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.
Another widely used algorithm is Normal Distribution Transform (NDT) which was initially proposed for 2D data @cite_10 and was later extended to three-dimensions. 3D-NDT @cite_33 is a point-to-distribution method in which the maximum likelihood estimate (MLE) of points in @math is maximized over the distribution of points in a gaussian mixture model derived from @math . Supervoxel based NDT (SV-NDT) @cite_30 is an extension to 3D-NDT in which segmentation on the basis of local-spatial structure is done over @math before creating a GMM model.
@cite_30 @cite_10 @cite_33
2096198554 131996945 1567242735 2150260301
In previous work on "transformed mixtures of Gaussians" and "transformed hidden Markov models", we showed how the EM algorithm in a discrete latent variable model can be used to jointly normalize data (e.g., center images, pitch-normalize spectrograms) and learn a mixture model of the normalized data. The only input to the algorithm is the data, a list of possible transformations, and the number of clusters to find. The main criticism of this work was that the exhaustive computation of the posterior probabilities over transformations would make scaling up to large feature vectors and large sets of transformations intractable. Here, we describe how a tremendous speed-up is acheived through the use of a variational technique for decoupling transformations, and a fast Fourier transform method for computing posterior probabilities. For N × N images, learning C clusters under N rotations, N scales, N x-translations and N y-translations takes only (C + 2 log N)N2 scalar operations per iteration. In contrast, the original algorithm takes CN6 operations to account for these transformations. We give results on learning a 4-component mixture model from a video sequence with frames of size 320×240. The model accounts for 360 rotations and 76,800 translations. Each iteration of EM takes only 10 seconds per frame in MATLAB, which is over 5 million times faster than the original algorithm. This paper describes a probabilistic generative model and its associated algorithm to jointly register multiple point sets. The vast majority of state-of-the-art registration techniques select one of the sets as the “model” and perform pairwise alignments between the other sets and this set. The main drawback of this mode of operation is that there is no guarantee that the model-set is free of noise and outliers, which contaminates the estimation of the registration parameters. Unlike previous work, the proposed method treats all the point sets on an equal footing: they are realizations of a Gaussian mixture (GMM) and the registration is cast into a clustering problem. We formally derive an EM algorithm that estimates both the GMM parameters and the rotations and translations that map each individual set onto the “central” model. The mixture means play the role of the registered set of points while the variances provide rich information about the quality of the registration. We thoroughly validate the proposed method with challenging datasets, we compare it with several state-of-the-art methods, and we show its potential for fusing real depth data. Matching 2D range scans is a basic component of many localization and mapping algorithms. Most scan match algorithms require finding correspondences between the used features, i.e. points or lines. We propose an alternative representation for a range scan, the normal distributions transform. Similar to an occupancy grid, we subdivide the 2D plane into cells. To each cell, we assign a normal distribution, which locally models the probability of measuring a point. The result of the transform is a piecewise continuous and differentiable probability density, that can be used to match another scan using Newton's algorithm. Thereby, no explicit correspondences have to be established. We present the algorithm in detail and show the application to relative position tracking and simultaneous localization and map building (SLAM). First results on real data demonstrate, that the algorithm is capable to map unmodified indoor environments reliable and in real time, even without using odometry data. This paper proposes a generative model-based speaker clustering algorithm in the maximum a posteriori adapted Gaussian mixture model (GMM) mean supervector space. The algorithm can be viewed as an extension of the standard expectation maximization algorithm for fitting a mixture model to the data, which iterates between two steps - a sample re-assignment step (E-step) and a model re-estimation step (M-step) - until it converges. The directional scattering patterns of GMM mean supervectors suggest that we employ a mixture of von Mises-Fisher distributions in the model re-estimation step. In the sample re-assignment step, four sample-to-mixture assignment strategies, namely soft, hard, stochastic, and deterministic annealing assignments, are used. Our experiments on the GALE Mandarin dataset show that the use of a mixture of von Mises-Fisher distributions as the underlying model yields significantly higher speaker clustering accuracies than the use of a mixture of Gaussian distributions. It is further shown that deterministic annealing assignment outperforms soft assignment, that soft assignment is comparable to stochastic assignment, and that both soft and stochastic assignments outperform hard assignment.