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Practical least-squares for computer graphics: Video files associated with this course are available from the citation page

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J. P. LewisAuthors Info & Claims

SIGGRAPH '07: ACM SIGGRAPH 2007 courses

Pages 1 - 57

https://doi.org/10.1145/1281500.1281598

Published: 05 August 2007 Publication History

Abstract

The course presents an overview of the least-squares technique and its variants. A wide range of problems in computer graphics can be solved using the least-squares technique (LS). Many graphics problems can be seen as finding the best set of parameters for a model given some data, and usually these parameters can be estimated using a least-squares approaches. For instance, a surface can be determined using data and smoothness penalties, a trajectory can be predicted using previous information, joint angles can be determined from end effector positions, etc. All these problems and many others can be formulated as minimizing the sum of squares of the errors.

Despite this apparent versatility, solving problems in the least-squares sense can produce poor results. This occurs when the nature of the problem error does not match the assumptions of the least-squares method. The course explains these assumptions and show how to circumvent some of them to apply LS to a wider range of problem.

The focus of the course is to provide a practical understanding of the techniques. Each technique will be explained using the simple example of fitting a line through data, and then illustrated through its use in one or more computer graphics papers.

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cover image ACM Conferences

SIGGRAPH '07: ACM SIGGRAPH 2007 courses

August 2007

6166 pages

ISBN:9781450318235

DOI:10.1145/1281500

Conference Chairs:
Sara McMains
University of California, Berkeley
,
Peter-Pike Sloan
Microsoft Corporation

Copyright © 2007 ACM.

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Published: 05 August 2007

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https://dl.acm.org/doi/10.1145/3610548.3618242
Grimm W(2022)Covariance‐invariant mapping of data points to nonlinear modelsMathematical Methods in the Applied Sciences10.1002/mma.871246:4(3597-3613)Online publication date: 14-Sep-2022
https://doi.org/10.1002/mma.8712
Smith BGoes FKim T(2019)Analytic Eigensystems for Isotropic Distortion EnergiesACM Transactions on Graphics10.1145/324104138:1(1-15)Online publication date: 15-Feb-2019
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