A Graph Theoretic Approach for Object Shape Representation in Compositional Hierarchies Using a Hybrid Generative-Descriptive Model

A graph theoretic approach is proposed for object shape representation in a hierarchical compositional architecture called Compositional Hierarchy of Parts (CHOP). In the proposed approach, vocabulary learning is performed using a hybrid generative-descriptive model. First, statistical relationships between parts are learned using a Minimum Conditional Entropy Clustering algorithm. Then, selection of descriptive parts is defined as a frequent subgraph discovery problem, and solved using a Minimum Description Length (MDL) principle. Finally, part compositions are constructed by compressing the internal data representation with discovered substructures. Shape representation and computational complexity properties of the proposed approach and algorithms are examined using six benchmark two-dimensional shape image datasets. Experiments show that CHOP can employ part shareability and indexing mechanisms for fast inference of part compositions using learned shape vocabularies. Additionally, CHOP provides better shape retrieval performance than the state-of-the-art shape retrieval methods.Comment: Paper : 17 pages. 13th European Conference on Computer Vision (ECCV 2014), Zurich, Switzerland, September 6-12, 2014, Proceedings, Part III, pp 566-581. Supplementary material can be downloaded from http://link.springer.com/content/esm/chp:10.1007/978-3-319-10578-9_37/file/MediaObjects/978-3-319-10578-9_37_MOESM1_ESM.pd

Human Body Part Labeling and Tracking Using Graph Matching Theory

International audienceProperly labeling human body parts in video sequencesis essential for robust tracking and motion interpretationframeworks. We propose to perform this task by usingGraph Matching. The silhouette skeleton is computed anddecomposed into a set of segments corresponding to the differentlimbs. A Graph capturing the topology of the segmentsis generated and matched against a 3D model of thehuman skeleton. The limb identification is carried out foreach node of the graph, potentially leading to the absenceof correspondence. The method captures the minimal informationabout the skeleton shape. No assumption about theviewpoint, the human pose, the geometry or the appearenceof the limbs is done during the matching process, making theapproach applicable to every configuration. Some correspondancesthat might be ambiguous only relying on topologyare enforced by tracking each graph node over time.Several results present the efficiency of the labeling, particularlyits robustness to limb detection errors that are likelyto occur in real situations because of occlusions or low levelsystem failures. Finally the relevance of the labeling in anoverall tracking system is pointed out

A local structural descriptor for image matching via normalized graph laplacian embedding

This paper investigates graph spectral approaches to the problem of point pattern matching. Specifically, we concentrate on the issue of how to effectively use graph spectral properties to characterize point patterns in the presence of positional jitter and outliers. A novel local spectral descriptor is proposed to represent the attribute domain of feature points. For a point in a given point-set, weight graphs are constructed on its neighboring points and then their normalized Laplacian matrices are computed. According to the known spectral radius of the normalized Laplacian matrix, the distribution of the eigenvalues of these normalized Laplacian matrices is summarized as a histogram to form a descriptor. The proposed spectral descriptor is finally combined with the approximate distance order for recovering correspondences between point-sets. Extensive experiments demonstrate the effectiveness of the proposed approach and its superiority to the existing methods

Hierarchical stochastic graphlet embedding for graph-based pattern recognition

This is the final version. Available on open access from Springer via the DOI in this recordDespite being very successful within the pattern recognition and machine learning community, graph-based methods are often unusable with many machine learning tools. This is because of the incompatibility of most of the mathematical operations in graph domain. Graph embedding has been proposed as a way to tackle these difficulties, which maps graphs to a vector space and makes the standard machine learning techniques applicable for them. However, it is well known that graph embedding techniques usually suffer from the loss of structural information. In this paper, given a graph, we consider its hierarchical structure for mapping it into a vector space. The hierarchical structure is constructed by topologically clustering the graph nodes, and considering each cluster as a node in the upper hierarchical level. Once this hierarchical structure of graph is constructed, we consider its various configurations of its parts, and use stochastic graphlet embedding (SGE) for mapping them into vector space. Broadly speaking, SGE produces a distribution of uniformly sampled low to high order graphlets as a way to embed graphs into the vector space. In what follows, the coarse-to-fine structure of a graph hierarchy and the statistics fetched through the distribution of low to high order stochastic graphlets complements each other and include important structural information with varied contexts. Altogether, these two techniques substantially cope with the usual information loss involved in graph embedding techniques, and it is not a surprise that we obtain more robust vector space embedding of graphs. This fact has been corroborated through a detailed experimental evaluation on various benchmark graph datasets, where we outperform the state-of-the-art methods.European Union Horizon 2020Ministerio de Educación, Cultura y Deporte, SpainGeneralitat de Cataluny

