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Fitting discrete polynomial curve and surface to noisy data

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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.

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  1. Fumiki Sekiya

    Present address: Graduate University for Advanced Studies SOKENDAI, Hayama, Japan

Authors and Affiliations

  1. Graduate School of Advanced Integration Science, Chiba University, Chiba, Japan

    Fumiki Sekiya

  2. National Institute of Informatics, Tokyo, Japan

    Akihiro Sugimoto

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  1. Fumiki Sekiya
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  2. Akihiro Sugimoto
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Correspondence to Fumiki Sekiya.

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Sekiya, F., Sugimoto, A. Fitting discrete polynomial curve and surface to noisy data. Ann Math Artif Intell 75, 135–162 (2015). https://doi.org/10.1007/s10472-014-9425-7

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  • DOI: https://doi.org/10.1007/s10472-014-9425-7

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