Closed-Form GPU-Accelerated Tensor Voting with Refinement

Helya Goharbavang, Omar Baig, Guoning Chen, David Mayerich

teaser
Structure tensor field labeling fiber orientation in an EM image of zebrafish tectum. Color indicates the eigenvector associated with \( |\lambda_0| \leq |\lambda_1| \). Saturation indicates eccentricity. (a) The raw EM image is used to produce a structure tensor field (b) using second-order finite differences. Methods to refine the field (all using \( \sigma=4 \)): (c) Gaussian blur, (d) original tensor voting, (e) tensor voting with refinement (\( p=6 \)), and (f) full implementation including the plate voting field. (h) The proposed method is shown overlayed on the original image, with insets showing a fiber bundle with each method shown as an overlay.

Abstract

Analyzing and visualizing the microvascular networks is an essential task for researchers to assess the health of the vasculature system in human organs. Over the past few years, advanced 3-D imaging techniques have replaced conventional 2-D methods to better view their intricate geometry and avoid differentiating vasculature networks from their surrounding tissue. Centerline extraction is an essential tool that enables researchers to understand the topology and connectivity of microvascular networks, as well as quantify parameters such as vessel length, diameter, and tortuosity. In this paper, we propose a comprehensive yet compact survey on skeletonization algorithms, which are essential for microvascular analysis and often require preprocessing steps including image binarization and segmentation processes.

Visualization

This is a demo of the 3D visualization toolkit for tensor fields. While the paper focuses on 2D tensor voting, this implementation extends to 3D and is available in the same repository. The toolkit enables interactive exploration of tensor fields, helping to analyze their structure and behavior.

teaser

Resources

Paper: Our paper is under review for publication.

Poster: Our poster is available here.

Code: Our code is available on Github.

Data: Our data (Serial EM) is available upon request.