The Formats of Spatial Representations

Mental representations are the essence of cognition. Yet, to understand how the mind works, we must understand not just the content of mental representations (i.e., what information is stored), but also the format of those representations (i.e., how that information is stored). If we want to understand how sensory information is translated into symbolic representations, if we want to know how the mind forms ‘cognitive maps’, if we want to know how the firing of neurons can lead to the emergent phenomenon of human cognition — all of these things require us to understand how information is organized in the mind. In this thesis, I describe three ‘case studies’ of representational format in the domain of spatial cognition. I focus on spatial cognition for several reasons. First, spatial cognition is ubiquitous in the animal kingdom; thus, understanding spatial cognition in the human mind has the potential to reveal insights that generalize to all minds. Second, spatial cognition may be the single domain for which we know the most about the format of representations; indeed, the field was essentially founded on the premise that there exists a discernable ‘cognitive map’ within the mind. As such, it serves as an apt domain to study representational format. Finally, spatial representations (location representations in particular) may serve as the format of other higher-level information (e.g., numerical information, social information, etc.). Understanding the formats of spatial representation, therefore, may shed light on how other kinds of information are represented and organized in the mind. The first case study I describe pertains to the format of location representations. I show that, using a simple ‘error correlation’ analysis, we can uncover from simple spatial tasks the coordinate systems underlying spatial behavior. Using this approach, I argue that locations are spontaneously represented in polar coordinates, but flexibly in other coordinate systems (e.g., Cartesian coordinates) as needed. The second case study I describe pertains to the format of size representations. It has been known for many decades that the perception of size is illusory; for example, larger objects are perceived as being relatively less large. However, these illusions are typically explained by vague, unfalsifiable theories of size perception. I offer a simpler (and falsifiable) explanation of size illusions: that perceived size is equal to the sum of an objects’ dimensions rather than the product. Here, I focus primarily on the perception of area in adults, but this phenomenon appears to be highly general: I briefly allude to similar illusions that children experience, as well as similar illusions of volume. The final case study I describe pertains to how spatial information is used as a format to represent other information. I show that task-irrelevant ‘spatial structure’ spontaneously improves working memory. This effect is specific to spatial information; color information and audio information produce no such benefit. I discuss how these findings relate to existing models of working memory, and help us to understand the relationship between space and memory more broadly. I conclude with some final remarks about how understanding spatial behavior in light of the formats of representations can help us to understand the building blocks of cognition

Similarity Assessment and Retrieval of CAD Models

Ph.DDOCTOR OF PHILOSOPH

Continuous Medial Models in Two-Sample Statistics of Shape

In questions of statistical shape analysis, the foremost is how such shapes should be represented. The number of parameters required for a given accuracy and the types of deformation they can express directly influence the quality and type of statistical inferences one can make. One example is a medial model, which represents a solid object using a skeleton of a lower dimension and naturally expresses intuitive changes such as "bending", "twisting", and "thickening". In this dissertation I develop a new three-dimensional medial model that allows continuous interpolation of the medial surface and provides a map back and forth between the boundary and its medial axis. It is the first such model to support branching, allowing the representation of a much wider class of objects than previously possible using continuous medial methods. A measure defined on the medial surface then allows one to write integrals over the boundary and the object interior in medial coordinates, enabling the expression of important object properties in an object-relative coordinate system. I show how these properties can be used to optimize correspondence during model construction. This improved correspondence reduces variability due to how the model is parameterized which could potentially mask a true shape change effect. Finally, I develop a method for performing global and local hypothesis testing between two groups of shapes. This method is capable of handling the nonlinear spaces the shapes live in and is well defined even in the high-dimension, low-sample size case. It naturally reduces to several well-known statistical tests in the linear and univariate cases

Hierarchical Image Descriptions for Classification and Painting

The overall argument this thesis makes is that topological object structures captured within hierarchical image descriptions are invariant to depictive styles and offer a level of abstraction found in many modern abstract artworks. To show how object structures can be extracted from images, two hierarchical image descriptions are proposed. The first of these is inspired by perceptual organisation; whereas, the second is based on agglomerative clustering of image primitives. This thesis argues the benefits and drawbacks of each image description and empirically show why the second is more suitable in capturing object strucutures. The value of graph theory is demonstrated in extracting object structures, especially from the second type of image description. User interaction during the structure extraction process is also made possible via an image hierarchy editor. Two applications of object structures are studied in depth. On the computer vision side, the problem of object classification is investigated. In particular, this thesis shows that it is possible to classify objects regardless of their depictive styles. This classification problem is approached using a graph theoretic paradigm; by encoding object structures as feature vectors of fixed lengths, object classification can then be treated as a clustering problem in structural feature space and that actual clustering can be done using conventional machine learning techniques. The benefits of object structures in computer graphics are demonstrated from a Non-Photorealistic Rendering (NPR) point of view. In particular, it is shown that topological object structures deliver an appropriate degree of abstraction that often appears in well-known abstract artworks. Moreover, the value of shape simplification is demonstrated in the process of making abstract art. By integrating object structures and simple geometric shapes, it is shown that artworks produced in child-like paintings and from artists such as Wassily Kandinsky, Joan Miro and Henri Matisse can be synthesised and by doing so, the current gamut of NPR styles is extended. The whole process of making abstract art is built into a single piece of software with intuitive GUI.EThOS - Electronic Theses Online ServiceGBUnited Kingdo