This study investigates the impact of the invariance of feature vectors for partial-to-partial point set registration under translation and rotation of input point sets, particularly in the realm of techniques based on deep learning and Gaussian mixture models (GMMs). We reveal both theoretical and practical problems associated with such deep-learning-based registration methods using GMMs, with a particular focus on the limitations of DeepGMR, a pioneering study in this line, to the partial-to-partial point set registration. Our primary goal is to uncover the causes behind such methods and propose a comprehensible solution for that. To address this, we introduce an attention-based reference point shifting (ARPS) layer, which robustly identifies a common reference point of two partial point sets, thereby acquiring transformation-invariant features. The ARPS layer employs a well-studied attention module to find a common reference point rather than the overlap region. Owing to this, it significantly enhances the performance of DeepGMR and its recent variant, UGMMReg. Furthermore, these extension models outperform even prior deep learning methods using attention blocks and Transformer to extract the overlap region or common reference points. We believe these findings provide deeper insights into registration methods using deep learning and GMMs.
Point cloud registration is a fundamental problem in 3D computer vision, graphics and robotics. For the last few decades, existing registration algorithms have struggled in situations with large transformations, noise, and time constraints. In this paper, we introduce Deep Gaussian Mixture Registration (DeepGMR), the first learning-based registration method that explicitly leverages a probabilistic registration paradigm by formulating registration as the minimization of KL-divergence between two probability distributions modeled as mixtures of Gaussians. We design a neural network that extract…
University of Technology Sydney（悉尼科技大学）；Fondazione Bruno Kessler（布鲁诺·凯塞勒基金会）；University of Trento（特伦托大学）
Probabilistic 3D point cloud registration methods have shown competitive performance in overcoming noise, outliers, and density variations. However, registering point cloud pairs in the case of partial overlap is still a challenge. This paper proposes a novel overlap-guided probabilistic registration approach that computes the optimal transformation from matched Gaussian Mixture Model (GMM) parameters. We reformulate the registration problem as the problem of aligning two Gaussian mixtures such that a statistical discrepancy measure between the two corresponding mixtures is minimized. We intro…
Point base registration is an important part in many machine VISIOn applications, medical diagnostics, agricultural studies etc. The goal of point set registration is to find correspondences between different data sets and estimate the appropriate transformation that can map one set to another. Here we introduce a novel method for matching of different data sets based on Laplacian distribution. We consider the alignment of two point sets as probability density estimation problem. By using maximum likelihood methods we try to fit the Laplacian mixture model (LMM) centroids (source point set) to…
This paper presents a robust probabilistic point registration method for estimating the rigid transformation (i.e. rotation matrix and translation vector) between two pointcloud dataset. The method improves the robustness of point registration and consequently the robot localization in the presence of outliers in the pointclouds which always occurs due to occlusion, dynamic objects, and sensor errors. The framework models the point registration task based on directional statistics on a unit sphere. In particular, a Kent distribution mixture model is adopted and the process of point registratio…
Current deep-learning-based registration algorithms often exploit intensity-based similarity measures as the loss function, where dense correspondence between a pair of moving and fixed images is optimized through backpropagation during training. However, intensity-based metrics can be misleading when the assumption of intensity class correspondence is violated, especially in cross-modality or contrast-enhanced images. Moreover, existing learning-based registration methods are predominantly applicable to pairwise registration and are rarely extended to groupwise registration or simultaneous re…
We present a flexible approach to colour transfer inspired by techniques recently proposed for shape registration. Colour distributions of the palette and target images are modelled with Gaussian Mixture Models (GMMs) that are robustly registered to infer a non linear parametric transfer function. We show experimentally that our approach compares well to current techniques both quantitatively and qualitatively. Moreover, our technique is computationally the fastest and can take efficient advantage of parallel processing architectures for recolouring images and videos. Our transfer function is …
Recently, Expectation-maximization (EM) algorithm has been introduced as an effective means to solve multi-view registration problem. Most of the previous methods assume that each data point is drawn from the Gaussian Mixture Model (GMM), which is difficult to deal with the noise with heavy-tail or outliers. Accordingly, this paper proposed an effective registration method based on Student's t Mixture Model (StMM). More specially, we assume that each data point is drawn from one unique StMM, where its nearest neighbors (NNs) in other point sets are regarded as the t-distribution centroids with…
Australian National University（澳大利亚国立大学）；National ICT Australia (NICTA)（澳大利亚国家信息通信技术中心）
