Point Set Registration: Coherent Point Drift
01 Dec 2010-IEEE Transactions on Pattern Analysis and Machine Intelligence (IEEE Computer Society)-Vol. 32, Iss: 12, pp 2262-2275
TL;DR: A probabilistic method, called the Coherent Point Drift (CPD) algorithm, is introduced for both rigid and nonrigid point set registration and a fast algorithm is introduced that reduces the method computation complexity to linear.
Abstract: 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.
Citations
More filters
TL;DR: This paper attempts to give an overview of deformable registration methods, putting emphasis on the most recent advances in the domain, and provides an extensive account of registration techniques in a systematic manner.
Abstract: Deformable image registration is a fundamental task in medical image processing. Among its most important applications, one may cite: 1) multi-modality fusion, where information acquired by different imaging devices or protocols is fused to facilitate diagnosis and treatment planning; 2) longitudinal studies, where temporal structural or anatomical changes are investigated; and 3) population modeling and statistical atlases used to study normal anatomical variability. In this paper, we attempt to give an overview of deformable registration methods, putting emphasis on the most recent advances in the domain. Additional emphasis has been given to techniques applied to medical images. In order to study image registration methods in depth, their main components are identified and studied independently. The most recent techniques are presented in a systematic fashion. The contribution of this paper is to provide an extensive account of registration techniques in a systematic manner.
1,434 citations
Cites background from "Point Set Registration: Coherent Po..."
...Myronenko and Song proposed to use residual complexity (RC) to account for complex spatially-varying intensity distortions [327]....
[...]
...Myronenko and Song [301] recast registration as a probability density estimation problem....
[...]
Posted Content•
TL;DR: This short book reviews OT with a bias toward numerical methods and their applications in data sciences, and sheds lights on the theoretical properties of OT that make it particularly useful for some of these applications.
Abstract: Optimal transport (OT) theory can be informally described using the words of the French mathematician Gaspard Monge (1746-1818): A worker with a shovel in hand has to move a large pile of sand lying on a construction site. The goal of the worker is to erect with all that sand a target pile with a prescribed shape (for example, that of a giant sand castle). Naturally, the worker wishes to minimize her total effort, quantified for instance as the total distance or time spent carrying shovelfuls of sand. Mathematicians interested in OT cast that problem as that of comparing two probability distributions, two different piles of sand of the same volume. They consider all of the many possible ways to morph, transport or reshape the first pile into the second, and associate a "global" cost to every such transport, using the "local" consideration of how much it costs to move a grain of sand from one place to another. Recent years have witnessed the spread of OT in several fields, thanks to the emergence of approximate solvers that can scale to sizes and dimensions that are relevant to data sciences. Thanks to this newfound scalability, OT is being increasingly used to unlock various problems in imaging sciences (such as color or texture processing), computer vision and graphics (for shape manipulation) or machine learning (for regression, classification and density fitting). This short book reviews OT with a bias toward numerical methods and their applications in data sciences, and sheds lights on the theoretical properties of OT that make it particularly useful for some of these applications.
1,355 citations
TL;DR: This paper presents a unified framework for the rigid and nonrigid point set registration problem in the presence of significant amounts of noise and outliers, and shows that the popular iterative closest point (ICP) method and several existing point setRegistration methods in the field are closely related and can be reinterpreted meaningfully in this general framework.
Abstract: In this paper, we present a unified framework for the rigid and nonrigid point set registration problem in the presence of significant amounts of noise and outliers. The key idea of this registration framework is to represent the input point sets using Gaussian mixture models. Then, the problem of point set registration is reformulated as the problem of aligning two Gaussian mixtures such that a statistical discrepancy measure between the two corresponding mixtures is minimized. We show that the popular iterative closest point (ICP) method and several existing point set registration methods in the field are closely related and can be reinterpreted meaningfully in our general framework. Our instantiation of this general framework is based on the the L2 distance between two Gaussian mixtures, which has the closed-form expression and in turn leads to a computationally efficient registration algorithm. The resulting registration algorithm exhibits inherent statistical robustness, has an intuitive interpretation, and is simple to implement. We also provide theoretical and experimental comparisons with other robust methods for point set registration.
909 citations
Cites background or methods from "Point Set Registration: Coherent Po..."
...In the first experiment, we compare the convergence range of the proposed registration algorithm against the CPD rigid registration [7]....
[...]
...On the 2D data sets, we provide comparisons with the CPD rigid registration [7]....
[...]
...Additionally, some quantitative evaluations were performed to depict the favorable performance of our nonrigid registration method compared to the competing nonrigid registration methods [2], [6], [7]....
[...]
...Interestingly, several existing point set registration methods, including [1], [2], [3], [4], [5], [6], [7], can be viewed as special cases in this generic framework....
[...]
...TABLE 1 Convergence Range of the Proposed Registration Method and the CPD Registration Method [7] in Terms of 2D Rotation Angles (in Radians) on Four Data Sets Shown in Fig....
[...]
TL;DR: This paper presents the first globally optimal algorithm, named Go-ICP, for Euclidean (rigid) registration of two 3D point-sets under the inline-formula notation, and derives novel upper and lower bounds for the registration error function.
