Fast Contour Matching Using Approximate Earth Mover's Distance

Weighted graph matching is a good way to align a pair of shapes represented by a set of descriptive local features; the set of correspondences produced by the minimum cost of matching features from one shape to the features of the other often reveals how similar the two shapes are. However, due to the complexity of computing the exact minimum cost matching, previous algorithms could only run efficiently when using a limited number of features per shape, and could not scale to perform retrievals from large databases. We present a contour matching algorithm that quickly computes the minimum weight matching between sets of descriptive local features using a recently introduced low-distortion embedding of the Earth Mover's Distance (EMD) into a normed space. Given a novel embedded contour, the nearest neighbors in a database of embedded contours are retrieved in sublinear time via approximate nearest neighbors search. We demonstrate our shape matching method on databases of 10,000 images of human figures and 60,000 images of handwritten digits.

Towards an Example-Based Image Compression Architecture for Video-Conferencing

This paper consists of two major parts. First, we present the outline of a simple approach to very-low bandwidth video-conferencing system relying on an example-based hierarchical image compression scheme. In particular, we discuss the use of example images as a model, the number of required examples, faces as a class of semi-rigid objects, a hierarchical model based on decomposition into different time-scales, and the decomposition of face images into patches of interest. In the second part, we present several algorithms for image processing and animation as well as experimental evaluations. Among the original contributions of this paper is an automatic algorithm for pose estimation and normalization. We also review and compare different algorithms for finding the nearest neighbors in a database for a new input as well as a generalized algorithm for blending patches of interest in order to synthesize new images. Finally, we outline the possible integration of several algorithms to illustrate a simple model-based video-conference system.

The Image Irradiance Equation: Its Solution and Application

How much information about the shape of an object can be inferred from its image? In particular, can the shape of an object be reconstructed by measuring the light it reflects from points on its surface? These questions were raised by Horn [HO70] who formulated a set of conditions such that the image formation can be described in terms of a first order partial differential equation, the image irradiance equation. In general, an image irradiance equation has infinitely many solutions. Thus constraints necessary to find a unique solution need to be identified. First we study the continuous image irradiance equation. It is demonstrated when and how the knowledge of the position of edges on a surface can be used to reconstruct the surface. Furthermore we show how much about the shape of a surface can be deduced from so called singular points. At these points the surface orientation is uniquely determined by the measured brightness. Then we investigate images in which certain types of silhouettes, which we call b-silhouettes, can be detected. In particular we answer the following question in the affirmative: Is there a set of constraints which assure that if an image irradiance equation has a solution, it is unique? To this end we postulate three constraints upon the image irradiance equation and prove that they are sufficient to uniquely reconstruct the surface from its image. Furthermore it is shown that any two of these constraints are insufficient to assure a unique solution to an image irradiance equation. Examples are given which illustrate the different issues. Finally, an overview of known numerical methods for computing solutions to an image irradiance equation are presented.

Learning from Ambiguity

There are many learning problems for which the examples given by the teacher are ambiguously labeled. In this thesis, we will examine one framework of learning from ambiguous examples known as Multiple-Instance learning. Each example is a bag, consisting of any number of instances. A bag is labeled negative if all instances in it are negative. A bag is labeled positive if at least one instance in it is positive. Because the instances themselves are not labeled, each positive bag is an ambiguous example. We would like to learn a concept which will correctly classify unseen bags. We have developed a measure called Diverse Density and algorithms for learning from multiple-instance examples. We have applied these techniques to problems in drug design, stock prediction, and image database retrieval. These serve as examples of how to translate the ambiguity in the application domain into bags, as well as successful examples of applying Diverse Density techniques.