Shock Graphs Research Articles

A Two Phase Hybrid Classifier based on Structure Similarities and Textural Features for Accurate Meningioma Classification

Meningioma subtype classification is a complex pattern classification problem of digital pathology due to het-erogeneity issues of tumor texture, low inter-class and high intra-class texture variations of tumor samples, and architec-tural variations of cellular components. The basic aim is the achievement of significantly high classification results for all the subtypes of meningioma while dealing with inherent complexity and texture variations. The ultimate goal is to mimic the prognosis decision of expert pathologists and assist newer pathologists in making right and quick decisions. In this paper, a novel hybrid classification framework based on nuclei shape matching and texture analysis is proposed for classification of four subtypes of grade-I benign meningioma. Meningothelial and fibroblastic subtypes are classified on basis of nuclei shape matching through skeletons and shock graphs while an optimized texture-based evolutionary framework is designed for the classification of transi-tional and psammomatous subtypes. Classifier-based evolutionary feature selection is performed using Genetic Algorithm (GA) in combination with Support Vector Machine (SVM) to select the optimal combination of higher-order statistical features extracted from morphologically processed RGB color channel images. The proposed hybrid classifier employed leave-one-patient-out 5-fold cross validation and achieved an overall 95.63% mean classification accuracy.

Construction of garment pattern shape information system using image analysis and shape recognition techniques

Purpose – As an extended work of the previous paper (Sul, 2010), this paper provides a guideline information for an anonymous garment pattern in sewing process. The purpose of this paper is to first, provide garment pattern database. By simply taking pictures of garment patterns, the shape database is constructed. Once the shape database is prepared, data retrieval can be done by image indexing, i.e., simply inserting garment pattern boundary shape again to the database. Using shock graph methodology, the pattern sets used for database preparation can be exactly retrieved. Second, to find the nearest shape of a given input pattern shape in the database. If the input garment pattern shape does not exist in the database, the shape matching algorithm provides the next similar pattern data. The user, who is assumed to be non-expert in garment sewing process, can easily predict the position and combination information of various patterns. Design/methodology/approach – Image processing is used to construct the garment pattern shape database. The boundary shapes are extracted from the photographs of garment patterns and their shape recognition information, especially shock graph, is also recorded for later pattern data retrieval. Findings – Using the image processing technique, garment patterns can be converted to electronic format easily. Also the prepared pattern database can be used for finding the nearest shape of an additional given input garment pattern. Patterns with irregular shapes were retrieved easily, while those with a simple shape, such as rectangle, showed a little erroneous result. Originality/value – Shape recognition has been adopted in various industrial areas, except for garment sewing process. Using the provided methodology, garment pattern shapes can be easily saved and retrieved only by taking pictures of them.

View Sphere Partitioning via Flux Graphs Boosts Recognition from Sparse Views

View-based 3D object recognition requires a selection of model object views against which to match a query view. Ideally, for this to be computationally efficient, such a selection should be sparse. To address this problem we partition the view sphere into regions within which the silhouette of a model object is qualitatively unchanged. This is accomplished using a flux-based skeletal representation and skeletal matching to compute the pairwise similarity between two views. Associating each view with a node of a view sphere graph, with the similarity between a pair of views as an edge weight, a clustering algorithm is used to partition the view sphere. Our experiments on exemplar level recognition using 19 models from the Toronto Database and category level recognition using 150 models from the McGill Shape Benchmark demonstrate that in a scenario of recognition from sparse views, sampling model views from such partitions consistently boosts recognition performance when compared against queries sampled randomly or uniformly from the view sphere. We demonstrate the improvement in recognition accuracy for a variety of popular 2D shape similarity approaches: shock graph matching, flux graph matching, shape context based matching and inner distance based matching.

Finding Median Point-Set Using Earth Mover's Distance

In this paper, we study a prototype learning problem, called Median Point-Set, whose objective is to construct a prototype for a set of given point-sets so as to minimize the total Earth Mover's Distances (EMD) between the prototype and the point-sets, where EMD between two point-sets is measured under affine transformation. For this problem, we present the first purely geometric approach. Comparing to existing graph-based approaches (e.g., median graph, shock graph), our approach has several unique advantages: (1) No encoding and decoding procedures are needed to map between objects and graphs, and therefore avoid errors caused by information losing during the mappings; (2) Staying only in the geometric domain makes our approach computationally more efficient and robust to noise. We evaluate the performance of our technique for prototype reconstruction on a random dataset and a benchmark dataset, handwriting Chinese characters. Experiments suggest that our technique considerably outperforms the existing graph-based methods.