This paper presents a framework for rigid point-set registration and merging using a robust continuous data representation. Our point-set representation is constructed by training a one-class support vector machine with a Gaussian radial basis function kernel and subsequently approximating the output function with a Gaussian mixture model. We leverage the representation's sparse parametrisation and robustness to noise, outliers and occlusions in an efficient registration algorithm that minimises the L2 distance between our support vector--parametrised Gaussian mixtures. In contrast, existing t…
INRIA Grenoble Rhône-Alpes（法国国立信息学与自动化研究院格勒诺布尔罗讷-阿尔卑斯分院）；University of Hong Kong（香港大学）
This paper addresses the issue of matching rigid and articulated shapes through probabilistic point registration. The problem is recast into a missing data framework where unknown correspondences are handled via mixture models. Adopting a maximum likelihood principle, we introduce an innovative EM-like algorithm, namely the Expectation Conditional Maximization for Point Registration (ECMPR) algorithm. The algorithm allows the use of general covariance matrices for the mixture model components and improves over the isotropic covariance case. We analyse in detail the associated consequences in t…
The goal of point set registration is to find point-by-point correspondences between point sets, each of which characterizes the shape of an object. Because local preservation of object geometry is assumed, prevalent algorithms in the area can often elegantly solve the problems without using geometric information specific to the objects. This means that registration performance can be further improved by using prior knowledge of object geometry. In this paper, we propose a novel point set registration method using the Gaussian mixture model with prior shape information encoded as a statistical…
Beihang University（北京航空航天大学）；Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；Beijing Academy of Artificial Intelligence（北京人工智能研究院）；Peng Cheng Laboratory（鹏城实验室）
Point set registration is an essential step in many computer vision applications, such as 3D reconstruction and SLAM. Although there exist many registration algorithms for different purposes, however, this topic is still challenging due to the increasing complexity of various real-world scenarios, such as heavy noise and outlier contamination. In this paper, we propose a novel probabilistic generative method to simultaneously align multiple point sets based on the heavy-tailed Laplacian distribution. The proposed method assumes each data point is generated by a Laplacian Mixture Model (LMM), w…
Point cloud registration sits at the core of many important and challenging 3D perception problems including autonomous navigation, SLAM, object/scene recognition, and augmented reality. In this paper, we present a new registration algorithm that is able to achieve state-of-the-art speed and accuracy through its use of a hierarchical Gaussian Mixture Model (GMM) representation. Our method constructs a top-down multi-scale representation of point cloud data by recursively running many small-scale data likelihood segmentations in parallel on a GPU. We leverage the resulting representation using …
Matching 3D rigid point clouds in complex environments robustly and accurately is still a core technique used in many applications. This paper proposes a new architecture combining error estimation from sample covariances and dual global probability alignment based on the convolution of adaptive Gaussian Mixture Models (GMM) from point clouds. Firstly, a novel adaptive GMM is defined using probability distributions from the corresponding points. Then rigid point cloud alignment is performed by maximizing the global probability from the convolution of dual adaptive GMMs in the whole 2D or 3D sp…
PSReg: Prior-guided Sparse Mixture of Experts for Point Cloud Registration
Shanghai Jiao Tong University（上海交通大学）；Jiangxi University of Finance and Economics（江西财经大学）；Shandong University（山东大学）；Anqing Normal University（安庆师范大学）；Huaihua University（怀化学院）
This paper addresses the issue of matching rigid 3D object points with 2D image points through point registration based on maximum likelihood principle in computer simulated images. Perspective projection is necessary when transforming 3D coordinate into 2D. The problem then recasts into a missing data framework where unknown correspondences are handled via mixture models. Adopting the Expectation Conditional Maximization for Point Registration (ECMPR), two different rotation and translation optimization algorithms are compared in this paper. We analyze in detail the associated consequences in…
University of Technology Sydney（悉尼科技大学）；Nokia Technologies（诺基亚科技）；Tsinghua University（清华大学）
Many types of 3D acquisition sensors have emerged in recent years and point cloud has been widely used in many areas. Accurate and fast registration of cross-source 3D point clouds from different sensors is an emerged research problem in computer vision. This problem is extremely challenging because cross-source point clouds contain a mixture of various variances, such as density, partial overlap, large noise and outliers, viewpoint changing. In this paper, an algorithm is proposed to align cross-source point clouds with both high accuracy and high efficiency. There are two main contributions:…
Probabilistic methods for point set registration have interesting theoretical properties, such as linear complexity in the number of used points, and they easily generalize to joint registration of multiple point sets. In this work, we improve their recognition performance to match state of the art. This is done by incorporating learned features, by adding a von Mises-Fisher feature model in each mixture component, and by using learned attention weights. We learn these jointly using a registration loss learning strategy (RLL) that directly uses the registration error as a loss, by back-propaga…
Inria Grand Est（法国国家信息与自动化研究所大东部分部）；Université de Lorraine（洛林大学）
