Pattern vectors from algebraic graph theory

Graphstructures have proven computationally cumbersome for pattern analysis. The reason for this is that, before graphs can be converted to pattern vectors, correspondences must be established between the nodes of structures which are potentially of different size. To overcome this problem, in this paper, we turn to the spectral decomposition of the Laplacian matrix. We show how the elements of the spectral matrix for the Laplacian can be used to construct symmetric polynomials that are permutation invariants. The coefficients of these polynomials can be used as graph features which can be encoded in a vectorial manner. We extend this representation to graphs in which there are unary attributes on the nodes and binary attributes on the edges by using the spectral decomposition of a Hermitian property matrix that can be viewed as a complex analogue of the Laplacian. To embed the graphs in a pattern space, we explore whether the vectors of invariants can be embedded in a low- dimensional space using a number of alternative strategies, including principal components analysis ( PCA), multidimensional scaling ( MDS), and locality preserving projection ( LPP). Experimentally, we demonstrate that the embeddings result in well- defined graph clusters. Our experiments with the spectral representation involve both synthetic and real- world data. The experiments with synthetic data demonstrate that the distances between spectral feature vectors can be used to discriminate between graphs on the basis of their structure. The real- world experiments show that the method can be used to locate clusters of graphs

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

A Framework for Symmetric Part Detection in Cluttered Scenes

The role of symmetry in computer vision has waxed and waned in importance during the evolution of the field from its earliest days. At first figuring prominently in support of bottom-up indexing, it fell out of favor as shape gave way to appearance and recognition gave way to detection. With a strong prior in the form of a target object, the role of the weaker priors offered by perceptual grouping was greatly diminished. However, as the field returns to the problem of recognition from a large database, the bottom-up recovery of the parts that make up the objects in a cluttered scene is critical for their recognition. The medial axis community has long exploited the ubiquitous regularity of symmetry as a basis for the decomposition of a closed contour into medial parts. However, today's recognition systems are faced with cluttered scenes, and the assumption that a closed contour exists, i.e. that figure-ground segmentation has been solved, renders much of the medial axis community's work inapplicable. In this article, we review a computational framework, previously reported in Lee et al. (2013), Levinshtein et al. (2009, 2013), that bridges the representation power of the medial axis and the need to recover and group an object's parts in a cluttered scene. Our framework is rooted in the idea that a maximally inscribed disc, the building block of a medial axis, can be modeled as a compact superpixel in the image. We evaluate the method on images of cluttered scenes.Comment: 10 pages, 8 figure

Perceptually Motivated Shape Context Which Uses Shape Interiors

In this paper, we identify some of the limitations of current-day shape matching techniques. We provide examples of how contour-based shape matching techniques cannot provide a good match for certain visually similar shapes. To overcome this limitation, we propose a perceptually motivated variant of the well-known shape context descriptor. We identify that the interior properties of the shape play an important role in object recognition and develop a descriptor that captures these interior properties. We show that our method can easily be augmented with any other shape matching algorithm. We also show from our experiments that the use of our descriptor can significantly improve the retrieval rates

Multi-view Convolutional Neural Networks for 3D Shape Recognition

A longstanding question in computer vision concerns the representation of 3D shapes for recognition: should 3D shapes be represented with descriptors operating on their native 3D formats, such as voxel grid or polygon mesh, or can they be effectively represented with view-based descriptors? We address this question in the context of learning to recognize 3D shapes from a collection of their rendered views on 2D images. We first present a standard CNN architecture trained to recognize the shapes' rendered views independently of each other, and show that a 3D shape can be recognized even from a single view at an accuracy far higher than using state-of-the-art 3D shape descriptors. Recognition rates further increase when multiple views of the shapes are provided. In addition, we present a novel CNN architecture that combines information from multiple views of a 3D shape into a single and compact shape descriptor offering even better recognition performance. The same architecture can be applied to accurately recognize human hand-drawn sketches of shapes. We conclude that a collection of 2D views can be highly informative for 3D shape recognition and is amenable to emerging CNN architectures and their derivatives.Comment: v1: Initial version. v2: An updated ModelNet40 training/test split is used; results with low-rank Mahalanobis metric learning are added. v3 (ICCV 2015): A second camera setup without the upright orientation assumption is added; some accuracy and mAP numbers are changed slightly because a small issue in mesh rendering related to specularities is fixe

Impact of Unexpected Events, Shocking News and Rumours on Foreign Exchange Market Dynamics

We analyze the dynamical response of the world's financial community to various types of unexpected events, including the 9/11 terrorist attacks as they unfolded on a minute-by-minute basis. We find that there are various 'species' of news, characterized by how quickly the news get absorbed, how much meaning and importance is assigned to it by the community, and what subsequent actions are then taken. For example, the response to the unfolding events of 9/11 shows a gradual collective understanding of what was happening, rather than an immediate realization. For news items which are not simple economic statements, and hence whose implications are not immediately obvious, we uncover periods of collective discovery during which collective opinions seem to oscillate in a remarkably synchronized way. In the case of a rumour, our findings also provide a concrete example of contagion in inter-connected communities. Practical applications of this work include the possibility of producing selective newsfeeds for specific communities, based on their likely impact