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...

Currently two major limitations to applying vision in real tasks are robustness in realworld, uncontrolled environments, and the computational resources required for real-time operation. In particular, many current robotic visual motion detection algorithms (optical flow) are not suited for practical applications such as segmentation and structure-frommotion because they either require highly specialized hardware or up to several minutes on a scientific workstation. In addition, many such algorithms depend on the computation of first and in some cases higher numerical derivatives, which are notoriously sensitive to noise. In fact the current trend in optical flow research is to stress accuracy under ideal conditions and not to consider computational resource requirements or resistance to noise, which are essential for real-time robotics. As a result robotic vision researchers are frustrated by an inability to obtain reliable optical flow estimates in real-world conditions, and practica...

Currently two major limitations to applying vision in real tasks are robustness in realworld, uncontrolled environments, and the computational resources required for real-time operation. In particular, many current robotic visual motion detection algorithms (optical flow) are not suited for practical applications such as segmentation and structure-frommotion because they either require highly specialized hardware or up to several minutes on a scientific workstation. In addition, many such algorithms depend on the computation of first and in some cases higher numerical derivatives, which are notoriously sensitive to noise. In fact the current trend in optical flow research is to stress accuracy under ideal conditions and not to consider computational resource requirements or resistance to noise, which are essential for real-time robotics. As a result robotic vision researchers are frustrated by an inability to obtain reliable optical flow estimates in real-world conditions, and practica...