Many applications in computer vision can be formulated as labeling problems of assigning each pixel a label where the labels represent some local quantities. To improve results of these labeling problems, smoothness-based priors can be enforced in the formulations.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 book, 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 book. 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. This book should be especially useful to professionals in computer vision fields.
