An Elliptic Operator for Constructing Conformal Metrics in Geometric Deformable Models

Abstract

The geometric deformable model (GDM) provides a useful framework for segmentation by integrating the energy minimization concept of classical snakes with the topologically flexible gradient flow. The key aspect of this technique is the image derived conformal metric for the configuration space. While the theoretical and numerical aspects of the geometric deformable model have been discussed in the literature, the formation of the conformal metric itself has not received much attention. Previous definitions of the conformal metric do not allow the GDM to produce reliable segmentation results in low-contrast or highblur regions. This paper examines the desired properties of the conformal metric with regard to the image information and proposes an elliptic partial differential equation to construct the metric. Our method produces similar results to other metric definitions in high-contrast regions, but produces better results in low-contrast, high-blur situations.

Acknowledgments

This work was funded partially by NIH grant No. 1 R01 CA 78485-01A1.