Metric representations for shape analysis and synthesis

Hu, Shanfeng (2020) Metric representations for shape analysis and synthesis. Doctoral thesis, Northumbria University.

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Abstract

2D and 3D geometric shapes are ubiquitous in computer graphics, computer animation, and computer-aided design and manufacturing. Two of the fundamental research challenges that underline these applications are the analysis and synthesis of shapes, with the former aiming to extract semantically meaningful knowledge of shapes and the latter focusing on generating plausible-looking shapes based on user inputs. Traditionally, shape analysis and synthesis are based on representations such as meshes, parameterisations, and Laplacians, which lead to mostly hand-crafted computation rules that are either suboptimal or treat related tasks separately. In this work, we propose to represent a 2D/3D shape as a square symmetric matrix that correlates every pair of geometric points on the shape, which allows us to formulate shape analysis and synthesis problems as principled optimisation problems that can be globally optimised. To demonstrate the usefulness of our new metric representation for shape analysis, we first address 3D mesh saliency detection by representing a shape as a pairwise feature distance matrix, whose principal eigenvector is experimentally shown to outperform the traditional saliency detection rules for capturing ground truth saliency annotations. Following this work, we then unify saliency detection and nonrigid shape matching via a jointly learned metric representation, which is shown to improve the accuracy of both tasks on the existing saliency detection and shape matching benchmarks. To also demonstrate the usefulness of our metric representation for shape synthesis, we address 2D facial shape beautification in images by representing a facial shape as the orthogonal projection matrix onto 2D facial landmarks, which is shown to improve the attractiveness of both frontal-neutral and non-frontal-non-neutral faces in the user studies. Finally, we show that adversarially learning the distributions of human shapes and poses in a hidden space produces higher quality human samples than in the geometry space. Together, these results show that our metric representation benefits both the analysis and synthesis of shapes, with the potential of unifying more diverse tasks such as part segmentation and labelling in the future work.

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