| Abstract: |
| The Euler Characteristic Transform of Turner et al. Is a TDA-inspired tool that can be used for statistical shape analysis. This transform enjoys many desirable mathematical properties that make it very appealing for applications. However, the transform is typically discretized, and this process complicates the maximal exploitation of the beautiful theory behind it.
In this talk, we present how this transform can be represented in a truly lossless way in the spirit of digitalization of the Kendall Shape Space. We demonstrate that this digital representation is practically feasible to compute and can be made auto-differentiable to benefit from synergies with deep learning.
We will also outline some directions for theoretical research that would allow us to tackle more ambitious applied problems with this new representation.
This is joint work with Xiaohan Wang. |
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