paigautam / CVPR21_FastSinkhornFilters

Sample code for Fast Sinkhorn Filters - from CVPR 2021

Fast-Sinkhorn-Filters

This is a sample demo-code for our CVPR 2021 paper: Fast Sinkhorn Filters - Using Matrix Scaling for Non-Rigid Shape Correspondence with Functional Maps, by Gautam Pai, Jing Ren, Simone Melzi, Peter Wonka and Maks Ovsjanikov.

Paper, Supplementary, Video, Poster

Main Functions

[S,T12,T21] = fast_sinkhorn_filter(KTar,KSrc,options)

%{
***Input***
(1.) KSrc -- a M X K Matrix of Features/Aligned Basis/Embedding in Source Shape with M Points and
K Features
(2.) KTar -- a N X K Matrix of Features/Aligned Basis/Embedding in Target Shape with N Points and
K Features
(3.) (optional) options struct - see below

***Output*** 
(1.) S -- The M X N doubly stochastic matrix after matrix scaling 
(2.) T12 -- pointwise forward map, i.e. Source(Src) to Target(Tar) 
(3.) T21 -- pointwise backward map, i.e. Target(Tar) to Source(Src)

***Parameters***
An options struct with the following
(1.) p -- (power of the distance for assignment matrix) - default set to 1
(2.) knn -- number of nearest neighbors for sparsifying kernel - default set to 50
(3.) distmax -- factor for choosing lambda, default value 500 as per https://marcocuturi.net/SI.html
(4.) maxiter -- number of matrix scaling iterations desired (~ 10-50)
(5.) kernel_type -- 'full' or 'sparse' (default) depending on nature of kernel desired. Choose 'sparse' for faster mode. 

***Additional Comments*** 
You can replace the knnsearch in this script with a possibly faster
k-nearest neighbor implementation for improved performance
%}

Comments

The script demo.m runs our Fast Sinkhorn Filter with 2 experiments:

1. A pointwise conversion using a ground-truth Adjoint Map operator (which we prove in the paper to be optimal for transferring delta functions in order to establish a pointwise correspondence from a functional representation) using the nearest neighbor and the proposed fast sinkhorn filter. We evaluate various geometric and functional metrics like: gt-error, bijectivity, spectral chamfer distance etc. as a function of the spectral basis size.

2. Comparing the original and Sinkhornized versions of ICP and Zoomout refinement algorithms. We show the ground truth error curves and also visualize the error map on ths source surface:

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