Why Is the Census Transform Good for Robust Optic Flow Computation?

David Hafner, Oliver Demetz, Joachim Weickert

Abstract: The census transform is becoming increasingly popular in the context of optic flow computation in image sequences. Since it is invariant under monotonically increasing grey value transformations, it forms the basis of an illumination-robust constancy assumption. However, its underlying mathematical concepts have not been studied so far. The goal of our paper is to provide this missing theoretical foundation. We study the continuous limit of the inherently discrete census transform and embed it into a variational setting. Our analysis shows two surprising results: The census-based technique enforces matchings of extrema, and it induces an anisotropy in the data term by acting along level lines. Last but not least, we establish links to the widely-used gradient constancy assumption and present experiments that confirm our findings.