Motivated by the guaranteed stability margins of linear quadratic regulators (LQRs) and standard Kalman filter (KF) in the frequency domain, this article extends these results to the distributed Kalman-consensus filter (DKCF) for distributed estimation in sensor networks. In particular, we study the robustness margins of DKCF in two cases, one of which is based on the direct target observation while the other uses estimates from neighbor sensors in the network. The loop transfer functions of the two cases are established, and gain and phase margin robustness results are derived for both. The robustness margins of DKCF are improved compared to the single-agent KF. Furthermore, as communication topology varies in sensor networks, graph overall coupling strengths change. We also analyze the correlation between overall coupling strengths and the robustness margins of DKCF.

A parameter free technique for finding changes between images is discussed. The technique uses the Helmholtz principle to find changes in an input image in situations where only one or two images are available to build a background model. The Helmholtz principle locates image regions that are unlikely to occur due to an a priori random image generation model, and it assigns a confidence level to each changed region. All previous algorithms based on the Helmholtz principle assumed that the image was generated using independent and identically distributed (IID) random variables. The IID assumption is replaced with the weaker exchangeable assumption, and a simple exchangeable random variable model based on the hypergeometric distribution is investigated. Furthermore, practical calculation methods are discussed. The calculation methods require new nonasymptotic bounds to the hypergeometric distribution, and a major contribution of this paper is the novel proof of this bound and its relationship to large deviation theory. The calculations also incorporate the fast level set transform tree structure of the image to create shape boundaries of changed regions. The algorithm is applied to the problems of change detection and coherent motion. We also illustrate that the exchangeable random variable model yields more consistent results than an equivalent IID random variable model.

Selecting salient points from two or more images for computing correspondence is a well-studied problem in image analysis. This paper describes a new and effective technique for selecting these tiepoints using condition numbers, with application to image registration and mosaicking. Condition numbers are derived for point-matching methods based on minimizing windowed objective functions for 1) translation, 2) rotation-scaling-translation (RST), and 3) affine transformations. Our principal result is that the condition numbers satisfy K/sub Trans/ /spl les/ K/sub RST/ /spl les/ K/sub Affine/. That is, if a point is ill-conditioned with respect to point-matching via translation, then it is also unsuited for matching with respect to RST and affine transforms. This is fortunate since K/sub Trans/ is easily computed whereas K/sub RST/ and K/sub Affine/ are not. The second half of the paper applies the condition estimation results to the problem of identifying tiepoints in pairs of images for the purpose of registration. Once these points have been matched (after culling outliers using a RANSAC-like procedure), the registration parameters are computed. The postregistration error between the reference image and the stabilized image is then estimated by evaluating the translation between these images at points exhibiting good conditioning with respect to translation. The proposed method of tiepoint selection and matching using condition number provides a reliable basis for registration. The method has been tested on a large number of diverse collection of images - multidate Landsat images, aerial images, aerial videos, and infrared images. A Web site where the users can try our registration software is available and is being actively used by researchers around the world.

Peer group image processing identifies a "peer group" for each pixel and then replaces the pixel intensity with the average over the peer group. Two parameters provide direct control over which image features are selectively enhanced: area (number of pixels in the feature) and window diameter (window size needed to enclose the feature). A discussion is given of how these parameters determine which features in the image are smoothed or preserved. We show that the Fisher discriminant can be used to automatically adjust the peer group averaging (PGA) parameters at each point in the image. This local parameter selection allows smoothing over uniform regions while preserving features like corners and edges. This adaptive procedure extends to multilevel and color forms of PGA. Comparisons are made with a variety of standard filtering techniques and an analysis is given of computational complexity and convergence issues.

A general variational framework for image approximation and segmentation is introduced. By using a continuous "line-process" to represent edge boundaries, it is possible to formulate a variational theory of image segmentation and approximation in which the boundary function has a simple explicit form in terms of the approximation function. At the same time, this variational framework is general enough to include the most commonly used objective functions. Application is made to Mumford-Shah type functionals as well as those considered by Geman and others. Employing arbitrary Lp norms to measure smoothness and approximation allows the user to alternate between a least squares approach and one based on total variation, depending on the needs of a particular image. Since the optimal boundary function that minimizes the associated objective functional for a given approximation function can be found explicitly, the objective functional can be expressed in a reduced form that depends only on the approximating function. From this a partial differential equation (PDE) descent method, aimed at minimizing the objective functional, is derived. The method is fast and produces excellent results as illustrated by a number of real and synthetic image problems.

We review and present examples for two new image processing methods based on scale space evolution under partial differential operators. These operators arise from minimizing variational objective functions and from a novel approach that respects the discrete nature of real images. The first method considered is a variational approach that provides a closed-form expression for the optimal boundary function. This method gives good results with a 2-norm penalty term for approximation error and a 1-norm smoothness term; in this case there is a strong connection with total variation methods. The second method is a peer group averaging approach (developed by Hewer et al.) that smooths the image without blurring edges. This is accomplished by averaging over window pixels with nearly the same intensity; these pixels are the 'peer group' of the window's central pixel. The direct correspondence between the object characteristics and the parameters of peer group size and window diameter make the parameter selection easier for peer group averaging than for standard variational methods. These methods are used in combination with PGA providing the initial approximation for the variational descent procedure. This is applied to real image examples and compared to existing methods including a new level-set histogram modification method (developed by Caselles et al. (see Hewlett Packard Technical Report HPL97-58, 1997)) that treats connected level-sets of pixels as individual units.

A general variational framework for image approximation and segmentation is introduced in which the boundary function has a simple explicit form in terms of the approximation function. At the same time, this variational framework is general enough to include the most commonly used objective functions. Since the optimal boundary function, that minimizes the associated objective functional for a given approximation function, can be found explicitly, the objective functional can be expressed in a reduced form that depends only on the approximating function. From this a partial differential equation descent method, aimed at minimizing the objective functional, is derived. The method is fast and produces excellent results as illustrated by a number of real and synthetic image problems.