Scale-space on image profiles about an object boundary

Traditionally, image blurring by diffusion is done in Euclidean space, in an image-based coordinate system. This will blur edges at object boundaries, making segmentation difficult. Geometry-driven diffusion [1] uses a geometric model to steer the blurring, so as to blur along the boundary (to overcome noise) but edge-detect across the object boundary. In this paper, we present a scale-space on image profiles taken about the object boundary, in an object-intrinsic coordinate system. The profiles are sampled from the image in the fashion of Active Shape Models [2], and a scale-space is constructed on the profiles, where diffusion is run only in directions tangent to the boundary. Features from the scale-space are then used to build a statistical model of the image structure about the boundary, trained on a population of images with corresponding geometric models. This statistical image match model can be used in an image segmentation framework. Results are shown in 2D on synthetic and real-world objects; the methods can also be extended to 3D.