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Published in:
2016 | OriginalPaper | Chapter
9. Ellipse Analysis and 3D Computation of Circles
Authors : Kenichi Kanatani, Yasuyuki Sugaya, Yasushi Kanazawa
Published in: Guide to 3D Vision Computation
Publisher: Springer International Publishing
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Abstract
Circular objects in the scene are projected onto the image plane as ellipses. By fitting ellipse equations to them as shown in Chap. 2, we can compute the 3D properties of the circular objects. This chapter describes typical procedures for such computations. First, we show how we can compute various attributes of ellipses such as intersections, centers, tangents, and perpendiculars. Then we describe the procedure for computing from an ellipse image of a circle the position and orientation of the circle in the scene and the 3D position of its center. These computations allow us to generate an image of the circle seen from the front. The basic principle underlying these computations is the analysis of homographies induced by hypothetical camera rotation around the viewpoint, where projective geometry plays a central role.