Learning Shapes by Convex Composition
This work addresses shape learning in computer vision, but it appears incremental as it builds on recent convexification approaches.
The paper tackles the problem of learning principal geometric elements in images or 3D objects by convex composition, deriving conditions for identifying target compositions and presenting two computational methods for optimization.
We present a mathematical and algorithmic scheme for learning the principal geometric elements in an image or 3D object. We build on recent work that convexifies the basic problem of finding a combination of a small number shapes that overlap and occlude one another in such a way that they "match" a given scene as closely as possible. This paper derives general sufficient conditions under which this convex shape composition identifies a target composition. From a computational standpoint, we present two different methods for solving the associated optimization programs. The first method simply recasts the problem as a linear program, while the second uses the alternating direction method of multipliers with a series of easily computed proximal operators.