The Complete Rank Transform: A Tool for Accurate and Morphologically Invariant Matching of Structures

Abstract

Most researchers agree that invariances are desirable in computer vision systems. However, one always has to keep in mind that this is at the expense of accuracy: By construction, all invariances inevitably discard information. The concept of morphological invariance is a good example for this trade-off and will be in the focus of this paper. Our goal is to develop a descriptor of local image structure that carries the maximally possible amount of local image information under this invariance. To fulfill this requirement, our descriptor has to encode the full ordering of the pixel intensities in the local neighbourhood. As a solution, we introduce the complete rank transform, which stores the intensity rank of every pixel in the local patch. As a proof of concept, we embed our novel descriptor in a prototypical TV−L 1 -type energy functional for optical flow computation, which we minimise with a traditional coarse-to-fine warping scheme. In this straightforward framework, we demonstrate that our descriptor is preferable over related features that exhibit the same invariance. Finally, we show by means of public benchmark systems that our method produces -in spite of its simplicity -results of competitive quality.

Simultaneous HDR and Optic Flow Computation

“…This observation is underlined by Table I that rates the quality of the computed flow fields in terms of the average angular error (AAE) [23]. Here, we also see that our joint method clearly outperforms the recent optic flow method by Demetz et al [24] that is specifically tailored to such illumination changes. It is worth mentioning that also further pre-alignment tests with top-ranked optic flow methods, which are not especially designed for such severe brightness variations, produced unsatisfactory results.…”

Efficient Joint Segmentation, Occlusion Labeling, Stereo and Flow Estimation

“…boundary−length (8) where we have left the dependence on I and d implicit and where N 8 is the set of pairs of 8-neighbor pixels. We now define the energy components in more detail.…”

Mathematical Foundations and Generalisations of the Census Transform for Robust Optic Flow Computation

“…Also the mutual information [42] turns out to be a useful feature for registering images with different illumination; see Hermosillo et al [16] and Panin [29]. In order to extract the maximal amount of information from a local neighbourhood while providing a morphological invariance, Demetz et al [8] introduce the complete rank transform in a variational optic flow setting.…”