Point Set Registration: Coherent Point Drift

By Andriy Myronenko, Xubo B. Song. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2009

2,835 citations recorded by the source corpus.

Point set registration is a key component in many computer vision tasks. The goal of point set registration is to assign correspondences between two sets of points and to recover the transformation that maps one point set to the other. Multiple factors, including an unknown nonrigid spatial transformation, large dimensionality of point set, noise, and outliers, make the point set registration a challenging problem. We introduce a probabilistic method, called the Coherent Point Drift (CPD) algorithm, for both rigid and nonrigid point set registration. We consider the alignment of two point sets as a probability density estimation problem. We fit the Gaussian mixture model (GMM) centroids (representing the first point set) to the data (the second point set) by maximizing the likelihood. We force the GMM centroids to move coherently as a group to preserve the topological structure of the point sets. In the rigid case, we impose the coherence constraint by reparameterization of GMM centroid locations with rigid parameters and derive a closed form solution of the maximization step of the EM algorithm in arbitrary dimensions. In the nonrigid case, we impose the coherence constraint by regularizing the displacement field and using the variational calculus to derive the optimal transformation. We also introduce a fast algorithm that reduces the method computation complexity to linear. We test the CPD algorithm for both rigid and nonrigid transformations in the presence of noise, outliers, and missing points, where CPD shows accurate results and outperforms current state-of-the-art methods.

Subfields: Aerospace Engineering, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/65c260fce4fb6fe44ac44562b75d38b0ac5c38f5

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Citations in the corpus

An Efficient Algorithm for Calculating the Exact Hausdorff Distance (2015, background): “Probabilistic based measures such as the distance between densities generally compare probability densities and other statistics of the point sets to measure the similarity [20], [14].”
Robust Point Matching via Vector Field Consensus (2014, background): “Although these methods are very successful in many situations they have had limited success if the geometrical constraints are non-parametric, for example if the real correspondence is non-rigid, and they also tend to degrade badly if the proportion of outliers in the putative correspondence set…”
Fast and Robust Iterative Closest Point (2020, methodology): “Other methods take a statistical approach and align two point sets via their Gaussian mixture representations [25], [26].”
Robust Feature Matching for Remote Sensing Image Registration via Locally Linear Transforming (2015, methodology): “We next give quantitative comparisons of our LLT with RANSAC [39], CPD [57], ICF [45], and GS [44] on the rigid, affine, and nonrigid data sets.”
Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid (2013, methodology): “Myronenko and Song [27] allow points to displace freely, and encourage the displacement vectors to point in similar directions by regularizing high-frequency components of the displacement field.”
Multimodal image-guided prostate fusion biopsy based on automatic deformable registration (2015, methodology): “However, it has been previously shown that the registration algorithm is robust in terms of outliers and able to cope with such artifacts as long as the majority of the surface is appropriately well captured [18].”
A comprehensive survey on point cloud registration (2021, methodology): “CPD [73] introduces a motion drift idea into the GMM framework by adding constraints to transformation estimation.”
Bayesian Inference of Bijective Non-Rigid Shape Correspondence (2016, methodology): “The problem is then solved via expectation-maximization by the coherent point drift algorithm [28].”
Towards 3D lidar point cloud registration improvement using optimal neighborhood knowledge (2013, methodology): “Simultaneous methods are very robust since the errors are distributed among all the points of the sets to limit distortion while preserving the geometry (Huber and Hebert, 2003a; Myronenko and Song, 2010).”
PointDSC: Robust Point Cloud Registration using Deep Spatial Consistency (2021, background): “, [8, 1, 47, 31, 44, 44]) have been comprehensively reviewed in [52].”
Non-Rigid Point Set Registration by Preserving Global and Local Structures (2015, methodology): “Note that the original CPD is not robust to changes in the outlier ratios, as it involves a fixed outlier ratio parameter, i.e., parameter γ in Eq.”
Go-ICP: Solving 3D Registration Efficiently and Globally Optimally (2013, methodology): “Probability density based techniques [18, 33, 27, 6] have been used to model the points with Gaussian Mixture Models.”
Go-ICP: A Globally Optimal Solution to 3D ICP Point-Set Registration (2016, background): “Although improved robustness to outliers and poor initializations could be achieved by GMM-based techniques [17], [29], [30], [31], the optimization was still based on local search.”
Elastic Fragments for Dense Scene Reconstruction (2013, background): “Non-rigid registration has a long history in medical imaging and computer vision, resulting in sophisticated techniques for aligning two-dimensional contours and three-dimensional shapes [19, 9, 33, 14, 10].”
Image Matching from Handcrafted to Deep Features: A Survey (2020, methodology): “Apart from the commonly used rigid model or non-rigid transformation model based on TPS (Chui and Rangarajan 2003) or Gaussian radial basis functions (Myronenko and Song 2010), additional complex deformations are also considered in the literature.”