Geometric Multi-model Fitting with a Convex Relaxation Algorithm

Abstract

We propose a novel method to fit and segment multistructural data via convex relaxation. Unlike greedy methodswhich maximise the number of inliers-this approach efficiently searches for a soft assignment of points to models by minimising the energy of the overall classification. Our approach is similar to state-of-the-art energy minimisation techniques which use a global energy. However, we deal with the scaling factor (as the number of models increases) of the original combinatorial problem by relaxing the solution. This relaxation brings two advantages: first, by operating in the continuous domain we can parallelize the calculations. Second, it allows for the use of different metrics which results in a more general formulation.We demonstrate the versatility of our technique on two different problems of estimating structure from images: plane extraction from RGB-D data and homography estimation from pairs of images. In both cases, we report accurate results on publicly available datasets, in most of the cases outperforming the state-of-the-art.

Multimotion Visual Odometry (MVO): Simultaneous Estimation of Camera and Third-Party Motions

“…MVO applies multimodel fitting techniques (e.g., CORAL [3]) to the traditional VO pipeline to simultaneously estimate the trajectories of all motions within a scene. Sparse, 3D visual features are decomposed into independent rigid motions and the trajectories of all of these motions, including the egomotion of the camera, are estimated simultaneously ( Fig.…”

Fast regularity-constrained plane fitting

“…Multimodel fitting is typically formulated as an optimization problem. For example, Delong et al [12] and Amayo et al [1] converted the problem to a multilabeling problem and solved it via α-expansion [5] and a primal-dual algorithm [9], respectively. Magri and Fusiello [25] cast the multimodel fitting problem as a set-coverage problem and solved it with integer linear programming.…”

“…However, they are quite different. First, the energy formulation in [12,1] only constrained the number of models (planes in our context). In contrast, Eq.…”

Primitive Fitting Using Deep Geometric Segmentation

“…Energy Minimization: Unlike the sequential and greedy nature of RANSAC based methods, it is appealing in theory to define a global energy function in terms of P2P membership that once minimized results in desired solution [30]- [33]. However most of them are only shown on relatively small number of points of simple scenes without much clutters or occlusions, and it is unclear how they will scale to larger datasets due to the intrinsic difficulty and slowness of minimizing the energy function.…”