Tensor voting is a computational framework that addresses the problem of perceptual organisation. It was designed to convey human perception principles into a unified framework that can be adapted to extract visually salient elements from possibly noisy or corrupted images. The original formulation featured some concerns that made it difficult or impractical to be applied directly. Therefore, several partial or total theoretical reformulations or augmentations have been proposed. These almost parallel publication were presented in different directions, with different priorities and even in a different notation. Thus, the authors observed the need for a coherent description and comparison of the different proposals. This work, after describing the original approach of tensor voting, reviews and explains a number of high impact theoretical modifications in a self‐contained manner and including possible future directions of work. The authors have selected and organised a number of formulations and unified the way the problem is addressed across the different proposals. The aim of this study is to contribute with a modern comprehensive source of information on the theoretical aspects of tensor voting.

We comment on a paper that describes a closed-form formulation to Tensor Voting, a technique to perceptually group clouds of points, usually applied to infer features in images. The authors proved an analytic solution to the technique, a highly relevant contribution considering that the original formulation required numerical integration, a time-consuming task. Their work constitutes the first closed-form expression for the Tensor Voting framework. In this work we first observe that the proposed formulation leads to unexpected results which do not satisfy the constraints for a Tensor Voting output, hence they cannot be interpreted. Given that the closed-form expression is said to be an analytic equivalent solution, unexpected outputs should not be encountered unless there are flaws in the proof. We analyzed the underlying math to find which were the causes of these unexpected results. In this commentary we show that their proposal does not in fact provide a proper analytic solution to Tensor Voting and we indicate the flaws in the proof.