A differential geometry approach for biomedical image processing.

We show in this paper how simple considerations about bio-arrays images lead to a peak segmentation allowing the genes activity analysis. Bio-arrays images have a particular structure and the aim of the paper is to present a mathematical method allowing their automatic processing. The differential geometry approach used here can be also employed for other types of images presenting grey level peaks corresponding to a functional activity or to a chemical concentration. The mathematical method is based on elementary techniques of differential geometry and dynamical systems theory and provides a simple efficient algorithm when the peaks to segment are isolated.