Hybrid Geometric Active Models for Shape Recovery in Medical Images

Abstract

In this paper, we propose extensions to a powerful geometric shape modeling scheme introduced in []. The extension allows the model to automatically cope with topological changes and for the first time, introduces the concept of a global shape into geometric/geodesic snake models. The ability to characterize global shape of an object using very few parameters facilitates shape learning and recognition. In this new modeling scheme, object shapes are represented using a parameterized function — called the generator — which accounts for the global shape of an object and the pedal curve/surface of this global shape with respect to a geometric snake to represent any local detail. Traditionally, pedal curves/surfaces are defined as the loci of the feet of perpendiculars to the tangents of the generator from a fixed point called the pedal point. We introduce physics-based control for shaping these geometric models by using distinct pedal points — lying on a snake — for each point on the generator. The model dubbed as a “snake pedal” allows for interactive manipulation via forces applied to the snake. Automatic topological changes of the model may be achieved by implementing the geometric active contour in a level-set framework.We demonstrate the applicability of this modeling scheme via examples of shape estimation from a variety of medical image data.