Closed-Form GPU-Accelerated Tensor Voting with Refinement

Tensor fields can encode local image features for downstream algorithms. Common examples include the structure tensor and Hessian, which encode the local gradient and curvature. However, the results are sensitive to noise because they rely on finite difference methods. While this can be mitigated through low-pass filtering, this comes at the cost of resolution. Tensor voting (TV) provides a method of distributing tensor information across neighboring pixels based on Gestalt principles. However, these basic assumptions do not translate well to biomedical images, particularly surface and fiber extraction. In this paper, we add several features to the TV framework enabling more robust control of the refined field. Specifically, we reformulate TV to enable (1) tuning the vote field's scope to reinforce highly directed structures, (2) normalized energy distribution so that TV can be applied iteratively or with other algorithms, (3) a closed-form solution for all terms and the corresponding plate tensor, and (4) a GPU-based algorithm for fast processing of large images.