  We propose Progressive-X+, a new algorithm for finding an unknown number of
geometric models, e.g., homographies. The problem is formalized as finding
dominant model instances progressively without forming crisp point-to-model
assignments. Dominant instances are found via RANSAC-like sampling and a
consolidation process driven by a model quality function considering previously
proposed instances. New ones are found by clustering in the consensus space.
This new formulation leads to a simple iterative algorithm with
state-of-the-art accuracy while running in real-time on a number of vision
problems. Also, we propose a sampler reflecting the fact that real-world data
tend to form spatially coherent structures. The sampler returns connected
components in a progressively growing neighborhood-graph. We present a number
of applications where the use of multiple geometric models improves accuracy.
These include using multiple homographies to estimate relative poses for global
SfM; pose estimation from generalized homographies; and trajectory estimation
of fast-moving objects.
