Geometric Multi-Model Fitting with a Convex Relaxation Algorithm

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.

DENSER Cities: A System for Dense Efficient Reconstructions of Cities

This paper is about the efficient generation of dense, colored models of city-scale environments from range data and in particular, stereo cameras. Better maps make for better understanding; better understanding leads to better robots, but this comes at a cost. The computational and memory requirements of large dense models can be prohibitive. We provide the theory and the system needed to create city-scale dense reconstructions. To do so, we apply a regularizer over a compressed 3D data structure while dealing with the complex boundary conditions this induces during the data-fusion stage. We show that only with these considerations can we swiftly create neat, large, "well behaved" reconstructions. We evaluate our system using the KITTI dataset and provide statistics for the metric errors in all surfaces created compared to those measured with 3D laser. Our regularizer reduces the median error by 40% in 3.4 km of dense reconstructions with a median accuracy of 6 cm. For subjective analysis, we provide a qualitative review of 6.1 km of our dense reconstructions in an attached video. These are the largest dense reconstructions from a single passive camera we are aware of in the literature.