Viewpoint Induced Deformation Statistics and the Design of Viewpoint Invariant Features: Singularities and Occlusions

Abstract

Abstract. We study the set of domain deformations induced on images of three-dimensional scenes by changes of the vantage point. We parametrize such deformations and derive empirical statistics on the parameters, that show a kurtotic behavior similar to that of natural image and range statistics. Such a behavior would suggest that most deformations are locally smooth, and therefore could be captured by simple parametric maps, such as affine ones. However, we show that deformations induced by singularities and occluding boundaries, although rare, are highly salient, thus warranting the development of dedicated descriptors. We therefore illustrate the development of viewpoint invariant descriptors for singularities, as well as for occluding boundaries. We test their performance on scenes where the current state of the art based on affine-invariant region descriptors fail to establish correspondence, highlighting the features and shortcomings of our approach.

On the Design and Analysis of Multiple View Descriptors

“…Clearly HOG depends on the latter, but it is insensitive to any deformation of the scene that would yield the same projection onto the (single) image. The two are related only at occluding boundaries, that however are excluded from our analysis, as well as from the typical use of local descriptors (although see [41,3]).…”

On the Distance Between Non-stationary Time Series

“…For instance, in the illustrative case just discussed, in the presence of noise one would have different realization produce different numbers and location of local minima. This can be minimized by defining a scale-space of features, rather than considering the signal only at the resolution defined by the sample frequency of the sensor [10], and [19] for a more thorough discussion on this issue.…”