Frederic F. Leymarie
Brown University, Engineering
3D Shape Representation via Shock Flows
We address the problem of representing 3D shapes when partial and unorganized data is obtained as an input, such as clouds of point samples
on the surface of a face, statue, solid, etc., of regular or arbitrary
complexity (free-form), as is commonly produced by photogrammetry, laser scanners, computerized tomography, and so on. Our starting point
is the medial axis (MA) representation which has been explored mainly
for 2D problems since the 1960's in pattern recognition and image analysis.
The MA makes explicit certain symmetries of an object, corresponding
to the shocks of waves initiated at the input samples, but is itself difficult
to directly use for recognition tasks and applications. Based on previous work
on the 2D problem, we propose a new representation in 3D which is derived
from the MA, producing a graph we call the shock scaffold. The nodes of this graph are defined to be certain singularities of the shock flow along the MA. This graph can represent exactly the MA --- and the original inputs --- or approximate it, leading to a hierarchical description of shapes. We will also summarize early applications of this directed graph representation to surface meshing, medial surfaces approximation, and geometric surface regularization, or in other words the hierarchical removal of protruding structures at varying scales.