NDLI: Fitting discrete polynomial curve and surface to noisy data

Content Provider	Springer Nature Link
Author	Sekiya, Fumiki Sugimoto, Akihiro
Copyright Year	2014
Abstract	Fitting geometric models such as lines, circles or planes is an essential task in image analysis and computer vision. This paper deals with the problem of fitting a discrete polynomial curve to given 2D integer points in the presence of outliers. A 2D discrete polynomial curve is defined as a set of integer points lying between two polynomial curves. We formulate the problem as a discrete optimization problem in which the number of points included in the discrete polynomial curve, i.e., the number of inliers, is maximized. We then propose a robust method that effectively achieves a solution guaranteeing local maximality by using a local search, called rock climbing, with a seed obtained by RANSAC. We also extend our method to deal with a 3D discrete polynomial surface. Experimental results demonstrate the effectiveness of our proposed method.
Starting Page	135
Ending Page	162
Page Count	28
File Format	PDF
ISSN	10122443
Journal	Annals of Mathematics and Artificial Intelligence
Volume Number	75
Issue Number	1-2
e-ISSN	15737470
Language	English
Publisher	Springer International Publishing
Publisher Date	2014-06-11
Publisher Place	Cham
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Curve fitting Surface fitting Discrete polynomial curve Discrete polynomial surface Local optimal Outliers Artificial Intelligence (incl. Robotics) Mathematics Computer Science Statistical Physics, Dynamical Systems and Complexity
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Artificial Intelligence

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