Abstract: The Iterative Closest Point (ICP) algorithm is one of the most widely used methods for point-set registration. However, being based on local iterative optimization, ICP is known to be susceptible to local minima. Its performance critically relies on the quality of the initialization and only local optimality is guaranteed. This paper presents the first globally optimal algorithm, named Go-ICP, for Euclidean (rigid) registration of two 3D point-sets under the $L_2$ error metric defined in ICP. The Go-ICP method is based on a branch-and-bound scheme that searches the entire 3D motion space $SE(3)$ . By exploiting the special structure of $SE(3)$ geometry, we derive novel upper and lower bounds for the registration error function. Local ICP is integrated into the BnB scheme, which speeds up the new method while guaranteeing global optimality. We also discuss extensions, addressing the issue of outlier robustness. The evaluation demonstrates that the proposed method is able to produce reliable registration results regardless of the initialization. Go-ICP can be applied in scenarios where an optimal solution is desirable or where a good initialization is not always available.
736 citations
Cites methods from "Point Set Registration: Coherent Po..."
...Fitzgibbon [16] proposed the LM-ICP method where the ICP error was optimized with the Levenberg–Marquardt algorithm [28]....
[...]
TL;DR: A novel fusion algorithm, named Gradient Transfer Fusion (GTF), based on gradient transfer and total variation (TV) minimization is proposed, which can keep both the thermal radiation and the appearance information in the source images.
729 citations
References
More filters
49,597 citations
Book•
01 Jan 1995TL;DR: This is the first comprehensive treatment of feed-forward neural networks from the perspective of statistical pattern recognition, and is designed as a text, with over 100 exercises, to benefit anyone involved in the fields of neural computation and pattern recognition.
Abstract: From the Publisher:
This is the first comprehensive treatment of feed-forward neural networks from the perspective of statistical pattern recognition. After introducing the basic concepts, the book examines techniques for modelling probability density functions and the properties and merits of the multi-layer perceptron and radial basis function network models. Also covered are various forms of error functions, principal algorithms for error function minimalization, learning and generalization in neural networks, and Bayesian techniques and their applications. Designed as a text, with over 100 exercises, this fully up-to-date work will benefit anyone involved in the fields of neural computation and pattern recognition.
19,056 citations
TL;DR: In this paper, the authors describe a general-purpose representation-independent method for the accurate and computationally efficient registration of 3D shapes including free-form curves and surfaces, based on the iterative closest point (ICP) algorithm, which requires only a procedure to find the closest point on a geometric entity to a given point.
Abstract: The authors describe a general-purpose, representation-independent method for the accurate and computationally efficient registration of 3-D shapes including free-form curves and surfaces. The method handles the full six degrees of freedom and is based on the iterative closest point (ICP) algorithm, which requires only a procedure to find the closest point on a geometric entity to a given point. The ICP algorithm always converges monotonically to the nearest local minimum of a mean-square distance metric, and the rate of convergence is rapid during the first few iterations. Therefore, given an adequate set of initial rotations and translations for a particular class of objects with a certain level of 'shape complexity', one can globally minimize the mean-square distance metric over all six degrees of freedom by testing each initial registration. One important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model, prior to shape inspection. Experimental results show the capabilities of the registration algorithm on point sets, curves, and surfaces. >
17,598 citations
TL;DR: The chapter discusses two important directions of research to improve learning algorithms: the dynamic node generation, which is used by the cascade correlation algorithm; and designing learning algorithms where the choice of parameters is not an issue.
Abstract: Publisher Summary This chapter provides an account of different neural network architectures for pattern recognition. A neural network consists of several simple processing elements called neurons. Each neuron is connected to some other neurons and possibly to the input nodes. Neural networks provide a simple computing paradigm to perform complex recognition tasks in real time. The chapter categorizes neural networks into three types: single-layer networks, multilayer feedforward networks, and feedback networks. It discusses the gradient descent and the relaxation method as the two underlying mathematical themes for deriving learning algorithms. A lot of research activity is centered on learning algorithms because of their fundamental importance in neural networks. The chapter discusses two important directions of research to improve learning algorithms: the dynamic node generation, which is used by the cascade correlation algorithm; and designing learning algorithms where the choice of parameters is not an issue. It closes with the discussion of performance and implementation issues.
13,033 citations
"Point Set Registration: Coherent Po..." refers background or methods in this paper
...We use the EM algorithm [29], [30] to find and (2)....
[...]
...by minimizing the expectation of the complete negative loglikelihood function [30],...
[...]
Book•
01 Jan 1977
8,009 citations
"Point Set Registration: Coherent Po..." refers methods in this paper
...ssumed to be unknown and non-rigid, which is generally broad class of transformations that can lead to an ill-posed problem. In order to deal with the problem we use Tikhonov regularization framework [37]–[39].We define the transformation as the 6 initial position plus a displacement function v: T (Y,v) = Y+ v(Y), (11) We regularize the norm of vto enforce the smoothness of the function [38]. Such appr...
[...]