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A General Framework for Geometry-Driven Evolution Equations

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Abstract

This paper presents a general framework to generate multi-scale representations of image data. The process is considered as an initial value problem with an acquired image as initial condition and a geometrical invariant as “driving force” of an evolutionary process. The geometrical invariants are extracted using the family of Gaussian derivative operators. These operators naturally deal with scale as a free parameter and solve the ill-posedness problem of differentiation. Stability requirements for numerical approximation of evolution schemes using Gaussian derivative operators are derived and establish an intuitive connection between the allowed time-step and scale. This approach has been used to generalize and implement a variety of nonlinear diffusion schemes. Results on test images and medical images are shown.

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Authors
  1. Wiro J. Niessen
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  2. Bart M. Ter Haar Romeny
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  3. Luc M.J. Florack
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  4. Max A. Viergever
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Niessen, W.J., Romeny, B.M.T.H., Florack, L.M. et al. A General Framework for Geometry-Driven Evolution Equations. International Journal of Computer Vision 21, 187–205 (1997). https://doi.org/10.1023/A:1007995731951

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