Disambiguating visual relations using loop constraints

Abstract

Repetitive and ambiguous visual structures in general pose a severe problem in many computer vision applications. Identification of incorrect geometric relations between images solely based on low level features is not always possible, and a more global reasoning approach about the consistency of the estimated relations is required. We propose to utilize the typically observed redundancy in the hypothesized relations for such reasoning, and focus on the graph structure induced by those relations. Chaining the (reversible) transformations over cycles in this graph allows to build suitable statistics for identifying inconsistent loops in the graph. This data provides indirect evidence for conflicting visual relations. Inferring the set of likely false positive geometric relations from these non-local observations is formulated in a Bayesian framework. We demonstrate the utility of the proposed method in several applications, most prominently the computation of structure and motion from images.

Non-sequential structure from motion

“…From a theoretical point of view, our main technical contributions are (i) showing that even though the estimation of two-view epipolar geometry may be ill-posed due to a short baseline, the relative rotation can still be reliably estimated, and (ii) a new mathematical model for robust estimation of orientations based on cycles and the notion of consistency. The theoretical results are of general nature and provide motivations not only for this paper, but also for other systems based on similar concepts such as [15,7,23].…”

“…In contrast, we remove incorrect pairwise rotations before estimating camera orientations and do not rely on identifying 4 good matches. Our system also has clear similarities to [23]. They set up a rather involved Bayesian model to detect outlier rotations based on cycle errors.…”

“…In [23] a method for removing inconsistent cycles is proposed. This method is however limited to cycles of length 6 (and uses a prior that is independent of cycle length).…”

Correcting for Duplicate Scene Structure in Sparse 3D Reconstruction

“…Loop constraints were exploited by Zach et al [30] to detect incorrect camera registrations. Their algorithm analyzes loops (cycles) of connected cameras in a graph in which cameras are nodes and pairwise transformations between cameras are edges.…”

Stable Structure from Motion for Unordered Image Collections

“…Furthermore, it does not handle outlier rotations. Zach et al [29] use cycles in the camera graph and a Bayesian framework to detect incorrect pairwise rota-tions. This leads to an intractable problem so they have to limit the length of the cycles to 6 edges.…”