This paper presents an efficient approach for solving jointly facade registration and semantic segmentation. Progress in facade detection and recognition enable good initialization for the registration of a reference facade to a newly acquired target image. We propose here to rely on semantic segmentation to improve the accuracy of that initial registration. Simultaneously we aim to improve the quality of the semantic segmentation through the registration. These two problems are jointly solved in a Expectation-Maximization framework. We especially introduce a bayesian model that use prior sema…
When fitting Gaussian Mixture Models to 3D geometry, the model is typically fit to point clouds, even when the shapes were obtained as 3D meshes. Here we present a formulation for fitting Gaussian Mixture Models (GMMs) directly to a triangular mesh instead of using points sampled from its surface. Part of this work analyzes a general formulation for evaluating likelihood of geometric objects. This modification enables fitting higher-quality GMMs under a wider range of initialization conditions. Additionally, models obtained from this fitting method are shown to produce an improvement in 3D reg…
Australian National University（澳大利亚国立大学）；National ICT Australia (NICTA)（澳大利亚国家信息与通信技术研究院（NICTA））
Gaussian mixture alignment is a family of approaches that are frequently used for robustly solving the point-set registration problem. However, since they use local optimisation, they are susceptible to local minima and can only guarantee local optimality. Consequently, their accuracy is strongly dependent on the quality of the initialisation. This paper presents the first globally-optimal solution to the 3D rigid Gaussian mixture alignment problem under the L2 distance between mixtures. The algorithm, named GOGMA, employs a branch-and-bound approach to search the space of 3D rigid motions SE(…
Registering accurately point clouds from a cheap low-resolution sensor is a challenging task. Existing rigid registration methods failed to use the physical 3D uncertainty distribution of each point from a real sensor in the dynamic alignment process mainly because the uncertainty model for a point is static and invariant and it is hard to describe the change of these physical uncertainty models in the registration process. Additionally, the existing Gaussian mixture alignment architecture cannot be efficiently implement these dynamic changes. This paper proposes a simple architecture combinin…
Xi’an Jiaotong University（西安交通大学）；Zhongnan University of Economics and Law（中南财经政法大学）；Kyushu Institute of Technology（九州工业大学）
Registration of multi-view point sets is a prerequisite for 3D model reconstruction. To solve this problem, most of previous approaches either partially explore available information or blindly utilize unnecessary information to align each point set, which may lead to the undesired results or introduce extra computation complexity. To this end, this paper consider the multi-view registration problem as a maximum likelihood estimation problem and proposes a novel multi-view registration approach under the perspective of Expectation-Maximization (EM). The basic idea of our approach is that diffe…
This paper addresses the problem of registering multiple point sets. Solutions to this problem are often approximated by repeatedly solving for pairwise registration, which results in an uneven treatment of the sets forming a pair: a model set and a data set. The main drawback of this strategy is that the model set may contain noise and outliers, which negatively affects the estimation of the registration parameters. In contrast, the proposed formulation treats all the point sets on an equal footing. Indeed, all the points are drawn from a central Gaussian mixture, hence the registration is ca…
National University of Singapore（新加坡国立大学）；Johns Hopkins University（约翰斯·霍普金斯大学）
Probabilistic point cloud registration methods are becoming more popular because of their robustness. However, unlike point-to-plane variants of iterative closest point (ICP) which incorporate local surface geometric information such as surface normals, most probabilistic methods (e.g., coherent point drift (CPD)) ignore such information and build Gaussian mixture models (GMMs) with isotropic Gaussian covariances. This results in sphere-like GMM components which only penalize the point-to-point distance between the two point clouds. In this paper, we propose a novel method called CPD with Loca…
Deep point cloud registration methods face challenges to partial overlaps and rely on labeled data. To address these issues, we propose UDPReg, an unsupervised deep probabilistic registration framework for point clouds with partial overlaps. Specifically, we first adopt a network to learn posterior probability distributions of Gaussian mixture models (GMMs) from point clouds. To handle partial point cloud registration, we apply the Sinkhorn algorithm to predict the distribution-level correspondences under the constraint of the mixing weights of GMMs. To enable unsupervised learning, we design …
We propose a framework, named Aggregated Wasserstein, for computing a dissimilarity measure or distance between two Hidden Markov Models with state conditional distributions being Gaussian. For such HMMs, the marginal distribution at any time position follows a Gaussian mixture distribution, a fact exploited to softly match, aka register, the states in two HMMs. We refer to such HMMs as Gaussian mixture model-HMM (GMM-HMM). The registration of states is inspired by the intrinsic relationship of optimal transport and the Wasserstein metric between distributions. Specifically, the components of …
The problem of non-rigid point set registration is a key problem for many computer vision tasks. In many cases the nature of the data or capabilities of the point detection algorithms can give us some prior information on point sets distribution. In non-rigid case this information is able to drastically improve registration results by limiting number of possible solutions. In this paper we explore use of prior information about point sets clustering, such information can be obtained with preliminary segmentation. We extend existing probabilistic framework for fitting two level Gaussian mixture…
