An emerging tool for processing visual or geometric data (among many other things) is optimal transport / earth mover’s distance / Wasserstein distance. For this reading, try to give an (extremely!) high-level description of the problem of optimal transport, and identify at least one interesting/cool/useful place where part of this theory has been applied. In addition to the links above, some good starting points for applications in image and geometry processing include
- de Goes et al, “An Optimal Transport Approach to Robust Reconstruction and Simplification of 2D Shapes”
- Wang et al, “An Optimal Transportation Approach for Nuclear Structure-Based Pathology”
- Lipman and Daubechies, “Conformal Wasserstein Distances: Comparing Surfaces in Polynomial Time”
- Julien et al, “Wasserstein Barycenter and its Application to Texture
- Solomon et al, “Convolutional Wasserstein Distances: Efficient Optimal Transportation on Geometric Domains”
- Ni et al, “Local Histogram Based Segmentation Using the Wasserstein
- Mémoli, “A Spectral Notion of Gromov–Wasserstein Distance and Related Methods”
As usual, you can probably Google for “optimal transport” plus any application and find something interesting. The goal here is not to get an in-depth understanding of the subject, but rather just get a feel for the kind of problems people are solving with optimal transport.
Submission: As usual, please send an email to firstname.lastname@example.org and email@example.com no later than 10:00 AM on Thursday, February 18th including the string DDGSpring2016 in your subject line. Your email for readings should always include:
- a short (2-3 sentence) summary of what you read, and
- at least one question about something you found confusing / interesting / incomplete / not addressed.