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Dual Approaches for Elliptic Hough Transform: Eccentricity/Orientation vs Center based
;
2019In Discrete Geometry for Computer Imagery
Peer reviewed

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Keywords :
ellipse detection; ellipse matching; Hough Transform; pencil of conics; tangential equation
Abstract :
[en] Ellipse matching is the process of extracting (detecting and ﬁtting) elliptic shapes from digital images. This process typically requires the determination of 5 parameters, which can be obtained by using an Elliptic Hough Transform (EHT) algorithm. In this paper, we focus on Elliptic Hough Transform (EHT) algorithms based on two edge points and their associated image gradients. For this set-up, it is common to ﬁrst reduce the dimension of the 5D EHT by means of some geometrical observations, and then apply a simpler HT. We present an alternative approach, with its corresponding algebraic framework, based on the pencil of bi-tangent conics, expressed in two dual forms: the point or the tangential forms. We show that, for both forms, the locus of the ellipse parameters is a line in a 5D space. With our framework, we can split the EHT into two steps. The ﬁrst step accumulates 2D lines, which are computed from planar projections of the parameter locus (5D line). The second part back-projects the peak of the 2D accumulator into the 5D space, to obtain the three remaining parameters that we then accumulate in a 3D histogram, possibly represented as three separated 1D histograms. For the point equation, the ﬁrst step extracts parameters related to the ellipse orientation and eccentricity, while the remaining parameters are related to the center and a sizing parameter of the ellipse. For the tangential equation, the ﬁrst step is the known center extraction algorithm, while the remaining parameters are related to the ellipse half-axes and orientation.
Research center :
Telim
Montefiore Institute - Montefiore Institute of Electrical Engineering and Computer Science - ULiège
Disciplines :
Computer science
Author, co-author :
Latour, Philippe ;  Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Dép. d'électric., électron. et informat. (Inst.Montefiore)
Van Droogenbroeck, Marc  ;  Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Télécommunications
Language :
English
Title :
Dual Approaches for Elliptic Hough Transform: Eccentricity/Orientation vs Center based
Publication date :
March 2019
Event name :
21st IAPR International Conference on Discrete Geometry for Computer Imagery
Event organizer :
Laboratoire d'Informatique Gaspard-Monge (LIGM) at ESIEE Paris, France
Event place :
Paris, France
Event date :
from 26/03/2019 to 28/03/2019
Audience :
International
Main work title :
Discrete Geometry for Computer Imagery
Publisher :
Springer
Collection name :
Lecture Notes in Computer Science 11414
Pages :
367-379
Peer reviewed :
Peer reviewed

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