Weighted Spectral Distance(WESD)

[msrepo]

Description

WESD between two binary segmentations is pose-invariant. This could be useful as a metric for retrieval-based methods. Current Implementation of Image-Space metrics such as DSC, ASD, HD are pose-sensitive.

Literature

Anatomy-Aware Inference of the 3D Standing Spine Posture from 2D Radiographs
WESD - Weighted Spectral Distance for Measuring Shape Dissimilarity
Discriminative Segmentation-based Evaluation through Shape Dissimilarity
Martin Reuter et al.
Laplace-Beltrami spectra as "Shape-DNA" of surfaces and solids
Computer-Aided Design 38(4):342-366, 2006
Discrete Laplace-Beltrami Operators for Shape Analysis and Segmentation

Reference

laplace-beltrami operation implementation
[Numerical Methods for Partial Differential Equations, Ames,Chapter 2]
Arnoldi's Method for eigenvalues of sparse matrix

Tasks

Include specific tasks in the order they need to be done in. Include links to specific lines of code where the task should happen at.

• Compute the Laplace-Beltrami spectrum using a linear finite element method
• compute eigenvalues via Arnoldi's method
• choose p,N for nWSD (N=200,p=2.0 for 3D was found to be good choice) and normalize WSD