On computing aspect graphs of smooth shapes from volumetric data

The authors address the problem of computing the aspect graph of an object from volumetric image data, with applications in medical image analysis and interpretation. Anatomical surfaces are assumed to be smooth and are identified as the zero set of a three-dimensional density function (e.g., a CT, MR, or ultrasound image). The orthographic-projection aspect graph is constructed by partitioning the view sphere at infinity into maximal regions bounded by visual event curves. These events are the intersections of the view sphere with surfaces ruled by singular tangent lines that graze the object's surface along a set of critical curves. For each visual event the proposed algorithm constructs a new density function from the original one and its derivatives, and computes the corresponding critical curve as the intersection of the object's surface with the zero set of the new density function. Once the critical curves have been traced, the regions of the sphere delineated by the corresponding visual events are constructed through cell decomposition, and a representative aspect is constructed for each region by computing the occluding contour for a sample viewing direction. A preliminary implementation of the proposed approach has been constructed and experiments with synthetic data and real medical data are presented. Extensions to the sectional imaging case are also discussed.