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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Geometriae dedicata 71 (1998), S. 237-261 
    ISSN: 1572-9168
    Keywords: symmetry set ; affine invariance ; skew symmetry ; singularities ; dual map ; affine invariant distance ; conics.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Affine invariant symmetry sets of planar curves are introduced and studied in this paper. Two different approaches are investigated. The first one is based on affine invariant distances, and defines the symmetry set as the closure of the locus of points on (at least) two affine normals and affine-equidistant from the corresponding points on the curve. The second approach is based on affine bitangent conics. In this case the symmetry set is defined as the closure of the locus of centers of conics with (at least) 3-point contact with the curve at two or more distinct points on the curve. This is equivalent to conic and curve having, at those points, the same affine tangent, or the same Euclidean tangent and curvature. Although the two analogous definitions for the classical Euclidean symmetry set are equivalent, this is not the case for the affine group. We present a number of properties of both affine symmetry sets, showing their similarities with and differences from the Euclidean case. We conclude the paper with a discussion of possible extensions to higher dimensions and other transformation groups, as well as to invariant Voronoi diagrams.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    International journal of computer vision 23 (1997), S. 115-129 
    ISSN: 1573-1405
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract It is known that the deformation of the apparent contours of a surface under perspective projection and viewer motion enable the recovery of the geometry of the surface, for example by utilising the epipolar parametrization. These methods break down with apparent contours that are singular i.e., with cusps . In this paper we study this situation and show how, nevertheless, the surface geometry (including the Gauss curvature and mean curvature of the surface) can be recovered by following the cusps. Indeed the formulae are much simpler in this case and require lower spatio-temporal derivatives than in the general case of nonsingular apparent contours. We also show that following cusps does not by itself provide us with information on viewer motion.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    International journal of computer vision 33 (1999), S. 51-72 
    ISSN: 1573-1405
    Keywords: curved surface ; epipolar geometry ; frontier point ; uncalibrated camera ; apparent contour ; silhouette ; motion extraction
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract In this paper we will discuss structure and motion problems for curved surfaces. These will be studied using the silhouettes or apparent contours in the images. The problem of determining camera motion from the apparent contours of curved three-dimensional surfaces, is studied. It will be shown how special points, called epipolar tangency points or frontier points, can be used to solve this problem. A generalised epipolar constraint is introduced, which applies to points, curves, as well as to apparent contours of surfaces. The theory is developed for both continuous and discrete motion, known and unknown orientation, calibrated and uncalibrated, perspective, weak perspective and orthographic cameras. Results of an iterative scheme to recover the epipolar line structure from real image sequences using only the outlines of curved surfaces, is presented. A statistical evaluation is performed to estimate the stability of the solution. It is also shown how the motion of the camera from a sequence of images can be obtained from the relative motion between image pairs.
    Type of Medium: Electronic Resource
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  • 4
    Book
    Book
    Cambridge u.a. :Cambridge University Press,
    Title: Visual motion of curves and surfaces
    Author: Cipolla, Roberto
    Contributer: Giblin, Peter
    Publisher: Cambridge u.a. :Cambridge University Press,
    Year of publication: 2000
    Pages: viii, 184 S.
    Type of Medium: Book
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