorithm that can get rid of scribbles and variable-width strokes to obtain clean 1-pixel lines. Other contributions include variants of pruning, merging and edge linking procedures to post-process the obtained paths. Finally, a modification of the original Schneider's vectorization algorithm is designed to obtain fewer control points in the resulting Bezier splines. All the proposed steps of the framework have been extensively tested and compared with state-of-the-art algorithms, showing (both qualitatively and quantitatively) its outperformance.
@cite_11 reported a first proposal of a framework transforming raw images to full vectorized representations. However, the binarization'' step is not considered at all, by presenting directly the skeleton processing and vectorization steps. In addition to this limitation, this paper also bases the vectorization to the simple fitting of straight lines and circular arcs (instead of using Bezier interpolation), which represents a too simplified and limited representation of the resulting path.
@cite_11
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The problem of large-scale image search has been traditionally addressed with the bag-of-visual-words (BOV). In this article, we propose to use as an alternative the Fisher kernel framework. We first show why the Fisher representation is well-suited to the retrieval problem: it describes an image by what makes it different from other images. One drawback of the Fisher vector is that it is high-dimensional and, as opposed to the BOV, it is dense. The resulting memory and computational costs do not make Fisher vectors directly amenable to large-scale retrieval. Therefore, we compress Fisher vectors to reduce their memory footprint and speed-up the retrieval. We compare three binarization approaches: a simple approach devised for this representation and two standard compression techniques. We show on two publicly available datasets that compressed Fisher vectors perform very well using as little as a few hundreds of bits per image, and significantly better than a very recent compressed BOV approach. Abstract Being motivated by the multilayer RECOS (REctified-COrrelations on a Sphere) transform, we develop a data-driven Saak (Subspace approximation with augmented kernels) transform in this work. The Saak transform consists of three steps: (1) building the optimal linear subspace approximation with orthonormal bases using the second-order statistics of input vectors, (2) augmenting each transform kernel with its negative, (3) applying the rectified linear unit (ReLU) to the transform output. The Karhunen-Loeve transform (KLT) is used in the first step. The integration of Steps 2 and 3 is powerful since they resolve the sign confusion problem, remove the rectification loss and allow a straightforward implementation of the inverse Saak transform at the same time. Multiple Saak transforms are cascaded to transform images of a larger size. All Saak transform kernels are derived from the second-order statistics of input random vectors in a one-pass feedforward manner. Neither data labels nor backpropagation is used in kernel determination. Multi-stage Saak transforms offer a family of joint spatial-spectral representations between two extremes; namely, the full spatial-domain representation and the full spectral-domain representation. We select Saak coefficients of higher discriminant power to form a feature vector for pattern recognition, and use the MNIST dataset classification problem as an illustrative example. This paper addresses the problem of converting a rasterized floorplan image into a vector-graphics representation. Unlike existing approaches that rely on a sequence of lowlevel image processing heuristics, we adopt a learning-based approach. A neural architecture first transforms a rasterized image to a set of junctions that represent low-level geometric and semantic information (e.g., wall corners or door end-points). Integer programming is then formulated to aggregate junctions into a set of simple primitives (e.g., wall lines, door lines, or icon boxes) to produce a vectorized floorplan, while ensuring a topologically and geometrically consistent result. Our algorithm significantly outperforms existing methods and achieves around 90 precision and recall, getting to the range of production-ready performance. The vector representation allows 3D model popup for better indoor scene visualization, direct model manipulation for architectural remodeling, and further computational applications such as data analysis. Our system is efficient: we have converted hundred thousand production-level floorplan images into the vector representation and generated 3D popup models. One. Introduction: On the Absence of Geometry from Morphometrics.- First Part. The Measurement of Biological Shape.- Two. Shapes and Measures of Shape.- A. Properties of the Euclidean Plane and Euclidean Space.- B. Outlines and Homologous Landmarks.- C. Definitions of Shape, Shape Change, Shape Measurement.- D. Shapes as Data.- Three. Critique of an Applied Field: Conventional Cephalometrics.- A. Landmarks, Curvature, and Growth.- B. Registration.- Four. New Statistical Methods for Shape.- A. Analysis of the Tangent Angle Function.- 1. History.- 2. Sampling from the tangent angle function.- 3. Conic replacement curves and their estimation Fit of a conic to a point - Geometric interpretation - Estimator for a circle - Estimation for the general conic - Computation of the extremum -Linear constraints.- 4. Conic splining Joint conic fitting under constraint -An example - Application - Analysis of parameters.- B. Extension to Three Dimensions: A Sketch.- C. Skeletons Definition - A multivariate statistical method - Bibliographic note.