S. Ravi Kumar

Spatial Color Indexing and Applications

We define a new image feature called the color correlogram and use it for image indexing and comparison. This feature distills the spatial correlation of colors and when computed efficiently, turns out to be both effective and inexpensive for content-based image retrieval. The correlogram is robust in tolerating large changes in appearance and shape caused by changes in viewing position, camera zoom, etc. Experimental evidence shows that this new feature outperforms not only the traditional color histogram method but also the recently proposed histogram refinement methods for image indexing/retrieval. We also provide a technique to cut down the storage requirement of the correlogram so that it is the same as that of histograms, with only negligible performance penalty compared to the original correlogram.We also suggest the use of color correlogram as a generic indexing tool to tackle various problems arising from image retrieval and video browsing. We adapt the correlogram to handle the problems of image subregion querying, object localization, object tracking, and cut detection. Experimental results again suggest that the color correlogram is more effective than the histogram for these applications, with insignificant additional storage or processing cost.

Combining supervised learning with color correlograms for content-based image retrieval

The paper addresses how relevance feedback can be used to improve the performance of content-based image retrieval. We present two supervised learning methods: learning the query and learning the metric. We combine the learning methods with the recently proposed color correlograms for image indexing/retrieval. Our results on a large image database of over 20; 000 images suggest that these learning methods are quite effective for content-based image retrieval.

An automatic hierarchical image classification scheme

Organizing images into semantic categories can be extremely useful for searching and browsing through large collections of images. Not much work has been done on automatic image classification, however. In this paper, we propose a method for hierarchical classification of images via supervised learning. This scheme relies on using a good low-level feature and subsequently performing feature-space reconfiguration using singular value decomposition to reduce noise and dimensionality. We use the training data to obtain a hierarchical classification tree that can be used to categorize new images. Our experimental results suggest that this scheme not only performs better than standard nearest-neighbor techniques, but also has both storage and computational advantages.

On learning bounded-width branching programs

In this paper, we study PAC-leaming algorithms for specialized classes of deterministic finite automata (DFA). Inpartictdar, we study branchingprogrsms, and we investigate the intluence of the width of the branching program on the difficulty of the learning problem. We first present a distribution-free algorithm for learning width-2 branching programs. We also give an algorithm for the proper learning of width-2 branching programs under uniform distribution on labeled samples. We then show that the existence of an efficient algorithm for learning width-3 branching programs would imply the existence of an efficient algorithm for learning DNF, which is not known to be the case. Fimlly, we show that the existence of an algorithm for learning width-3 branching programs would also yield an algorithm for learning a very restricted version of parity with noise.

A note on optical routing on trees

Bandwidth is a very valuable resource in wavelength division multiplexed optical networks. The problem of finding an optimal assignment of wavelengths to requests is of fundamental importance in bandwidth utilization. We present a polynomial-time algorithm for this problem on fixed constant-size topologies. We combine this algorithm with ideas from Raghavan and Upfal (1994) to obtain an optimal assignment of wavelengths on constant degree undirected trees. Mihail, Kaklamanis, and Rao (1995) posed the following open question: what is the complexity of this problem on directed trees? We show that it is NP-complete both on binary and constant depth directed trees.

Self-Testing without the Generator Bottleneck

Suppose P is a program designed to compute a function f defined on a group G. The task of self-testing P, that is, testing if P computes f correctly on most inputs, usually involves testing explicitly if P computes f correctly on every generator of G. In the case of multivariate functions, the number of generators, and hence the number of such tests, becomes prohibitively large. We refer to this problem as the generator bottleneck. We develop a technique that can be used to overcome the generator bottleneck for functions that have a certain nice structure, specifically if the relationship between the values of the function on the set of generators is easily checkable. Using our technique, we build the first efficient self-testers for many linear, multilinear, and some nonlinear functions. This includes the FFT, and various polynomial functions. All of the self-testers we present make only O(1) calls to the program that is being tested. As a consequence of our techniques, we also obtain efficient program result-checkers for all these problems.

Approximating Latin Square Extensions

Abstract. In this paper we investigate the problem of computing the maximum number of entries which can be added to a partially filled latin square. The decision version of this question is known to be NP-complete. We present two approximation algorithms for the optimization version of this question. We first prove that the greedy algorithm achieves a factor of 1/3. We then use insights derived from the linear relaxation of an integer program to obtain an algorithm based on matchings that achieves a better performance guarantee of 1/2. These are the first known polynomial-time approximation algorithms for the latin square completion problem that achieve nontrivial worst-case performance guarantees. Our study is motivated by applications to lightpath assignment and switch configuration in wavelength routed multihop optical networks.

Automatic hierarchical color image classification

Organizing images into semantic categories can be extremely useful for content-based image retrieval and image annotation. Grouping images into semantic classes is a difficult problem, however. Image classification attempts to solve this hard problem by using low-level image features. In this paper, we propose a method for hierarchical classification of images via supervised learning. This scheme relies on using a good low-level feature and subsequently performing feature-space reconfiguration using singular value decomposition to reduce noise and dimensionality. We use the training data to obtain a hierarchical classification tree that can be used to categorize new images. Our experimental results suggest that this scheme not only performs better than standard nearest-neighbor techniques, but also has both storage and computational advantages.

Checking Approximate Computations of Polynomials and Functional Equations

A majority of the results on self-testing and correcting deal with programs which purport to compute the correct results precisely. We relax this notion of correctness and show how to check programs that compute only a numerical approximation to the correct answer. The types of programs that we deal with are those computing polynomials and functions defined by certain types of functional equations. We present results showing how to perform approximate checking, self-testing, and self-correcting of polynomials, settling in the affirmative a question raised by [P. Gemmell et al., Proceedings of the 23rd ACM Symposium on Theory of Computing, 1991, pp. 32--42; R. Rubinfeld and M. Sudan, Proceedings of the Third Annual ACM-SIAM Symposium on Discrete Algorithms, Orlando, FL, 1992, pp. 23--43; R. Rubinfeld and M. Sudan, SIAM J. Comput., 25 (1996), pp. 252--271]. We obtain this by first building approximate self-testers for linear and multilinear functions. We then show how to perform approximate checking, self-testing, and self-correcting for those functions that satisfy addition theorems, settling a question raised by [R. Rubinfeld, SIAM J. Comput., 28 (1999), pp. 1972--1997]. In both cases, we show that the properties used to test programs for these functions are both robust (in the approximate sense) and stable. Finally, we explore the use of reductions between functional equations in the context of approximate self-testing. Our results have implications for the stability theory of functional equations.

Checking properties of polynomials

In this paper we show how to construct efficient checkers for programs that supposedly compute properties of polynomials. The properties we consider are roots, norms, and other analytic/algebraic functions of polynomials. In our model, both the program II and the polynomial p are available to the checker each as a black box. We show how to check programs that compute a specific root (e.g., the largest) or a subset of roots of the given polynomial.