| Along with the development of human recognition and the ability to change the nature, extracting features from object and recognizing them have became a basic activity. With the appearance of mordern computer and development of information science, the computer vision recognition system releases man from the repeating labor and high intensity work. Many valuable results have been achieved. These results are widely used in industry, national defense, agriculture, medical, meteorology, astronomy and so on. After the deep analysis of the architecture of vision system carefully, feature extraction is one of the core issues in classification recognition, in which geometric invariant is important method to recognize object no matter how complex of environment. Geometric invariant can be applied to differentiate an object from the other, and it can also find same object after some transformations. However, at present, geometric invariant related research is still facing many challenges, for example, how to compute geometric invariant more efficiently in large dataset, and how to design stable geometric invariant for complex transformations.With the application background of image processing, biometric identification, three-dimensional reconstruction and visual inspection, base on a summary of previous works, this paper encompasses the problems of current research of geometric invariant and puts a deep forward researchs to some efficient algorithms and the stable construction of geometric invariant. It focuses on practical feature extraction algorithm of geometric invariant that satisfy fine discrimination, fast calculation speed, wide application range. The main works of the paper are as follows.1. In view of the existing issue on long computiational time of convex hull algorithm in large scale two-dimensional point set, a novel fast two-dimensional convex hull algorithm is proposed for large dataset based on visual attention mechanism using affine transformation. Convex hull is a geometric invariant in feature extraction. The characters of density, centroid position and width about two-dimensional distribution are made comprehensive consideration. According to the deformation invariant properties of affine transformation, initial estimation of the geometry distribution of point set is established through visual attention mechanism. After mapping the point set into a new point set by an affine transformation, we discard the non-vertex interior points in the polygon by an inscribed circle. Meanwhile, two theorems are also proposed and proved to solve an unconstrained optimization problem instead of the iteration method. The experiments on different data sets in six distributions(multivariate normal distribution, uniform distribution, exponential distribution, extreme value distribution, lognormal distribution, and Johnson distribution) prove that the proposed algorithm can generate convex hull much faster than some traditional algorithms and achieve a lower the time complexity and memory resource overhead in large scale dateset computation.2. To solve the issue of error increase and low efficiency in feature extraction for geometric invariant algorithms which require a number of iterations or matching, a construction algorithm of geometric invariant based on area ratio is proposed. First, the algorithm gets the convex hull of a gray image after binaryzation and computes the coordinate positions of a centroid and a pseudo centroid. Then, the line passes through these two points will partition the image to some areas. Finally, after some computations, the area ratio vector of geometric invariant can be achived by our algorithm. The experiments in the fish database and Coil-100 of Columbia University show that invariant extracted by the proposed algorithm satisfies affine invariance, the proposed algorithm can compute invariant without iterations and reduce the impact of the cumulative error effectively. Meanwhile, the trend between invariant feature curve in a certain range of occlusion(eg. erased, coated and occluded) for image of object and orginal image without occlusion is basically the same. Feature vector curve has discrimination ability.3. In order to provide cost-efficient and rapid retrieval and matching speed in recognition system for massive high dimensional face data, a rough face classification algorithm based on geometric invariant extractd from face contour is proposed in chapter 4. The proposed algorithm gets geometric invariant features extracted from face contour, and builds a multilevel hierarchical index structure in face database according to the invariant features. The faces with similar contour features will be divided into one candidate sub database. The face recognition process will be limited to one or several similar sub databases without whole database. The experiments in MUCT face database and Aberdeen face database from PICS show that face contour is a vital criteria in fast rough face classification, the classification results of the proposed algorithm can guarantee relative stability, the ability of classification and recognition with a low retrieval cost in massive face database.4. The convex hull in three-dimensional is also important in many fileds, such as computer simulation, atmospheric modeling, etc. With the rapid development of computer technology and the new demands in three-dimensional, we proposed a three-dimensional convex hull algorithm based on ellipsoid. The algorithm uses an ellipsoid to replace the prism in the initial step to remove non-vertex points as much as possible. The experimental data in multivariate normal distribution, uniform distribution, exponential distribution, extreme value distribution, lognormal distribution, and Johnson distribution show that the proposed algorithm can be applied to the massive three-dimensional data for convex hull, it only use 1.78 seconds to get convex hull for ten million point under multivariate normal distribution, and the computational time is better than Quickhull algorithm when the data volume of three-dimensional point set increases.
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