A variational approach to joint denoising, edge detection and motion estimation

The estimation of optical flow fields from image sequences is incorporated in a Mumford–Shah approach for image denoising and edge detection. Possibly noisy image sequences are considered as input and a piecewise smooth image intensity, a piecewise smooth motion field, and a joint discontinuity set are obtained as minimizers of the functional. The method simultaneously detects image edges and motion field discontinuities in a rigorous and robust way. It comes along with a natural multi–scale approximation that is closely related to the phase field approximation for edge detection by Ambrosio and Tortorelli. We present an implementation for 2D image sequences with finite elements in space and time. It leads to three linear systems of equations, which have to be iteratively in the minimization procedure. Numerical results underline the robustness of the presented approach and different applications are shown

Spatiotemporal Analysis of Range Imagery

The present thesis handles the topic of how to determine the three dimensional motion field from a corresponding sequence of range images. We investigate signals given by range cameras that are based on the time-of-flight principle for which they employ the novel optoelectronic photonic-mixer-device (PMD). Its signal comprises information about the range, the mean radiant flux and its modulation amplitude. We discuss how to take advantage of this wealth of information. The estimation of a motion field from image sequences is an ill-posed inverse problem which can not be solved in general. Moreover, the spatiotemporal signal of a PMD-camera is corrupted by several kind of, partially rather specific, errors of systematic and statistical nature depending explicitly on time and space (motion-artifacts). We analyze those errors and develop a method to correct for systematic errors in the range signal. By means of a novel two-state-channel-smoothing we improve range images corrupted by noise and outliers. We use and extend the structure tensor approach to come for the first time to an improved motion estimate that exploits the PMD-signal and provides an inherent measure for its confidence. The presented algorithms were developed under the premise to be of a computational complexity that not forbids their application within an embedded system. They are tested on synthetic and real images and image sequences