Absfruet-A new approach to regularization methods for image processing is introduced and developed using as a vehicle the problem of computing dense optical flow fields in an image sequence. Standard formulations of this problem require the computationally intensive solution of an elliptic partial differential equation that arises from the often used “smoothness constraint” ’yl”. regularization. The interpretation of the smoothness constraint is utilized as a “fractal prior ” to motivate regularization based on a recently introduced class of multiscale stochastic models. The solution of the new problem formulation is computed with an efficient multiscale algorithm. Experiments on several image sequences demonstrate the substantial computational savings that can be achieved due to the fact that the algorithm is noniterative and in fact has a per pixel computational complexity that is independent of image size. The new approach also has a number of other important advantages. Specifically, multiresolution flow field estimates are available, allowing great flexibility in dealing with the tradeoff between resolution and accuracy. Multiscale error covariance information is also available, which is of considerable use in assessing the accuracy of the estimates. In particular, these error statistics can be used as the basis for a rational procedure for determining the spatially-varying optimal reconstruction resolution. Furthermore, if there are compelling reasons to insist upon a standard smoothness constraint, our algorithm provides an excellent initialization for the iterative algorithms associated with the smoothness constraint problem formulation. Finally, the usefulness of our approach should extend to a wide variety of ill-posed inverse problems in which variational techniques seeking a “smooth ” solution are generally Used. I.

In this thesis, we develop image processing algorithms and applications for a particular class of multiscale stochastic models. First, we provide background on the model class, including a discussion of its relationship to wavelet transforms and the details of a two-sweep algorithm for estimation. A multiscale model for the error process associated with this algorithm is derived. Next, we illustrate how the multiscale models can be used in the context of regularizing ill-posed inverse problems and demonstrate the substantial computational savings that such an approach offers. Several novel features of the approach are developed including a technique for choosing the optimal resolution at which to recover the object of interest. Next, we show that this class of models contains other widely used classes of statistical models including 1-D Markov processes and 2-D Markov random fields, and we propose a class of multiscale models for approximately representing Gaussian Markov random fields...

We propose two methods for visual control of a robotic system which do not require the formulation of an explicit calibration between image space and the world coordinate system. Calibration is known to be a difficult and error prone process. By extracting control information directly from the image, we free our techniques from the errors normally associated with a fixed calibration. The two algorithms we propose both utilize feedback from a simple geometric effect, rotational invariance, to control the positioning servo loop. We attach a camera system to a robot such that the camera system and the robot's gripper rotate simultaneously. We also constrain the camera to lie in a position where it can observe the gripper's rotational axis. As the camera system rotates about the gripper's rotational axis, the circular path traced out by a point-like feature projects to an elliptical path in image space. We gather the projected feature points over part of a rotation (=2 radians) ...

Our objective is to automatically recognize parts in a structured environment (such as a factory) using inexpensive and widely-available hardware. We consider the planar problem of determining the convex shape of a polygonal part from a sequence of projections. Projecting the part onto an axis in the plane of the part produces a scalar measure, the diameter, which is a function of the angle of projection. The diameter of a part at a particular angle can be measured using an instrumented parallel-jaw gripper. Previously presented negative results results motivate us to consider the problem of recognizing a part from a known (finite) set of parts. Given a set of polygonal parts with a total of N faces, can we find the shortest sensing plan for disambiguating the parts? Only diameters at n N stable faces can be measured. We construct an internal representation of these stable diameters in O(N + n³) time and then give two planning algorithms: one constructs an optimal sensing plan in...