We present methods for estimating forces which drive motion observed in density image sequences. Using these forces, we also present methods for predicting velocity and density evolution. To do this, we formulate and apply a Minimum Energy Flow (MEF) method which is capable of estimating both incompressible and compressible flows from time-varying density images. Both the MEF and force-estimation techniques are applied to experimentally obtained density images, spanning spatial scales from micrometers to several kilometers. Using density image sequences describing cell splitting, for example, we show that cell division is driven by gradients in apparent pressure within a cell. Using density image sequences of fish shoals, we also quantify 1) intershoal dynamics such as coalescence of fish groups over tens of kilometers, 2) fish mass flow between different parts of a large shoal, and 3) the stresses acting on large fish shoals.

We propose statistical data association techniques/or visual tracking of enormously large numbers of objects. We do not assume any prior knowledge about the numbers involved, and the objects may appear or disappear anywhere in the image frame and at any time in the sequence. Our approach combines the techniques of multitarget track initiation, recursive Bayesian tracking, clutter modeling, event analysis, and multiple hypothesis filtering. The original multiple hypothesis filter addresses an NP-hard problem and is thus not practical. We propose two cluster-based data association approaches that are linear in the number of detections and tracked objects. We applied the method to track wildlife in infrared video. We have successfully tracked hundreds of thousands of bats which were flying at high speeds and in dense formations.

Analytic conditions that are necessary for the maximum likelihood estimate to become asymptotically unbiased and attain minimum variance are derived for estimation problems in computer vision. In particular, problems of estimating the parameters that describe the 3D structure of rigid objects or their motion are investigated. It is common practice to compute Cramer-Rao lower bounds (CRLB) to approximate the mean-square error in parameter estimation problems, but the CRLB is not guaranteed to be a tight bound and typically underestimates the true mean-square error. The necessary conditions for the Cramer-Rao lower bound to be a good approximation of the mean-squareerror are derived. The tightness of the bound depends on the noise level, the number of pixels on the surface of the object, and the texture of the surface. We examine our analytical results experimentally using polyhedral objects that consist of planar surface patches with various textures that move in 3D space. We provide necessary conditions for the CRLB to be attained that depend on the size, texture, and noise level of the surface patch.

Following the theory of statistical estimation, the problem of recognizing objects imaged in complex real-world scenes is examined from a parametric perspective. A scalar measure of an object's complexity, which is invariant under affine transformation and changes in image noise level, is extracted from the object's Fisher information. The volume of Fisher information is shown to provide an overall statistical measure of the object's recognizability in a particular image, while the complexity provides an intrinsically physical measure that characterizes the object in any image. An information-conserving method is then developed for recognizing an object imaged in a complex scene. Here the term information-conserving means that the method uses all the measured data pertinent to the object's recognizability, attains the theoretical lower bound on estimation error for any unbiased estimate, and therefore is statistically optimal. This method is then successfully applied to finding objects imaged in thousands of complex real-world scenes.

A fast simulated annealing algorithm is developed for automatic object recognition. The object recognition problem is addressed as the problem of best describing a match between a hypothesized object and an image. The normalized correlation coefficient is used as a measure of the match. Templates are generated on-line during the search by transforming model images. Simulated annealing reduces the search time by orders of magnitude with respect to an exhaustive search. The algorithm is applied to the problem of how landmarks, e.g., traffic signs, can be recognized by a navigating robot. We illustrate the performance of our algorithm with real-world images of complicated scenes with traffic signs. False positive matches occur only for templates with very small information content. To avoid false positive matches, we propose a method to select model images for robust object recognition by measuring the information content of the model images. The algorithm works well in noisy images for model images with high information content.>