This thesis focuses on the problems of object segmentation and semantic segmentation which aim at separating objects from background or assigning a specific semantic label to each pixel in an image. We propose two approaches for the object segmentation and one approach for semantic segmentation. The first proposed approach for object segmentation is based on saliency detection. Motivated by our ultimate goal for object segmentation, a novel saliency detection model is proposed. This model is formulated in the low-rank matrix recovery model by taking the information of image structure derived from bottom-up segmentation as an important constraint. The object segmentation is built in an iterative and mutual optimization framework, which simul...