Robust and Fast 3D Scan Alignment using Mutual Information

This paper presents a mutual information (MI) based algorithm for the estimation of full 6-degree-of-freedom (DOF) rigid body transformation between two overlapping point clouds. We first divide the scene into a 3D voxel grid and define simple to compute features for each voxel in the scan. The two scans that need to be aligned are considered as a collection of these features and the MI between these voxelized features is maximized to obtain the correct alignment of scans. We have implemented our method with various simple point cloud features (such as number of points in voxel, variance of z-height in voxel) and compared the performance of the proposed method with existing point-to-point and point-to- distribution registration methods. We show that our approach has an efficient and fast parallel implementation on GPU, and evaluate the robustness and speed of the proposed algorithm on two real-world datasets which have variety of dynamic scenes from different environments

LASS: a simple assignment model with Laplacian smoothing

We consider the problem of learning soft assignments of $N$ items to $K$ categories given two sources of information: an item-category similarity matrix, which encourages items to be assigned to categories they are similar to (and to not be assigned to categories they are dissimilar to), and an item-item similarity matrix, which encourages similar items to have similar assignments. We propose a simple quadratic programming model that captures this intuition. We give necessary conditions for its solution to be unique, define an out-of-sample mapping, and derive a simple, effective training algorithm based on the alternating direction method of multipliers. The model predicts reasonable assignments from even a few similarity values, and can be seen as a generalization of semisupervised learning. It is particularly useful when items naturally belong to multiple categories, as for example when annotating documents with keywords or pictures with tags, with partially tagged items, or when the categories have complex interrelations (e.g. hierarchical) that are unknown.Comment: 20 pages, 4 figures. A shorter version appears in AAAI 201

A Sampling Strategy for High-Dimensional Spaces Applied to Free-Form Gravitational Lensing

We present a novel proposal strategy for the Metropolis-Hastings algorithm designed to efficiently sample general convex polytopes in 100 or more dimensions. This improves upon previous sampling strategies used for free-form reconstruction of gravitational lenses, but is general enough to be applied to other fields. We have written a parallel implementation within the lens modeling framework GLASS. Testing shows that we are able to produce uniform uncorrelated random samples which are necessary for exploring the degeneracies inherent in lens reconstruction.Comment: 10 pages, 9 figures. Accepted for publication in MNRA