Abstract: Two methods of edge detection and segmentation based on partial differential equation (PDE) are introduced, they are Snake Model and Level Set Methods. We worked out Euler equation corresponding to Snake using variational method and proved nonstability of the three discrete schemes which are forward differential, backward differential and center differential. We detectd the edge of microscopic cell image by constructing algorithms with upwind differential scheme. The results suggest it is stable and convergent.

Key words: edge detection and segmentation, level set, upwind differential scheme, microscopic cell image