A Generative Model for the Joint Registration of Multiple Point Sets

Abstract

International audienceThis 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

A Systematic Approach for Cross-Source Point Cloud Registration by Preserving Macro and Micro Structures

“…x i1i2 x j1j2 k q c1c2 (4) where X ∈ {0, 1} n1×n2 denotes the node correspondence, for example, if i It is more convenient to write J(X) in a quadratic form, x T Kx, where x = vec(X) ∈ {0, 1} n1n2 is an indicator vector and K ∈ R n1n2×n1n2 is computed as follows:…”

“…For comparison purposes, we select the representative 3D registration algorithms ICP [7], Go-ICP [14], 4PCS [15], super-4PCS [16], TPS-RPM [8], GMMReg [2], CPD [1] and JP-MPC [4] as our compared methods. Experiments cannot be conducted on a large number of point cloud registrations using TPS-RPM and JR-MPC due to the memory cost, so to make a fair and reasonable comparison, we downsample the original point cloud and let the number of points be approximately 2000.…”

“…We only consider points with positive z coordinates. For each view, following [4], the original models are rotated in the xzplane and the points with negative z coordinates are rejected. In this way, only a part of the object is viewed in each set; the point sets do not fully overlap, and the extent of the overlap depends on the rotation angle, as in real scenarios.…”

A Multi-resolution T-Mixture Model Approach to Robust Group-Wise Alignment of Shapes

“…Existing probabilistic approaches to rigid [1,2,3] and non-rigid [4] group-wise point set registration are based on Gaussian mixture models (GMMs) which, while affording efficient solutions for associated model parameters, lack robustness to outliers. An elegant solution to this limitation is to adopt a t-mixture model (TMM) formulation, which is inherently more robust due to TMMs' so-called heavy tails.…”

“…However, group-wise registration methods are, in general, preferable as they provide an unbiased solution to the registration problem [1]. Use of TMMs in the latter context was recently proposed in [7], wherein rigid transformation parameters were estimated numerically by gradient ascent optimisation.…”