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  • discrete iterative processes  (1)
  • normal optical flow  (1)
  • time to collision  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Migration Processes II: The Discrete Case (1998)
    Springer
    Journal of mathematical imaging and vision 8 (1998), S. 27-40 
    Details
    ISSN: 1573-7683
    Keywords: discrete iterative processes ; discrete deformation of sets ; contour evolution ; discrete active models
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Following the study of migration processes in the continuous domain in Part I of this paper, we reformulate the concept of migration in the discrete domain (Zm) and define Discrete Migration Processes (DMP). We demonstrate that this model is a natural discrete representation of the continuous model and maintains the model's features in a qualitative sense. We show that under discrete migration any discrete set shrinks to a limit in finitely many iterations. The discrete representation provides an advantageous basis for digitally implementing the MP model. Using this implementation we illustrate the discrete migration of various types of sets under various types of constraints.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008258132513
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    The Applicability of Green's Theorem to Computation of Rate of Approach (1999)
    Springer
    International journal of computer vision 31 (1999), S. 83-98 
    Details
    ISSN: 1573-1405
    Keywords: time to collision ; rate of approach ; Green's theorem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract The rate of approach (ROA) of a moving observer toward a scene point, as estimated at a given instant, is proportional to the component of the observer's instantaneous velocity in the direction of the point. In this paper we analyze the applicability of Green's theorem to ROA estimation. We derive a formula which relates three quantities: the average value of the ROA for a surface patch in the scene; a surface integral that depends on the surface slant of the patch; and the contour integral of the normal motion field around the image of the boundary of the patch. We analyze how much larger the ROA on the surface patch can be than the value of the contour integral, for given assumptions about the variability of the distance to points on the surface patch. We illustrate our analysis quantitatively using synthetic data, and we also validate it qualitatively on real image sequences.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008098810511
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Egomotion analysis based on the Frenet-Serret motion model (1995)
    Springer
    International journal of computer vision 15 (1995), S. 105-122 
    Details
    ISSN: 1573-1405
    Keywords: constraint intersection ; curvature and torsion ; dominant motion ; egomotion analysis ; Frenet-Serret motion model ; normal optical flow ; screw-motion equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract In this paper we propose a new model,Frenet-Serret motion, for the motion of an observer in a stationary environment. This model relates the motion parameters of the observer to the curvature and torsion of the path along which the observer moves. Screw-motion equations for Frenet-Serret motion are derived and employed for geometrical analysis of the motion. Normal flow is used to derive constraints on the rotational and translational velocity of the observer and to compute egomotion by intersecting these constraints in the manner proposed in (Durić and Aloimonos 1991) The accuracy of egomotion estimation is analyzed for different combinations of observer motion and feature distance. We explain the advantages of controlling feature distance to analyze egomotion and derive the constraints on depth which make either rotation or translation dominant in the perceived normal flow field. The results of experiments on real image sequences are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01450851
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    Paper (German National Licenses)
    Fulltext
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