Generative shape deformation with optimal transport using learned transformations

Shape deformation is a fundamental problem in computer graphics and computer vision, with numerous applications in fields such as animation, medical imaging, robotics to cite a few. We propose a method for shape deformation based on applying learned transformations with optimal transport (OT). Our method combines the power of the latter with the flexibility of learned transformations to provide an efficient and effective solution for 2D and 3D shape deformation. We formulate the problem as an OT task, where the goal is to learn the optimal way to move the mass distribution of a shape to another. We then use the learned geometric transformations, to achieve shape deformation. Our method can be applied to a wide range of shapes and applications. Interestingly, we show that it requires a small amount of data to learn the transformations. We demonstrate the performance of our method on our own crafted dataset of 2D and 3D shapes and evaluate its effectiveness using various metrics. The promising results obtained suggest that our method can be applied in a wide range of real-world applications.