Affine invariant detection: edges, active contours, and segments

In this paper we undertake a systematic investigation of affine invariant object detection. Edge detection is first presented from the point of view of the affine invariant scale-space obtained by curvature based motion of the image level-sets. In this case, affine invariant edges are obtained as a weighted difference of images at different scales. We then introduce the affine gradient as the simplest possible affine invariant differential function which has the same qualitative behavior as the Euclidean gradient magnitude. These edge detectors are the basis both to extend the affine invariant scale-space to a complete affine flow for image denoising and simplification, and to define affine invariant active contours for object detection and edge integration. The active contours are obtained as a gradient flow in a conformally Euclidean space defined by the image on which the object is to be detected. That is, we show that objects can be segmented in an affine invariant manner by computing a path of minimal weighted affine distance, the weight being given by functions of the affine edge detectors. The geodesic path is computed via an algorithm which allows to simultaneously detect any number of objects independently of the initial curve topology.