A General Framework for Geometry-Driven Evolution Equations

Authors:
Wiro J. Niessen;Bart M. Ter Haar Romeny;Luc M. J. Florack;Max A. Viergever
Affiliations:
Image Sciences Institute, University Hospital Utrecht, 3584 CX Utrecht, The Netherlands;Image Sciences Institute, University Hospital Utrecht, 3584 CX Utrecht, The Netherlands;Image Sciences Institute, University Hospital Utrecht, 3584 CX Utrecht, The Netherlands;Image Sciences Institute, University Hospital Utrecht, 3584 CX Utrecht, The Netherlands
Venue:
International Journal of Computer Vision
Year:
1997

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Abstract

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