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ROBOTICS Handbook of Computer Vision Algorithms in Image Algebra Part 13

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Tham khảo tài liệu 'robotics handbook of computer vision algorithms in image algebra part 13', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Figure 10.8.1 Centroid and angle of orientation. The moment of inertia about the line in the direction s can be written as M m20sin2j - 2musmt cos m02cos2 . The moment of inertia is minimized by solving r . . in n 2 for critical values of . Using the identity - t T t f the search for critical values leads to the quadratic equation . 2 n . so - . u . _ tan 0 d-------- ------- tan V 1 0. mil Solving the quadratic equations leads to two solutions for tan s and hence two angles min and max. These are the angles of the axes about which the object has minimum and maximum moments of inertia respectively. Determining which solution of the quadratic equation minimizes or maximizes the moment of inertia requires substitution back into the equation for M. Previous Table of Contents Next HOME SUBSCRIBE SEARCH FAQ SITEMAP CONTACT US Products Contact Us About Us Privacy Ad Info Home Use of this site is subject to certain Terms Conditions Copyright 1996-2000 EarthWeb Inc. All rights reserved. Reproduction whole or in part in any form or medium without express written permission of EarthWeb is prohibited. Read EarthWeb s privacy statement. fa Sa The image algebra formulas for the central moments of order 2 used to compute the angle of orientation are given by ÍH2Ú 52 pi - - a 11 52 ipi p2 ỹ a 52 tp - ỹ a. 10.9. Region Description Using Moments Moment invariants are image statistics that are independent of rotation translation and scale. Moment invariants are uniquely determined by an image and conversely uniquely determine the image modulus rotation translation and scale . These properties of moment invariants facilitate pattern recognition in the visual field that is independent of size position and orientation. See Hu 11 for experiments using moment invariants for pattern recognition. The moments invariants defined by Hu 11 12 are derived from the definitions of moments centralized moments and normalized central moments. These statistics are defined as follows Let be a .