| Many applications in computer vision can be formulated as labeling problems of assigning each pixel a label where the labels represent some local quantities. If all pixels are regarded as independent, i.e., the label of each pixel has nothing to do with the labels of other pixels, such labeling problems are seriously sensitive to noise. On the other hand, for applications in videos, if the inter-frame information is neglected, the performance of the algorithms will be degraded.;To improve results of these labeling problems, smoothness-based priors can be enforced in the formulations. For a single image, the smoothness is the spatial coherence, which means that spatially close pixels trend to have similar labels. For a video, an additional temporal coherence is enforced, which means that the corresponding pixels in different frames should have similar labels. The spatial coherence constraint makes algorithms robust to noise and the temporal coherence constraint utilizes the inter-frame information for better video-based applications.;Such labeling problems with smoothness-based priors can be solved by minimizing a Markov energy. According to different definitions of the energy functions, different optimization tools can be used to obtain the results. In this thesis, three optimization approaches are used due to their good performance: graph cuts, belief propagation, and optimization with a closed form solution.;Five algorithms in different applications are proposed in this thesis. All of them are formulated as smoothness based labeling problems, including single image segmentation, video object cutout, image/video completion, image denoising, and image matting. According to different definitions, different optimization approaches are used in these algorithms. In single image segmentation and video object cutout, the graph-cut algorithms are used; in image/video completion, belief propagation is used; and in image denoising and image matting, closed form optimization is implemented.;Successful performance of the five proposed algorithms, with comparisons to related methods, demonstrates that the proposed models of the labeling problems using the smoothness-based priors work very well in these computer vision applications. |
