Visual Model Based On Sparse Coding And Its Applications

Vision perception is one of the intriguing problems which attracts humanbeings for a long time. It is a challenge to design and construct a fast ande?cient visual system that can compete with human visual systems. With thedevelopment of the science and technology, including the rapid improvement ofcomputer ability, the popularization of high precision and speed image acquisitionhardware, emergence of new vision algorithm and more data from neurobiologyexperiments, designing a system that can be competent for human vision basictasks such as fact detection and recognition is still a challenge problem. Theapproach to learn and simulate the features and internal working mechanism ofbiological vision systems is treated as a e?ective way to solve the problem.In this thesis, we brie?y introduce the human vision system - especiallythe primate visual cortex - and its structure and characteristics. Meanwhile, wedescribe the modern modeling tools, including probabilistic model and linear gen-erative framework. Based on these tools, we also depict the primary componentanalysis, independent component analysis, sparse coding and their modeling onhuman primate visual systems. The features learned by these methods can re-veal some important characteristics such as sparse, overcomplete and topography.The main contributions of the paper are:1. Sparsity prior criterion The sparse property is considered as one of the rea-sons accounting for the e?ciency and high speed of human brain. However,how to define sparsity is still not well defined. There are still some subjectfacts in judging some distributions are spare while some others are not. Thepaper derives that some priors in classical sparse coding model will tend tospread a neuron's activations to the rest of neurons'to reduce the objec-tive value. This phenomenon breaks the assumption of sparse. We definethe value reduced as"duplicate bonus"and deduce that the sparse func-tion should satisfy subadditive property. We evaluate di?erent distributionunder this criterion and validate it by experiments. 2. Learning topographic structure through similarity function We introduceone layer network model that can learn the topographic structure of simplecell receptive fields in V1. One fact is that even without the topographicprior, the simple cells obtained by classical sparse coding inherently containthe topographic information. Hence, contrasting to previous topographicmodel with two layer network, the new single layer model can also behavethe topographic features.3. Topographic non-negative sparse coding Non-negative matrix factorizationis well suitable to the biology facts that activation cannot be negative andthe NMF can obtain the part-based features by training on the specificdata sets. These help the method become one of hot topic in the researcharea. In this paper, we propose a method that adds the topographic priorto the existed non-negative sparse coding. A multiplicative iterative equa-tion based on corresponding NMF equation is derived. The multiplicativeiterative equation is more e?cient than gradient descent method and theexperiment results is more close to biology facts and show the similar to-pographic organization comparing to traditional methods.