Detecting Ellipses in Elongated Shapes Using the Thickness Profile
This paper presents a method that detects elliptical parts of a given elongated shape. For this purpose, first, the shape is represented by its skeleton. In case of branches, the skeleton is partitioned into a set of lines/curves. Second, the ellipse para
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Abstract. This paper presents a method that detects elliptical parts of a given elongated shape. For this purpose, first, the shape is represented by its skeleton. In case of branches, the skeleton is partitioned into a set of lines/curves. Second, the ellipse parameters are estimated using the thickness profile along each line/curve, and the properties of its first and second derivatives. The proposed method requires no prior information about the model, number of ellipses and their parameter values. The detected ellipses are then used in our second proposed approach for ellipse-based shape description. It can be applied for analysing motion and deformation of biological objects like roots, worms, and diatoms.
Keywords: Shape analysis
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· Shape description · Ellipse detection
Introduction
The advantages of modelling the structure of the shape with ellipses cover various aspects. Human perceptual system interprets the significant parts of the shape or the rigid parts of articulated objects with the ellipses [10]. Also the ellipsoids and super quadrics provide a strong cue about the orientation of anisotropic phenomena [11]. Indeed, the major axis of the ellipse, when interpreted as an orientation, becomes useful for judging the motion direction or for constraining the motion of articulated parts of the object [29]. The √ eccentricity of the ellipse, ε, characterizes its elongation, and is estimated as ( a2 − b2 )/a, where a and b are the lengths of the semi-major and semi-minor axes of the ellipse respectively. It can be applied for analysis of deformations like shrinking and stretching. Tuning the ellipse elongation along its orientation can be used to enhance the traditional skeletonization algorithms for the problem of representing the intersection of two straight lines (or, alternatively, a cross), compare cases (a) and (d) in Fig. 1. Another advantage of using ellipses refers back to the paper of Rosenfeld [23]. He defines the ribbon-like shapes that can be represented given a spine and a A. Gabdulkhakova—Supported by the Austrian Agency for International Cooperation in Education and Research (OeAD) within the OeAD Sonderstipendien program, financed by the Vienna PhD School of Informatics. c Springer International Publishing AG 2016 A. Robles-Kelly et al. (Eds.): S+SSPR 2016, LNCS 10029, pp. 412–423, 2016. DOI: 10.1007/978-3-319-49055-7 37
Detecting Ellipses in Elongated Shapes Using the Thickness Profile
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generator (disc or line segment). There are also algorithms that use ellipse as the generator [27]. To the best of our knowledge the ellipse was not assumed as a unified generator that can degenerate into a disc (ε = 0) and/or into a line segment (ε = 1). On one side, this provides a smooth transition between the rectangular parts of the object that have different properties, compare Fig. 1, cases (b) and (e). On the other side, symmetric shapes with a high positive curvature can be represented by a single spine instead of a branched skeleton, compare Fig. 1, cases (c) and (f).
Fig. 1. Advantages of us
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