Charles S. Kenney

An efficient color representation for image retrieval

A compact color descriptor and an efficient indexing method for this descriptor are presented. The target application is similarity retrieval in large image databases using color. Colors in a given region are clustered into a small number of representative colors. The feature descriptor consists of the representative colors and their percentages in the region. A similarity measure similar to the quadratic color histogram distance measure is defined for this descriptor. The representative colors can be indexed in the three-dimensional (3-D) color space thus avoiding the high-dimensional indexing problems associated with the traditional color histogram. For similarity retrieval, each representative color in the query image or region is used independently to find regions containing that color. The matches from all of the query colors are then combined to obtain the final retrievals. An efficient indexing scheme for fast retrieval is presented. Experimental results show that this compact descriptor is effective and compares favorably with the traditional color histogram in terms of overall computational complexity.

Peer group filtering and perceptual color image quantization

In the first part of this work, peer group filtering (PGF), a nonlinear algorithm for image smoothing and impulse noise removal in color images is presented. The algorithm replaces each image pixel with the weighted average of its peer group members, which are classified based on the color similarity of the neighboring pixels. Results show that it effectively removes the noise and smooths the color images without blurring edges and details. In the second part of the work, PGF is used as a preprocessing step for color quantization. Local statistics obtained after PGF are used as weights in the quantization to suppress color clusters in detailed regions, since human perception is less sensitive to the differences in these areas. As a result, very coarse quantization can be obtained while preserving the color information in the original images. This can be useful in color image segmentation and color image retrieval applications.

The multiRANSAC algorithm and its application to detect planar homographies

A RANSAC based procedure is described for detecting inliers corresponding to multiple models in a given set of data points. The algorithm we present in this paper (called multiRANSAC) on average performs better than traditional approaches based on the sequential application of a standard RANSAC algorithm followed by the removal of the detected set of inliers. We illustrate the effectiveness of our approach on a synthetic example and apply it to the problem of identifying multiple world planes in pairs of images containing dominant planar structures.

The matrix sign function

A survey of the matrix sign function is presented including some historical background, definitions and properties, approximation theory and computational methods, and condition theory and estimation procedures, Applications to areas such as control theory, eigendecompositions, and roots of matrices are outlined, and some new theoretical results are also given. >

The sensitivity of the stable Lyapunov equation

An analysis is presented of the sensitivity of the solution of the Lyapunov equation A*X + XA = -W, where A is stable. This analysis leads to a spectral norm bound on the relative perturbation of the solution which is optimal for a certain class of estimates and which is essentially equivalent to the Frobenius norm bound obtained from the associated Kronecker product system. The latter bound can be expressed in terms of sep(A*, -A) and is known to accurately reflect the sensitivity of the Lyapunov problem, but it is hard to interpret in terms of the original matrix A. In contrast, the spectral norm bound which we derive is directly related to the minimal L2 damping of the dynamical system z = Az. Moreover, this dynamical link with the sensitivity problem leads to a new method of systematically investigating the norm behavior of eAt as well as providing a wealth of information about control theoretic aspects of z = Az, when A is the closed loop state matrix.

Rational iterative methods for the matrix sign function

In this paper an analysis of rational iterations for the matrix sign function is presented. This analysis is based on Pade approximations of a certain hypergeometric function and it is shown that l...

Condition Estimates for Matrix Functions

A sensitivity theory based on Frechet derivatives is presented that has both theoretical and computational advantages. Theoretical results such as a generalization of Van Loan’s work on the matrix exponential are easily obtained: matrix functions are least sensitive at normal matrices. Computationally, the central problem is to estimate the norm of the Frechet derivative, since this is equal to the function’s condition number. Two norm-estimation procedures are given; the first is based on a finite-difference approximation of the Frechet derivative and costs only two extra function evaluations. The second method was developed specifically for the exponential and logarithmic functions; it is based on a trapezoidal approximation scheme suggested by the chain rule for the identity

Approximating the Logarithm of a Matrix to Specified Accuracy

e^X = ( e^{X/2^n } )^{2^n }

The sensitivity of the algebraic and differential riccati equations

. This results in an infinite sequence of coupled Sylvester equations that, when truncated, is uniquely suited to the “scaling and squaring” procedure for

Small-sample statistical condition estimates for general matrix functions

e^X