Projective Analysis for 3D Shape Segmentation

We introduce projective analysis for semantic segmentation and labeling of 3D shapes. The analysis treats an input 3D shape as a collection of 2D projections, labels each projection by transferring knowledge from existing labeled images, and back-projects and fuses the labelings on the 3D shape. The image-space analysis involves matching projected binary images of 3D objects based on a novel bi-class Hausdorff distance. The distance is topology-aware by accounting for internal holes in the 2D figures and it is applied to piecewise-linearly warped object projections to compensate for part scaling and view discrepancies. Projective analysis simplifies the processing task by working in a lower-dimensional space, circumvents the requirement of having complete and well-modeled 3D shapes, and addresses the data challenge for 3D shape analysis by leveraging the massive available image data. A large and dense labeled set ensures that the labeling of a given projected image can be inferred from closely matched labeled images. We demonstrate semantic labeling of imperfect (e. g., incomplete or self-intersecting) 3D models which would be otherwise difficult to analyze without taking the projective analysis approach.