Specifications

Source title: IEEE Transactions on Image Processing
Abbreviated source title: IEEE Trans Image Process
Volume: 22
Issue: 6
Issue date: 2013
Publication year: 2013
Pages: 2207-2218
Article number: 6459596
Language: English
ISSN: 10577149
CODEN: IIPRE4
Document type: Journal article (JA)
Publisher: Institute of Electrical and Electronics Engineers Inc., 445 Hoes Lane / P.O. Box 1331,
Piscataway, NJ 08855-1331, United States
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 $l1\hbox{-}l2$ 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. ©
1992-2012 IEEE.
Number of references: 28
Main heading: Statistics
Controlled terms: Algorithms - Biometrics - Edge detection - Errors -
Optimization
Uncontrolled terms: Diameter control - Edge point - Ellipse fitting - Iris recognition
- Least squares - Minimax criterion - outliers - Overdetermined systems - Silicon
single crystals - Sparse representation
Classification code: 922.2 Mathematical Statistics - 921.5 Optimization Techniques - 921
Mathematics - 732 Control Devices - 723 Computer Software, Data Handling and
Applications - 716 Telecommunication; Radar, Radio and Television - 461 Bioengineering