Lie group method: A new approach to image matching with arbitrary orientations

Abstract

In this article, we develop a new method for image matching of any two images with arbitrary orientations. The idea comes from the workpiece localization in machining industry. We first describe an image as a 3D point set other than the common 2D function f(x, y), then, making the sets corresponding to the compared images form solid surfaces, we equivalently translate the matching problem into an optimization problem on the Lie group SE(3). Through developing a kind of steepest descent algorithms on a general Lie group, we present an practical algorithm for matching problem. Simulations of eye detection and face detection are presented to show the feasibility and efficiency of the proposed algorithm. Key words: template matching; Lie groups; Lie algebras; steepest descent algorithm I. INTRODUCTIONTemplate matching is a commonly used technique in many fields, such as face detecting (Yang et al., 2002), biophysical data processing (Yao et al., 2003) and photogrammetry and remote sensing (Keipke, 1996), etc. In template matching, we are given a template image T to find the desired pattern in a test image P (usually much larger) by sliding the window of T in a pixel-by-pixel basis and meanwhile computing the correlation between T and the window-overlapping part of P (Theodoridis and Koutroumbas, 2003). However, this pixel-bypixel template matching is very time-consuming. In fact, it has been shown that for a test image of size R 3 S and a template image of size M 3 N, the computational complexity is O(M 3 N 3 R 3 S), provided the orientations in both compared images T and P are coincident (Tsai and Chiang, 2002). The computational complexity will become much higher when the orientation of the pattern we desire to find is unknown, for instance, when rotation (in-plane and/or out-ofplane rotation) is present in the test image. In practice, it is almost impossible to employ the pixel-by-pixel template matching to robustly deal with the presence of arbitrary rotation.

Kernel-Free Quadratic Surface Minimax Probability Machine for a Binary Classification Problem

“…Machine learning is an important branch in the field of artificial intelligence, which has a wide range of applications in various fields of contemporary science [1]. With the development of machine learning, the classification problem has been widely concerned and studied in the fields of pattern recognition [2], text classification [3], image processing [4], financial time series prediction [5], skin disease [6], intrusion detection systems [7], etc. The classification problem is a vital task in supervised learning that learns a classification rule from a training set with known labels and then uses it to assign a new sample to a class.…”