Shock Graph and Shape matching

The aim of this paper to develop a theory for generic representation of 2-D shape, where structural descriptions are derived from the shocks (singularities) of a curve evolution process, acting on bounding contours. The shocks are organized into a directed, acyclic shock graph and complexity is managed by attending to the most significant (central) shape components first. The space of all such graphs is highly structured and can be characterized by the rules of a shock graph grammar which permits a reduction of a shock graph to a unique rooted shock tree. A novel tree matching algorithm which finds the best set of corresponding nodes between two shock trees in polynomial time.

Research and Perspective on Shape Matching

摘要: 形状匹配及分类是计算机视觉中的重要问题. 近年来,以形状上下文为代表的基于轮廓的形状匹配方法和以奇点图为代表的基于骨架的形状匹配方法获得了长足的发展. 本文介绍了形状匹配问题的基本概念, 分析了形状匹配问题的难点, 按照基于轮廓和基于骨架的分类方法对近年来最新出现的形状表示与形状匹配的方法进行了详尽的介绍, 并介绍了基于度量学习的形状检索方法, 本文还详细介绍了近年来形状匹配研究领域常用的一些测试数据库, 之后对局部形状匹配和形状分类等有潜力的研究方向进行了展望. 最后对形状匹配的整体框架及其应用前景进行了总结. 关键词: 形状表示 / 形状匹配 / 形状分类 / 轮廓 / 骨架

Object categorization using bone graphs

The bone graph (Macrini et al., in press, 2008) [23,25] is a graph-based medial shape abstraction that offers improved stability over shock graphs and other skeleton-based descriptions that retain unstable ligature structure. Unlike the shock graph, the bone graph’s edges are attributed, allowing a richer specification of relational information, including how and where two medial parts meet. In this paper, we propose a novel shape matching algorithm that exploits this relational information. Formulating the problem as an inexact directed acyclic graph matching problem, we extend a leading bipartite graph-based algorithm for matching shock graphs (Siddiqi et al., 1999) [41]. In addition to accommodating the relational information, our new algorithm is better able to enforce hierarchical and sibling constraints between nodes, resulting in a more general and more powerful matching algorithm. We evaluate our algorithm with respect to a competing shock graph-based matching algorithm, and show that for the task of view-based object categorization, our algorithm applied to bone graphs outperforms the competing algorithm. Moreover, our algorithm applied to shock graphs also outperforms the competing shock graph matching algorithm, demonstrating the generality and improved performance of our matching algorithm.

Bone graphs: Medial shape parsing and abstraction

The recognition of 3-D objects from their silhouettes demands a shape representation which is stable with respect to minor changes in viewpoint and articulation. This can be achieved by parsing a silhouette into parts and relationships that do not change across similar object views. Medial descriptions, such as skeletons and shock graphs, provide part-based decompositions but suffer from instabilities. As a result, similar shapes may be represented by dissimilar part sets. We propose a novel shape parsing approach which is based on identifying and regularizing the ligature structure of a medial axis, leading to a bone graph, a medial abstraction which captures a more stable notion of an object’s parts. Our experiments show that it offers improved recognition and pose estimation performance in the presence of within-class deformation over the shock graph.

Skeleton Search: Category-Specific Object Recognition and Segmentation Using a Skeletal Shape Model

We describe a top-down object detection and segmentation approach that uses a skeleton-based shape model and that works directly on real images. The approach is based on three components. First, we propose a fragment-based generative model for shape that is based on the shock graph and has minimal dependency among its shape fragments. The model is capable of generating a wide variation of shapes as instances of a given object category. Second, we develop a progressive selection mechanism to search among the generated shapes for the category instances that are present in the image. The search begins with a large pool of candidates identified by a dynamic programming (DP) algorithm and progressively reduces it in size by applying series of criteria, namely, local minimum criterion, extent of shape overlap, and thresholding of the objective function to select the final object candidates. Third, we propose the Partitioned Chamfer Matching (PCM) measure to capture the support of image edges for a hypothesized shape. This measure overcomes the shortcomings of the Oriented Chamfer Matching and is robust against spurious edges, missing edges, and accidental alignment between the image edges and the shape boundary contour. We have evaluated our approach on the ETHZ dataset and found it to perform well in both object detection and object segmentation tasks.

Fast and Simple 2D Shape Retrieval Using Discrete Shock Graph

In this letter, we propose an effective method to retrieve images from a 2D shape image database using discrete shock graphs combined with an adaptive selection algorithm. Experimental results show that our method is more accurate and fast than conventional approaches and reduces computational complexity.

