I could try between points embeded in high dimensions with the spectral embedding we use to sample meshes for instance

We had experiments using the toy datasets of some ML papers (between gaussians for example) in dimension up to 20 (and it behave well!) but we mainly lacked interesting data, if you have ideas or references to get some in that kind of dimensions that would be great 🙏

Of course! That would be awesome!

The code interface is very simple (at least in the bijective case).

We mainly tested BSP-OT on graphics applications in low dimension, I hope that POT users would still find it usefull !

Check the paper : baptiste-genest.github.io/papers/bsp-o...

Code : github.com/baptiste-gen...

I will present this work during the conference! (15-18 december)

We show that this approach can be applied to standard applications of OT, like image stippling, shape interpolation, color transfer, partial point cloud registration, intrinsic mesh sampling and Topological Data Analysis (a domain where bijectivity is required!).

We also extend it to partial matchings, and general sparse transport plans between non-uniform measures.

Then, in the bijective and injective cases, we exploit this extreme sparsity to efficiently merge two assignments using very simple discrete optimization.

Remarkably, this procedure is also a generalization of the (projection + 1D assignment) step used at the core of Sliced OT! The difference being that it preserves much more information than a single projection, which yields couplings of much higher quality, with the same complexity.

BSP Matchings generalize the Quicksort algorithm. We simultaneously build two BSP trees on each point cloud and match their leaves.

This is a joint work with @nbonneel.bsky.social, Vincent Nivoliers and @dcoeurjo.bsky.social @cnrsinformatics.bsky.social

Our pipeline is simple: we use BSP (Binary Space Partitioning) matchings to efficiently generate random bijections before merging them into a single one of low transport cost.

Thank you so much for your feedback 🤗🤗🤗 I was very lucky, the ideas were very simple and worked very quickly. From the first ideas to the submission it took around 4 months and a half🙏

Thank you so much for your comment🙏🙏 it means the world to us🤗

Thank you! It's really nice of you🙏

It was made during an intership at @adobe.com
. This is a joint work with Pierre Gueth, Jérémy Levallois and Stephanie Wang, who supervised me during my internship. Many thanks to them!

Here is the submitted version of the article: baptiste-genest.github.io/papers/impli...

You can then use these coordinates to enhance SDF rendering with textures, normal maps, and even displacement maps!

You also can use it with shell maps to define a 3D coordinate system from the 2D ones, and more!

We use concepts from differential geometry to first define local uv-fields that are evaluatable point-wise. We then show how we can merge multiple fields into larger ones to get high quality uv-fields on large smooth patches of the shape.

We introduce the first method to compute uv coordinates on implicit surfaces, without discretization, in real-time in a sphere-tracing pipeline!

It allows you to get full control over the appearance of the shape, with textures, without losing the benefits of implicit representations!