Modeling and Fitting 3D Shapes via Shape Grammar

Abstract

In this thesis, we introduce a 3D Shape Grammar for generating man-made objects and an optimization algorithm to fit the structure and parameters of the grammar to a given point cloud. While simple grammars, e.g. for bounding box arrangements, have been used to define prior knowledge for reconstruction before, we take this approach to the next level, by attempting to fit complex grammars with many rules, many parameters, and curved geometric primitives. To tackle this challenge, we propose two major components. First, we propose a new shape grammar framework suitable to describe man-made objects. We also develop a complex rule set for one particular shape class, chairs, to highlight the expressiveness of the shape grammar framework. Our rule set can represent up to 55.7k unique structures. An essential design requirement of the grammar was to make it differentiable for a shape-fitting application. Second, we propose a probabilistic framework to fit the shape of grammar to a point cloud. We combine probabilistic sampling of the grammar structure with differentiable optimization of grammar parameters to that effect.