- Second Part. The Measurement of Shape Change Using Biorthogonal Grids.- Five. The Study of Shape Transformation after D'Arcy Thompson.- A. The Original Method.- 1. Thompson's own work.- 2. Later examples.- 3. Difficulties.- B. Analysis of Growth Gradients.- C. Simulations.- D. Other Morphometric Schemes Vector displacements - Multivariate morphometrics.- Six. The Method of Biorthogonal Grids.- A. Representation of Affine Transformations.- B. General Lines of Growth and Biorthogonal Grids.- C. Summarizing the Grids.- Technical Note 1. Existence and Form of Biorthogonal Grids.- Technical Note 2. Interpolation from Landmark Locations and Arcs The measure of roughness - The vector space and its associated functions - Interpolation from boundary values - Interpolation from boundary values and interior points - Note on computation.- Technical Note 3. Construction of Integral Curves.- Technical Note 4. On Homologous Points.- Seven. Examples of Biorthogonal Analysis.- A. Comparison of Square and Biorthogonal Grids: Thompson's Diodon Figure.- B. Phylogeny and Ontogeny of Primate Crania.- 1. Functional craniology and craniometrics.- 2. Data for this exercise.- 3. Two types of transformations.- 4. Comparative ontogeny of the apes and man.- Eight. Future Directions for Transformation Analysis.- A. Statistical Methods The symmetric tensor field - Concordance -Linear methods.- B. Computation Other kinds of information about homology -Three dimensions.- C. Likely Applications Computed tomography - Orthodontics - Developmental biology.- Nine. Envoi.- Literature Cited. We address the problem of image search on a very large scale, where three constraints have to be considered jointly: the accuracy of the search, its efficiency, and the memory usage of the representation. We first propose a simple yet efficient way of aggregating local image descriptors into a vector of limited dimension, which can be viewed as a simplification of the Fisher kernel representation. We then show how to jointly optimize the dimension reduction and the indexing algorithm, so that it best preserves the quality of vector comparison. The evaluation shows that our approach significantly outperforms the state of the art: the search accuracy is comparable to the bag-of-features approach for an image representation that fits in 20 bytes. Searching a 10 million image dataset takes about 50ms. Semantic parsing is the process of mapping a natural language sentence into a formal representation of its meaning. In this work we use the neural network approach to transform natural language sentence into a query to an ontology database in the SPARQL language. This method does not rely on handcraft-rules, high-quality lexicons, manually-built templates or other handmade complex structures. Our approach is based on vector space model and neural networks. The proposed model is based in two learning steps. The first step generates a vector representation for the sentence in natural language and SPARQL query. The second step uses this vector representation as input to a neural network (LSTM with attention mechanism) to generate a model able to encode natural language and decode SPARQL. Associative memories are conventionally used to represent data with very simple structure: sets of pairs of vectors. This paper describes a method for representing more complex compositional structure in distributed representations. The method uses circular convolution to associate items, which are represented by vectors. Arbitrary variable bindings, short sequences of various lengths, simple frame-like structures, and reduced representations can be represented in a fixed width vector. These representations are items in their own right and can be used in constructing compositional structures. The noisy reconstructions extracted from convolution memories can be cleaned up by using a separate associative memory that has good reconstructive properties. > In various application domains, including image recognition, it is natural to represent each example as a set of vectors. With a base kernel we can implicitly map these vectors to a Hilbert space and fit a Gaussian distribution to the whole set using Kernel PCA. We define our kernel between examples as Bhattacharyya's measure of affinity between such Gaussians. The resulting kernel is computable in closed form and enjoys many favorable properties, including graceful behavior under transformations, potentially justifying the vector set representation even in cases when more conventional representations also exist. Hand-drawn schematized maps traditionally make extensive use of curves. However, there are few automated approaches for curved schematization; most previous work focuses on straight lines. We present a new algorithm for area-preserving curved schematization of territorial outlines. Our algorithm converts a simple polygon into a schematic crossing-free representation using circular arcs. We use two basic operations to iteratively replace consecutive arcs until the desired complexity is reached. Our results are not restricted to arcs ending at input vertices. The method can be steered towards different degrees of “curviness”: we can encourage or discourage the use of arcs with a large central angle via a single parameter. Our method creates visually pleasing results even for very low output complexities. To evaluate the effectiveness of our design choices, we present a geometric evaluation of the resulting schematizations. Besides the geometric qualities of our algorithm, we also investigate the potential of curved schematization as a concept. We conducted an online user study investigating the effectiveness of curved schematizations compared to straight-line schematizations. While the visual complexity of curved shapes was judged