lecnotes21

# lecnotes21 - 13.472J/1.128J/2.158J/16.940J COMPUTATIONAL...

This preview shows pages 1–4. Sign up to view the full content.

13.472J/1.128J/2.158J/16.940J COMPUTATIONAL GEOMETRY Lecture 21 Dr. K. H. Ko Prof. N. M. Patrikalakis Copyright c 2003 Massachusetts Institute of Technology Contents 21 Object Matching 2 21.1 Various matching methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 21.2 Methods through localization/registration . . . . . . . . . . . . . . . . . . . . 2 21.3 Classification of matching methods . . . . . . . . . . . . . . . . . . . . . . . . 2 21.4 Problem statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 21.4.1 Distance metric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 21.4.2 Distance between a point and a parametric surface . . . . . . . . . . . 4 21.4.3 Distance metric function . . . . . . . . . . . . . . . . . . . . . . . . . . 4 21.5 Matching problems : CGWOS, CPWOS, CGWS or CPWS . . . . . . . . . . . 5 21.5.1 Resolving the scaling effects . . . . . . . . . . . . . . . . . . . . . . . . 5 21.5.2 Rotation and translation . . . . . . . . . . . . . . . . . . . . . . . . . . 5 21.6 Matching problems : IGWOS, IPWOS, IGWS or IPWS . . . . . . . . . . . . . 6 21.6.1 Iterative Closest Point (ICP) algorithm [1] for IGWOS or IPWOS . . . 6 21.6.2 ICP algorithm for scaling effects . . . . . . . . . . . . . . . . . . . . . . 6 21.7 Matching problems : NGWOS or NPWOS . . . . . . . . . . . . . . . . . . . . 7 21.7.1 Search method [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 21.7.2 KH method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 21.8 Matching problems : NGWS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 21.9 Matching problems : NPWS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 21.9.1 Umbilical point method [7] . . . . . . . . . . . . . . . . . . . . . . . . . 9 21.9.2 Optimization method [7] . . . . . . . . . . . . . . . . . . . . . . . . . . 12 21.10Matching problems : offset method . . . . . . . . . . . . . . . . . . . . . . . . 13 21.10.1Distance function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 21.10.2Objective function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 21.10.3Gradient vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Bibliography 16 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Lecture 21 Object Matching 21.1 Various matching methods Moment method Principal component Contour and silhouette New representation Localization/registration Miscellaneous approaches 21.2 Methods through localization/registration A basic goal of matching through localization/registration is to find the best rigid body trans- formation which aligns two objects as closely as possible. The correspondence search between two objects is a key issue in finding the best transformation for matching. Correspondence can be established by calculating distinct features of one object and locating the same ones on the other object. Therefore, the features have to be carefully chosen such that they are robustly extracted and invariant with respect to various transformations. Among various fea- tures, intrinsic differential properties are used for matching purposes. They are independent of parametrization and methods of representation, and only depend on the geometric shape of the object. Moreover, they are invariant under any rigid body transformations (rotation and translation). 21.3 Classification of matching methods Two types of matching can be considered: global and partial . Simply, the global matching is regarded as the matching for whole objects, while the partial matching is considered as 2
the matching of part of objects. Matching problems can be further categorized based on the availability of correspondence or initial transformation information between two objects and the application of scaling. The classification of matching problems is summarized in Table 21.1. In the table, acronyms are used for simplification as follows: C : Correspondence information is provided. I : Initial information on correspondence is provided.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern