  We propose 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 a 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 - at least
two orders of magnitude faster than the competitors on two-view motion
estimation. Also, we propose a deterministic sampler reflecting the fact that
real-world data tend to form spatially coherent structures. The sampler returns
connected components in a progressively densified neighborhood-graph. We
present a number of applications where the use of multiple geometric models
improves accuracy. These include pose estimation from multiple generalized
homographies; trajectory estimation of fast-moving objects; and we also propose
a way of using multiple homographies in global SfM algorithms. Source code:
https://github.com/danini/clustering-in-consensus-space.
