DEFORMABLE MODELS FOR IMAGE SEGMENTATION


Jussi Tohka
Signal Processing Laboratory
Tampere University of Technology

MOTIVATION AND BACKGROUND

  • A problem is well-posed if

  • DEFORMABLE MODELS

  • Note that the exact shape of O is not known.  That is, fitting rigid contour models (registration) is not possible. Also location and orientation of O in an image I is unknown.
  • As said object O does not usually have clear boundary, so straightforward approaches using edge detectors or other local operators would lead to trouble.
  • In the framework of deformable models and regularization P1 is reformulated as
  • P2: Find the contour CO that minimizes the energy function

    where Eimage is energy term that depends on underlying image, Einternal is the regularization term that depends only on the shape of the C, and  is the regularization parameter that weights the two energy types.
     
  • Above formula captures the essence of deformable models that is quite the same than the idea of Bayesian Maximum A Posteriori (MAP) estimation.  Indeed, deformable models can, with suitable assumptions, be put into a probabilistic framework and then it turns out that minimizing the energy of the contour is equivalent with finding the contour that maximizes certain a posteriori probability.
  • To actually do some computations we have to fix a representation for the arbitrary contour  C. There are basically three types of representations available:
  • Discrete: C is just an ordered set of points, which are though to form a polygonal line.
  • Parametrized representation leads to `snakes' in their traditional formulation. They however rely on user interaction, and as such are not very suitable for fully automated target extraction.

  • DISCRETE SNAKES

    where the simple prediction
    is used.
    where  denotes some edge operator (e.g. Sobel).

    ENERGY MINIMIZATION


    CONCLUDING REMARKS


    SOME LITERATURE



    Last modified 30.10.2000 by Jussi Tohka