Measuring the similarity between 3D shapes is a fundamental problem, with applications in computer vision, molecular biology, computer graphics, and a variety of other fields. A challenging aspect of this problem is to find a suitable shape signature that can be constructed and compared quickly, while still discriminating between similar and dissimilar shapes. In this paper, we propose and analyze a method for computing shape signatures for arbitrary (possibly degenerate) 3D polygonal models. The key idea is to represent the signature of an object as a shape distribution sampled from a shape function measuring global geometric properties of an object. The primary motivation for this approach is to reduce the shape matching problem to the comparison of probability distributions, which is a simpler problem than the comparison of 3D surfaces by traditional shape matching methods that require pose registration, feature correspondence, or model fitting. We find that the dissimilarities be...

this paper, we propose and analyze a method for computing shape signatures for arbitrary (possibly degenerate) 3D polygonal models. The key idea is to represent the signature of an object as a shape distribution sampled from a shape function measuring global geometric properties of an object. The primary motivation for this approach is to reduce the shape matching problem to the comparison of probability distributions, which is simpler than traditional shape matching methods that require pose registration, feature correspondence, or model fitting

In this paper, we address the problem of detecting pedestrians in crowded real-world scenes with severe overlaps. Our basic premise is that this problem is too difficult for any type of model or feature alone. Instead, we present a novel algorithm that integrates evidence in multiple iterations and from different sources. The core part of our method is the combination of local and global cues via a probabilistic top-down segmentation. Altogether, this approach allows to examine and compare object hypotheses with high precision down to the pixel level. Qualitative and quantitative results on a large data set confirm that our method is able to reliably detect pedestrians in crowded scenes, even when they overlap and partially occlude each other. In addition, the flexible nature of our approach allows it to operate on very small training sets. 1.

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.

The advantages of discriminative learning algorithms and kernel machines are combined with generative modeling using a novel kernel between distributions. In the probability product kernel, data points in the input space are mapped to distributions over the sample space and a general inner product is then evaluated as the integral of the product of pairs of distributions. The kernel is straightforward to evaluate for all exponential family models such as multinomials and Gaussians and yields interesting nonlinear kernels. Furthermore, the kernel is computable in closed form for latent distributions such as mixture models, hidden Markov models and linear dynamical systems. For intractable models, such as switching linear dynamical systems, structured mean-field approximations can be brought to bear on the kernel evaluation. For general distributions, even if an analytic expression for the kernel is not feasible, we show a straightforward sampling method to evaluate it. Thus, the kernel permits discriminative learning methods, including support vector machines, to exploit the properties, metrics and invariances of the generative models we infer from each datum. Experiments are shown using multinomial models for text, hidden Markov models for biological data sets and linear dynamical systems for time series data.

The explosion of on-line information has given rise to many query-based search engines (such as Alta Vista) and manually constructed topic hierarchies (such as Yahoo! ). But with the current growth rate in the amount of information, query results grow incomprehensibly large and manual classification in topic hierarchies creates an immense information bottleneck. Therefore, these tools are rapidly becoming inadequate for addressing users' information needs. In this dissertation, we address these problems with a system for topical information space navigation that combines the query-based and taxonomic approaches. Our system, named SONIA (Service for Organizing Networked Information Au- tonomously), is implemented as part of the Stanford Digital Libraries testbed. It enables the creation of dynamic hierarchical document categorizations based on the full-text of articles. Using probability theory as a formal foundation, we develop several Machine Learning methods to allow document collections to be automatically organized at a topical level. First, to generate such topical hierarchies, we employ a novel probabilistic clustering scheme that outperforms traditional methods used in both Information Retrieval and Probabilistic Reasoning. Furthermore, we develop methods for classifying new articles into such automatically generated, or existing manually generated, hierarchies. In contrast to standard classification approaches which do not make use of the taxonomic relations in a topic hierarchy, our method explicitly uses the existing hierarchical relationships between topics, leading to improvements in classification accuracy. Much of this improvement is derived from the fact that the classification decisions in such a hierarchy can be made by considering only the presence (o...

It is evident that the process of face recognition, by definition, should be based on the content of a face. The problem is: what is a "face"? Recently, a state-of-the-art statistics-based face recognition system, the PCA plus LDA approach, has been proposed [1]. However, the authors used "face" images that included hair, shoulders, face and background. Our intuition tells us that only a recognition process based on a "pure" face portion can be called face recognition. The mixture of irrelevant data may result in an incorrect set of decision boundaries. In this paper, we propose a statistics-based technique to quantitatively prove our assertion. For the purpose of evaluating how the different portions of a face image will influence the recognition results, a hypothesis testing model is proposed. We then implement the above mentioned face ...

This paper presents a preliminary study for mapping sea ice patterns (texture) with 100-m ERS-1 synthetic aperture radar (SAR) imagery. We used gray-level co-occurrence matrices (GLCM) to quantitatively evaluate textural parameters and representations and to determine which parameter values and representations are best for mapping sea ice texture. We conducted experiments on the quantization levels of the image and the displacement and orientation values of the GLCM by examining the effects textural descriptors such as entropy have in the representation of different sea ice textures. We showed that a complete gray-level representation of the image is not necessary for texture mapping, an eight-level quantization representation is undesirable for textural representation, and the displacement factor in texture measurements is more important than orientation. In addition, we developed three GLCM implementations and

Abstract. In this paper, we propose to combine an efficient image representation based on local descriptors with a Support Vector Machine classifier in order to perform object categorization. For this purpose, we apply kernels defined on sets of vectors. After testing different combinations of kernel / local descriptors, we have been able to identify a very performant one. 1

We introduce a new class of kernels between distributions. These induce a kernel on the input...