Total Bregman divergence and its applications to shape retrieval

Abstract

Shape database search is ubiquitous in the world of biometric systems, CAD systems etc. Shape data in these domains is experiencing an explosive growth and usually requires search of whole shape databases to retrieve the best matches with accuracy and efficiency for a variety of tasks. In this paper, we present a novel divergence measure between any two given points in double-struckRn or two distribution functions. This divergence measures the orthogonal distance between the tangent to the convex function (used in the definition of the divergence) at one of its input arguments and its second argument. This is in contrast to the ordinate distance taken in the usual definition of the Bregman class of divergences [4]. We use this orthogonal distance to redefine the Bregman class of divergences and develop a new theory for estimating the center of a set of vectors as well as probability distribution functions. The new class of divergences are dubbed the total Bregman divergence (TBD). We present the l1-norm based TBD center that is dubbed the t-center which is then used as a cluster center of a class of shapes The t-center is weighted mean and this weight is small for noise and outliers. We present a shape retrieval scheme using TBD and the t-center for representing the classes of shapes from the MPEG-7 database and compare the results with other state-of-the-art methods in literature.

A Robust One -Class Support Vector Machine Using Gaussian -Based Penalty Factor and Its Application to Fault Detection

“…To deal with these circumstances, S. Yin et al [3] have proposed a robust one-class SVM technique which modifies the penalty factor  N / 1 of the traditional OCSVM and is formulated as is the maximum distance between the point x i and the centre of the dataset x c . The centre x c is calculated by the tSL-centre technique [6], [7] which is robust to noise and outliers and it is expressed as…”

“…According to (6), the influence of outliers in the formation of the decision boundary is reduced by applying a small penalty factor to samples which are far away from the centre so that the outliers will be forced to fall outside the boundary.…”

Shape and image retrieval by organizing instances using population cues

“…The aim of a similarity measure ´Ë Ë µ is to reliably define the similarity between the two instances Ë and Ë . In previous works, various measures such as [13,12,24,15,14] have been proposed for shapes. However, most of these only consider the similarity in shape-based features of a pair of shape instances while calculating ´Ë Ë µ and increase the chances that two shape instances will incorrectly be characterized as very similar (or dissimilar).…”

“…Specifically, Ling and Jacobs [13] introduce Inner-Distance Shape Context (IDSC) which further improves the widely-known Shape Context descriptor [5], while [14] introduces a framework called Aspect Space which aims to balance deformability and discriminability for describing a shape. Further, Liu et al [15] apply Total Bregman Divergence to characterize the similarity between two shapes and classify them into groups of similar shapes, while Lin et al [12] introduce the Layered Graph Matching algorithm. In addition to these measures, Temlyakov et al [23] present the "strand" and "stretch" strategies (S&S) that simplify the geometry of a given shape to improve the performance of these shape descriptors and similarity measures.…”

“…More recently [13,12,15,14] introduce new methods which find the similarity between two shapes, as defined by various shape-based measures, with greater accuracy. Specifically, Ling and Jacobs [13] introduce Inner-Distance Shape Context (IDSC) which further improves the widely-known Shape Context descriptor [5], while [14] introduces a framework called Aspect Space which aims to balance deformability and discriminability for describing a shape.…”