Measuring 3D shape similarity by graph-based matching of the medial scaffolds

We propose to measure 3D shape similarity by matching a medial axis ( MA ) based representation—the medial scaffold ( MS ) . Shape similarity is measured as the minimum extent of deformation necessary for one shape to match another, guided by representing the shapes using the MS . This approach is an extension of an approach to match 2D shapes by matching their shock graphs, whereas here in 3D the MS is in an extended form of a hypergraph. The MS representation is both hierarchical and complete. Our approach approximates the theoretical optimal deformation path between two shapes by modeling shape deformations as discrete topological changes (the transitions) of the MS hypergraphs, where each graphical transition is associated with a cost measurement defined by the transition. Our algorithm first regularizes the MS hypergraphs and uses the graduated assignment graph-matching scheme to match the hypergraphs. A set of compatibility functions is defined to measure the pairwise similarity between the MS nodes, curves (graph links), and sheets (hyperlinks). Results on matching carpal bones and shapes from the SHREC’10 non-rigid dataset promise its potential in a range of applications.

Weak solution for the Hele-Shaw problem: Viscous shocks and singularities

In Hele-Shaw flows, a boundary of a viscous fluid develops unstable fingering patterns. At vanishing surface tension, fingers evolve to cusp-like singularities preventing a smooth flow. We show that the Hele-Shaw problem admits a weak solution where a singularity triggers viscous shocks. Shocks form a growing, branching tree of a line distribution of vorticity where pressure has a finite discontinuity. A condition that the flow remains curl-free at a macroscale uniquely determines the shock graph structure. We present a self-similar solution describing shocks emerging from a generic (2, 3)-cusp singularity—an elementary branching event of a branching shock graph.

Transitions of the 3D Medial Axis under a One-Parameter Family of Deformations

The instabilities of the medial axis of a shape under deformations have long been recognized as a major obstacle to its use in recognition and other applications. These instabilities, or transitions, occur when the structure of the medial axis graph changes abruptly under deformations of shape. The recent classification of these transitions in 2D for the medial axis and for the shock graph was a key factor in the development of an object recognition system where the classified instabilities were utilized to represent deformation paths. The classification of generic transitions of the 3D medial axis could likewise potentially lead to a similar representation in 3D. In this paper, these transitions are classified by examining the order of contact of spheres with the surface, leading to an enumeration of possible transitions which are then examined on a case-by-case basis. Some cases are ruled out as never occurring in any family of deformations, while others are shown to be nongeneric in a one-parameter family of deformations. Finally, the remaining cases are shown to be viable by developing a specific example for each. Our work is inspired by that of Bogaevsky, who obtained the transitions as part of an investigation of viscosity solutions of Hamilton-Jacobi equations. Our contribution is to give a more down-to-earth approach, bringing this work to the attention of the computer vision community, and to provide explicit constructions for the various transitions using simple surfaces. We believe that the classification of these transitions is vital to the successful regularization of the medial axis in its use in real applications.

Learning articulated appearance models for tracking humans: A spectral graph matching approach

Tracking an unspecified number of people in real-time is one of the most challenging tasks in computer vision. In this paper, we propose an original method to achieve this goal, based on the construction of a 2D human appearance model. The general framework, which is a region-based tracking approach, is applicable to any type of object. We show how to specialize the method for taking advantage of the structural properties of the human body. We segment its visible parts by using a skeletal graph matching strategy inspired by the shock graphs. Only morphological and topological information is encoded in the model graph, making the approach independent of the pose of the person, the viewpoint, the geometry or the appearance of the limbs. The limbs labeling makes it possible to build and update an appearance model for each body part. The resulting discriminative feature, that we denote as an articulated appearance model, captures both color, texture and shape properties of the different limbs. It is used to identify people in complex situations (occlusion, field of view exit, etc.), and maintain the tracking. The model to image matching has proved to be much more robust and better-founded than with existing global appearance descriptors, specifically when dealing with highly deformable objects such as humans. The only assumption for the recognition is the approximate viewpoint correspondence between the different models during the matching process. The method does not make use of skin color detection, which allows us to perform tracking under any viewpoint. Occlusions can be detected by the generic part of the algorithm, and the tracking is performed in such cases by means of a particle filter. Several results in complex situations prove the capacity of the algorithm to learn people appearance in unspecified poses and viewpoints, and its efficiency for tracking multiple humans in real-time using the specific updated descriptors. Finally, the model provides an important clue for further human motion analysis process.

