Scale-driven image decomposition with applications to recognition, registration, and segmentation

In this thesis, we propose to solve several computer vision problems using a novel fundamental idea, the scale difference between different patterns. In order to achieve our goal, we utilize the recently proposed total variation regularized L1 functional, which has an unique geometric feature of decomposing an additive image according to scales of the patterns within the image. We analyze and study the geometric properties of the TV-L1 model. We discuss different properties and provide intuitively proofs. We also discuss the properties when this model is applied to an image containing irregular shaped patterns, which were rarely discussed in literature. We then modify the TV-L1 model and develop novel algorithms to solve problems in different application areas.; Other than proposing the direct use of the TV-L 1 model for uneven background correction, we develop several novel algorithms based on this scale-driven image decomposition model. Our extensions and modifications are threefold: recognition, registration, and segmentation. In recognition, instead of decomposing an additive signal, we propose to factorize an image under multiplicative illumination fields based on the TV- L1 model. The effectiveness of this factorization is validated by a significant improvement of face recognition under varying illumination. In registration, we propose a non-rigid registration framework using a novel scale hierarchy established by the TV-L 1 model. We obtain robust and accurate registration on both 2D satellite images and 3D brain MR images with this framework. At last, a probabilistic method and a multi-resolution method are used to improve the limitations of the TV-L1 model for image segmentation. The proposed segmentation method is able to extract brain regions from head images. It can also be used to extract large scale patterns in general images. Experiment results validate the effectiveness of our work in different application areas.; We believe our works have significant contributions and have brought new possibilities to computer vision, public security, surveillance, medical image analysis, and other related fields.