Ellipse Fitting Using the Finite Rate of Innovation Sampling Principle

Mulleti, Satish and Seelamantula, Chandra Sekhar (2016) Ellipse Fitting Using the Finite Rate of Innovation Sampling Principle. In: IEEE TRANSACTIONS ON IMAGE PROCESSING, 25 (3). pp. 1451-1464.

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Abstract

Standard approaches for ellipse fitting are based on the minimization of algebraic or geometric distance between the given data and a template ellipse. When the data are noisy and come from a partial ellipse, the state-of-the-art methods tend to produce biased ellipses. We rely on the sampling structure of the underlying signal and show that the x- and y-coordinate functions of an ellipse are finite-rate-of-innovation (FRI) signals, and that their parameters are estimable from partial data. We consider both uniform and nonuniform sampling scenarios in the presence of noise and show that the data can be modeled as a sum of random amplitude-modulated complex exponentials. A low-pass filter is used to suppress noise and approximate the data as a sum of weighted complex exponentials. The annihilating filter used in FRI approaches is applied to estimate the sampling interval in the closed form. We perform experiments on simulated and real data, and assess both objective and subjective performances in comparison with the state-of-the-art ellipse fitting methods. The proposed method produces ellipses with lesser bias. Furthermore, the mean-squared error is lesser by about 2 to 10 dB. We show the applications of ellipse fitting in iris images starting from partial edge contours, and to free-hand ellipses drawn on a touch-screen tablet.

Item Type:	Journal Article
Publication:	IEEE TRANSACTIONS ON IMAGE PROCESSING
Publisher:	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Additional Information:	Copy right for this article belongs to the IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 445 HOES LANE, PISCATAWAY, NJ 08855-4141 USA
Keywords:	Ellipse fitting; conic section; annihilating filter; finite rate of innovation (FRI); nonuniform sampling; random amplitude modulation
Department/Centre:	Division of Electrical Sciences > Electrical Engineering
Date Deposited:	02 Apr 2016 09:22
Last Modified:	02 Apr 2016 09:22
URI:	http://eprints.iisc.ac.in/id/eprint/53540

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