Isotree: Tree clustering via metric embedding

One of the problems that hinders the spectral analysis of trees is that they have a strong tendency to be co-spectral. As a result, structurally distinct trees possess degenerate graph-spectra, and spectral methods can be reliably used to neither compute distances between trees nor to cluster trees. The aim of this paper is to describe a method that can be used to alleviate this problem. We use the ISOMAP algorithm to embed the trees in a Euclidean space using the pattern of shortest distances between nodes. From the arrangement of nodes in this space, we compute a weighted proximity matrix, and from the proximity matrix a Laplacian matrix is computed. By transforming the graphs in this way we lift the co-spectrality of the trees. The spectrum of the Laplacian matrix for the embedded graphs may be used for purposes of comparing trees and for clustering them. Experiments on sets of shock graphs reveal the utility of the method on real-world data.

3D object retrieval approach based on directed acyclic graph lightfield feature

A new 3D object retrieval methodology is proposed by exploiting a novel directed acyclic graph lightfield feature (DLF), in which the so-called lightfield is made up of around 2000–5000 colour views. The descriptor overcomes the disadvantages of the existing view-based 3D object retrieval methods. Benefiting from shock graph and Bayesian network learning, this DLF is simple, accurate and noise robust as compared to existing methods. Results of experiments show that the proposed method is superior to others.

Shock Graph for Representation and Modeling of Posture

Skeleton transform of which the medial axis transform is the most popular has been proposed as a useful shape abstraction tool for the representation and modeling of human posture. This paper explains this proposition with a description of the areas in which skeletons could serve to enable the representation of shapes. We present algorithms for two-dimensional posture modeling using the developed simplified shock graph (SSG). The efficacy of SSG extracted feature vectors as shape descriptors are also evaluated using three different classifiers, namely, decision tree, multilayer perceptron, and support vector machine. The paper concludes with a discussion of the issues involved in using shock graphs to model and classify human postures.

DIFFERENTIAL SHAPE STATISTICAL ANALYSIS

A novel statistical approach that involves differential shape is proposed to analyze contour segments. First, a moment-based algorithm to represent the differential contour segment in an efficient way is introduced. Then, a curvature mean-shift method is adopted to search for the salient features. An optimized function is also developed to segment a contour into parts based on its structural properties. Compared with some other methods used in CSS (Curvature Scale Space) and shock graphs, our method is more powerful for shape contour analysis, especially for the incomplete or occluded contours. Experiments show that our method can track salient parts in real-time and give a judgment of the basic shape properties such as symmetry.

Learning shape-classes using a mixture of tree-unions

This paper poses the problem of tree-clustering as that of fitting a mixture of tree unions to a set of sample trees. The tree-unions are structures from which the individual data samples belonging to a cluster can be obtained by edit operations. The distribution of observed tree nodes in each cluster sample is assumed to be governed by a Bernoulli distribution. The clustering method is designed to operate when the correspondences between nodes are unknown and must be inferred as part of the learning process. We adopt a minimum description length approach to the problem of fitting the mixture model to data. We make maximum-likelihood estimates of the Bernoulli parameters. The tree-unions and the mixing proportions are sought so as to minimize the description length criterion. This is the sum of the negative logarithm of the Bernoulli distribution, and a message-length criterion that encodes both the complexity of the union-trees and the number of mixture components. We locate node correspondences by minimizing the edit distance with the current tree unions, and show that the edit distance is linked to the description length criterion. The method can be applied to both unweighted and weighted trees. We illustrate the utility of the resulting algorithm on the problem of classifying 2D shapes using a shock graph representation.

Indexing hierarchical structures using graph spectra

Hierarchical image structures are abundant in computer vision and have been used to encode part structure, scale spaces, and a variety of multiresolution features. In this paper, we describe a framework for indexing such representations that embeds the topological structure of a directed acyclic graph (DAG) into a low-dimensional vector space. Based on a novel spectral characterization of a DAG, this topological signature allows us to efficiently retrieve a promising set of candidates from a database of models using a simple nearest-neighbor search. We establish the insensitivity of the signature to minor perturbation of graph structure due to noise, occlusion, or node split/merge. To accommodate large-scale occlusion, the DAG rooted at each nonleaf node of the query "votes" for model objects that share that "part," effectively accumulating local evidence in a model DAG's topological subspaces. We demonstrate the approach with a series of indexing experiments in the domain of view-based 3D object recognition using shock graphs.