Technical Report PHD-2019-07

Title: Non Isometric Shape Correspondence
Authors: Danielle Ezuz
Supervisors: Mirela Ben-Chen
PDFCurrently accessibly only within the Technion network
Abstract: Shape correspondence is a fundamental task in shape analysis, and has a variety of applications in computer graphics and computer vision. Generally, given two shapes, the goal is to compute for each point on the source shape a corresponding point on the target shape. Example applications include morphing (gradually deforming one shape to another), deformation or texture transfer, and statistical shape analysis.

Shape correspondence can be classified into different categories, based on the properties of the input shapes, and the desired properties of the result. A common category is isometric shape correspondence, that usually characterizes matching between the same object in different poses. In other cases, where correspondence is computed between different objects, the task is more challenging and not well defined mathematically.

This research studies non isometric shape correspondence. The main challenge is to explicitly define the mathematical properties of the desired results, and to design algorithms that generate results with the desired properties. As the desired result mostly depend on the downstream application, it is instrumental to consider the application when designing the method.

We propose semi-automatic methods for computation of shape correspondence between highly non isometric shapes, as well as a method that optimizes an existing correspondence method for shape classification and retrieval using deep learning. Our shape correspondence methods are designed to generate locally smooth results, that are advantageous for applications in computer graphics such as texture transfer and shape interpolation. This document contains a detailed description of the problem and the motivation, the proposed algorithms, and demonstrates the results and a variety of applications.

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