higher than that of straight-line shapes, users generally preferred curved schematizations. We observed that curves significantly improved the ability of users to match schematized shapes of moderate complexity to their unschematized equivalents. This paper presents a method for vectorizing the graphical parts of paper-based line drawings. The method consists of separating the input binary image into layers of homogeneous thickness, skeletonizing each layer, segmenting the skeleton by a method based on random sampling, and simplifying the result. The segmentation method is robust with a best bound of 50 percent noise reached for indefinitely long primitives. Accurate estimation of the recognized vector's parameters is enabled by explicitly computing their feasibility domains. Theoretical performance analysis and expression of the complexity of the segmentation method are derived. Experimental results and comparisons with other vectorization systems are also provided. We report a method to convert discrete representations of molecules to and from a multidimensional continuous representation. This model allows us to generate new molecules for efficient exploration and optimization through open-ended spaces of chemical compounds. A deep neural network was trained on hundreds of thousands of existing chemical structures to construct three coupled functions: an encoder, a decoder, and a predictor. The encoder converts the discrete representation of a molecule into a real-valued continuous vector, and the decoder converts these continuous vectors back to discrete molecular representations. The predictor estimates chemical properties from the latent continuous vector representation of the molecule. Continuous representations of molecules allow us to automatically generate novel chemical structures by performing simple operations in the latent space, such as decoding random vectors, perturbing known chemical structures, or interpolating between molecules. Continuous represent... Graph Neural Networks (GNNs) are an effective framework for representation learning of graphs. GNNs follow a neighborhood aggregation scheme, where the representation vector of a node is computed by recursively aggregating and transforming representation vectors of its neighboring nodes. Many GNN variants have been proposed and have achieved state-of-the-art results on both node and graph classification tasks. However, despite GNNs revolutionizing graph representation learning, there is limited understanding of their representational properties and limitations. Here, we present a theoretical framework for analyzing the expressive power of GNNs to capture different graph structures. Our results characterize the discriminative power of popular GNN variants, such as Graph Convolutional Networks and GraphSAGE, and show that they cannot learn to distinguish certain simple graph structures. We then develop a simple architecture that is provably the most expressive among the class of GNNs and is as powerful as the Weisfeiler-Lehman graph isomorphism test. We empirically validate our theoretical findings on a number of graph classification benchmarks, and demonstrate that our model achieves state-of-the-art performance. We consider 3D object retrieval in which a polygonal mesh serves as a queryand similar objects are retrieved from a collection of 3D objects. Algorithms proceed first bya normalization step in which models are transformed into canonical coordinates. Second, feature vectors are extracted and compared with those derived from normalized models in the search space. In the feature vector space nearest neighbors are computed and ranked. Retrieved objects are displayed for inspection, selection, and processing. Our feature vectors are based on rays cast from the center of mass of the object. For each raythe object extent in the raydirection yields a sample of a function on the sphere. We compared two kinds of representations of this function, namelyspherical harmonics and moments. Our empirical comparison using precision-recall diagrams for retrieval results in a data base of 3D models showed that the method using spherical harmonics performed better. First steps are taken toward a formulation of quantum mechanics which avoids the use of probability amplitudes and is expressed entirely in terms of observable probabilities. Quantum states are represented not by state vectors or density matrices but by “probability tables,” which contain only the probabilities of the outcomes of certain special measurements. The rule for computing transition probabilities, normally given by the squared modulus of the inner product of two state vectors, is re-expressed in terms of probability tables. The new version of the rule is surprisingly simple, especially when one considers that the notion of complex phases, so crucial in the evaluation of inner products, is entirely absent from the representation of states used here. Symbol recognition is a well-known problem in the field of graphics. A symbol can be defined as a structure within document that has a particular meaning in the context of the application. Due to their representational power, graph structures are usually used to represent line drawings images.An accurate vectorization constitutes a first approach to solve this goal. But vectorization only gives the segments constituting the document and their geometrical attributes.Interpreting a document such as P&ID (Process & Instrumentation)diagram requires an additional stage viz. recognition of symbols in terms of its shape. Usually a P&ID diagram contain several types of elements, symbols and structural connectivity. For those symbols that can be defined by a prototype pattern, we propose an iterative learning strategy based on Hopfield