DocumentCode :
52459
Title :
Robust Ellipse Fitting Based on Sparse Combination of Data Points
Author :
Junli Liang ; Miaohua Zhang ; Ding Liu ; Xianju Zeng ; Ojowu, O. ; Kexin Zhao ; Zhan Li ; Han Liu
Author_Institution :
Sch. of Autom. & Inf. Eng., Xi´an Univ. of Technol., Xi´an, China
Volume :
22
Issue :
6
fYear :
2013
fDate :
Jun-13
Firstpage :
2207
Lastpage :
2218
Abstract :
Ellipse fitting is widely applied in the fields of computer vision and automatic industry control, in which the procedure of ellipse fitting often follows the preprocessing step of edge detection in the original image. Therefore, the ellipse fitting method also depends on the accuracy of edge detection besides their own performance, especially due to the introduced outliers and edge point errors from edge detection which will cause severe performance degradation. In this paper, we develop a robust ellipse fitting method to alleviate the influence of outliers. The proposed algorithm solves ellipse parameters by linearly combining a subset of (“more accurate”) data points (formed from edge points) rather than all data points (which contain possible outliers). In addition, considering that squaring the fitting residuals can magnify the contributions of these extreme data points, our algorithm replaces it with the absolute residuals to reduce this influence. Moreover, the norm of data point errors is bounded, and the worst case performance optimization is formed to be robust against data point errors. The resulting mixed l1-l2 optimization problem is further derived as a second-order cone programming one and solved by the computationally efficient interior-point methods. Note that the fitting approach developed in this paper specifically deals with the overdetermined system, whereas the current sparse representation theory is only applied to underdetermined systems. Therefore, the proposed algorithm can be looked upon as an extended application and development of the sparse representation theory. Some simulated and experimental examples are presented to illustrate the effectiveness of the proposed ellipse fitting approach.
Keywords :
computer vision; edge detection; image representation; optimisation; automatic industry control; computer vision; current sparse representation theory; data point sparse combination; edge detection; edge point error; image preprocessing step; interior-point method; mixed l1-l2 optimization problem; outliers influence; robust ellipse fitting method; second- order cone programming; Bayesian methods; Fitting; Image edge detection; Mathematical model; Robustness; Vectors; Diameter control; Iris recognition; edge points; ellipse fitting; least squares (LS); minimax criterion; outliers; overdetermined system; silicon single crystal; sparse representation; Algorithms; Bayes Theorem; Computer Simulation; Humans; Image Processing, Computer-Assisted; Iris; Least-Squares Analysis; Signal Processing, Computer-Assisted;
fLanguage :
English
Journal_Title :
Image Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1057-7149
Type :
jour
DOI :
10.1109/TIP.2013.2246518
Filename :
6459596
Link To Document :
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