Learning Shapes by Convex Composition

Alireza Aghasi; Justin Romberg

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arXiv · 1602.07613

Learning Shapes by Convex Composition

Alireza Aghasi·Justin Romberg

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Abstract

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.

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Alireza Aghasi, Justin Romberg. 2016-02-23. Learning Shapes by Convex Composition. https://arxiv.org/abs/1602.07613

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