model to learn the symbols, for subsequent recognition in the P&ID diagram. In a typical shape recognition problem one has to account for transformation invariance. Here the transformation invariance is circumvented by using an iterative learning approach which can learn symbols with high degree of correlation. Geometric transformations are most commonly represented as square matrices in computer graphics. Following simple geometric arguments we derive a natural and geometrically meaningful definition of scalar multiples and a commutative addition of transformations based on the matrix representation, given that the matrices have no negative real eigenvalues. Together, these operations allow the linear combination of transformations. This provides the ability to create weighted combination of transformations, interpolate between transformations, and to construct or use arbitrary transformations in a structure similar to a basis of a vector space. These basic techniques are useful for synthesis and analysis of motions or animations. Animations through a set of key transformations are generated using standard techniques such as subdivision curves. For analysis and progressive compression a PCA can be applied to sequences of transformations. We describe an implementation of the techniques that enables an easy-to-use and transparent way of dealing with geometric transformations in graphics software. We compare and relate our approach to other techniques such as matrix decomposition and quaternion interpolation. This study presents a method for resampling detection. By combining texture analysis with resampling detection, the task of resampling detection is considered as a texture classification problem. In other words, the influence of resampling operations on a raw single-sampled image is viewed as an alteration of the image texture in a fine scale. First, local linear transform is used to obtain textural detail sub-bands. A 36-D feature vector is then extracted from the normalized characteristic function moments of textural detail sub-bands to train a support vector machine classifier. Finally, experimental results are reported on three databases, with each having almost 10,000 images. Comparison with the previous study reveals that the proposed method is effective for resampling detection. In addition, extensive experiments on cover and stego bitmap images illustrate that the proposed method is essential for constructing accurate targeted and blind steganalysis methods for heterogeneous images, raw single-sampled images, and images resampled at different scales. Document image binarization is one of the critical initial steps for document analysis and understanding. Previous work mostly focused on exploiting hand-crafted features to build statistical models for distinguishing text from background. However, these approaches only achieved limited success because: (a) the effectiveness of hand-crafted features is limited by the researcher's domain knowledge and understanding on the documents, and (b) a universal model cannot always capture the complexity of different document degradations. In order to address these challenges, we propose a convolutional encoder-decoder model with deep learning for document image binarization in this paper. In the proposed method, mid-level document image representations are learnt by a stack of convolutional layers, which compose the encoder in this architecture. Then the binarization image is obtained by mapping low resolution representations to the original size through the decoder, which is composed by a series of transposed convolutional layers. We compare the proposed binarization method with other binarization algorithms both qualitatively and quantitatively on the public dataset. The experimental results show that the proposed method has comparable performance to the other hand-crafted binarization approaches and has more generalization capabilities with limited in-domain training data. A simple and efficient pipeline for word spotting in handwritten documents is proposed. The method allows for extremely rapid querying, while still maintaining high accuracy. The dataset images that are to be queried are preprocessed by a simple binarization operation, followed by the extraction of multiple overlapping candidate targets. Each binary target, as well as the binarized query, is resized to fit a fixed-size rectangle and represented by conventional image descriptors. Then, a cosine similarity operator—followed by maximum pooling over random groups—is used to represent each target or query as a concise 250D vector. Retrieval is performed in a fraction of a second by nearest-neighbor search within that space, followed by a simple suppression of extra overlapping candidates. Continuous word representations, trained on large unlabeled corpora are useful for many natural language processing tasks. Popular models to learn such representations ignore the morphology of words, by assigning a distinct vector to each word. This is a limitation, especially for languages with large vocabularies and many rare words. In this paper, we propose a new approach based on the skipgram model, where each word is represented as a bag of character n-grams. A vector representation is associated to each character n-gram, words being represented as the sum of these representations. Our method is fast, allowing to train models on large corpora quickly and allows to compute word representations for words that did not appear in the training data. We evaluate our word representations on nine different languages, both on word similarity and analogy tasks. By comparing to recently proposed morphological word representations, we show that our vectors achieve state-of-the-art performance on these tasks.