Affine Invariant Feature Extraction Of Images

How to extract affine invariant features from images of different views is a common problem in many fields such as object or scene recognition, image registration, scene matching, image retrieval, etc. Compared with other features, affine invariant features are invariant to the viewpoint changing and camera parameter variance, and have great advantage over robust, repeatability, distinction and applicability, hence the theory and method of affine invariant feature extraction have became an active and challenging field. This thesis is primarily concerned with the problem of using new theory and tool to extract affine invariant features, which is based on the physic model of affine transform between images and the invariance in the mathematics.As the foundation of following chapters, a comprehensive exploration of the geometric transform between images of different views is proposed in chapter 2. This chapter provides a mathematic model for the transformation between two images obtained from the same scene. Based on pin-hole camera model, the relationship between the coordination of two images is discussed using two camera models, and it is proved that geometric relationship of two images obtained from one scene satisfies affine transformation. At the same time, the conditions of affine transform approximation are given in this chapter.A new framework of affine invariant feature extraction is introduced in chapter 3 based on the functional analysis. Three significant contributions are made in this chapter. First, a model for invariant feature extraction is developed in the functional space, in which extracting invariant features is boiled down to finding particular kernel functions. Second, a framework of finding invariant kernel space for any single parameter group is developed based on the fixed point theory of contractive mapping. Scale-invariant and rotate-invariant kernel spaces are derived as examples of the framework, and promising result are shown in experiments. Finally, the methods for deriving initial function and kernel parameters are proposed. The initial function can be found by solving a group of particular differential equations and the kernel parameters are decided by a model similarly to Fisher ruler.Compared with the invariant features of single parameter group, entirely global affine invariant features are more applicable, and chapter 4 introduces a new global affine invariant feature extraction method called EC-ARC, which is based on the invariance in affine geometry. Some important properties of affine geometry are analyzed firstly. Then two new conceptions called Extended Centroid (EC) and Affine Region Cutting (ARC) are introduced. A series of ECs are extracted by iterative ARC, and invariant features are constructed using the coordinate of ECs. The EC-ARC based method shows good performance in computational complexity and stability to the illumination and 3D rotation in certain range.Local affine invariant features are more applicable than global affine invariant features when used in real and complex scene. Howere it is difficult to develop the local affine invariant feature extraction method in a systemic way. Chapter 5 aimes at this difficulty and presents a novel rotate-invariant local descriptor based on the differential geometry, and this descriptor is also invariant to the scale transform in certain range. The problems for the region detector and feature descriptor are analyzed thoroughly, and a model for region detector is developed based on the properties of differential geometry. In this modle, the size and shape of support region are decided by the Gaussian curvature in differential geometry. Given the support regions, ellipse-SIFT features with highly distinctive and rotate-invariant are developed in ellipse-like support regions. Experimental results show that the proposed descriptor is also robust to the scale transform, noise and illumination variance.The last chapter summarizes the properties of three methods proposed in this thesis and compares their principles and applicabilities, which services as the a for the application of these methods.