Geometric Multi-Model Fitting with a Convex Relaxation Algorithm
This addresses the challenge of scaling multi-model fitting in computer vision, offering a more general and parallelizable solution, though it appears incremental as it builds on existing energy minimization techniques.
The paper tackles the problem of fitting and segmenting multi-structural data by proposing a convex relaxation algorithm that efficiently searches for soft assignments to minimize classification energy, demonstrating accurate results on plane extraction and homography estimation tasks, often outperforming state-of-the-art methods.
We propose a novel method to fit and segment multi-structural data via convex relaxation. Unlike greedy methods --which 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.