Optimization-based approaches in computer vision

Abstract

This thesis concerns how to define a function for the optimal solution to a vision problem and how to find the solution. For most vision systems, the extensive use of optimization is due to uncertainties in the visual process. In an image of cluttered and complex scenes, image interpretation through detection of concerned objects or 2-D/3-D shapes is usually very difficult. That is, the vision tasks need an inexact means to permit the noisy conditions, and thereby optimization-based method has been introduced as a useful tool. To optimize energy functions describing the concerned visual processes, particularly to solve the low-level processing problem such as image smoothing, 2-D/3-D object segmentation / tracking problem under a noisy scene and occlusion, this thesis uses several optimization algorithms such as Dynamic Programming (DA), Simulated Annealing (SA), or Graduated Non-Convexity (GNC). For example, DP method is an optimal search technique performing energy-minimization from definition of a reasonable functional using some geometric constraints given in the image. In these methods, the geometric neighborhood (i.e., Markovianity) constraint is a most effective clue guiding to an approximated global minimum through the sub-optimal search strategy, and broadly used in thesis as a central approach. Concerned vision problems are divided into three main elements - features, relations, and optimization. Features correspond to points, lines or pixels in image lattice, while relations describe spatial or contextual interaction between the features. Hence, the relations mean a meaningful and consistent relation that includes local or global contextual constraints. Propagation of the consistent relations is performed through an adequate and task-oriented optimization method. Because we use local or global consistent properties according to the given task, selection of the optimization method also depends on the specific relations on the task. First of all, we...