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.

Accurate definition of the similarity measure is a key component in image registration. Most commonly used intensity-based similarity measures rely on the assumptions of independence and stationarity of the intensities from pixel to pixel. Such measures cannot capture the complex interactions among the pixel intensities, and often result in less satisfactory registration performances, especially in the presence of spatially-varying intensity distortions. We propose a novel similarity measure that accounts for intensity nonstationarities and complex spatially-varying intensity distortions in mono-modal settings. We derive the similarity measure by analytically solving for the intensity correction field and its adaptive regularization. The final measure can be interpreted as one that favors a registration with minimum compression complexity of the residual image between the two registered images. One of the key advantages of the new similarity measure is its simplicity in terms of both computational complexity and implementation. This measure produces accurate registration results on both artificial and real-world problems that we have tested, and outperforms other state-of-the-art similarity measures in these cases.

Accurate definition of similarity measure is a key component in image registration. Most commonly used intensity-based similarity measures rely on the assumptions of independence and stationarity of the intensities from pixel to pixel. Such measures cannot capture the complex interactions among the pixel intensities, and often result in less satisfactory registration performances, especially in the presence of nonstationary intensity distortions. We propose a novel similarity measure that accounts for intensity non-stationarities and complex spatially-varying intensity distortions. We derive the similarity measure by analytically solving for the intensity correction field and its adaptive regularization. The final measure can be interpreted as one that favors a registration with minimum compression complexity of the residual image between the two registered images. This measure produces accurate registration results on both artificial and real-world problems that we have tested, whereas many other state-of-the-art similarity measures have failed to do so.

Active contours is a popular technique for image segmentation. However, active contour tend to converge to the closest local minimum of its energy function and often requires a close boundary initialization. We introduce a new approach that overcomes the close boundary initialization problem by reformulating the external energy term. We treat the active contour as a mean curve of the probability density function p(x). It moves to minimize the Kullback-Leibler (KL) divergence between p(x) and the probability density function derived from the image. KL divergence forces p(x) to “cover all image areas” and the uncovered areas are heavily penalized, which allows the active contour to go over the edges. Also we use deterministic annealing on the width of p(x) to implement a coarse-to-fine search strategy. In the limit, when the width of p(x) goes to zero, the KL divergence function converges to the conventional external energy term (which can be seen a special case) of active contours. Our method produces robust segmentation results from arbitrary initialization positions.

We introduce a novel probabilistic approach for non-parametric nonrigid image registration using generalized elastic nets, a model previously used for topographic maps. The idea of the algorithm is to adapt an elastic net (a constrained Gaussian mixture) in the spatial-intensity space of one image to fit the second image. The resulting net directly represents the correspondence between image pixels in a probabilistic way and recovers the underlying image deformation. We regularize the net with a differential prior and develop an efficient optimization algorithm using linear conjugate gradients. The nonparametric formulation allows for complex transformations having local deformation. The method is generally applicable to registering point sets of arbitrary features. The accuracy and effectiveness of the method are demonstrated on different medical image and point set registration examples with locally nonlinear underlying deformations.

Tracking of speckles in echocardiography enables the study of myocardium deformation, and thus can provide insights about heart structure and function. Most of the current methods are based on 2D speckle tracking, which suffers from errors due to through-plane decorrelation. Speckle tracking in 3D overcomes such limitation. However, 3D speckle tracking is a challenging problem due to relatively low spatial and temporal resolution of 3D echocardiography. To ensure accurate and robust tracking, high level spatial and temporal constraints need to be incorporated. In this paper, we introduce a novel method for speckle tracking in 3D echocardiography. Instead of tracking each speckle independently, we enforce a motion coherence constraint, in conjunction with a dynamic model for the speckles. This method is validated on in vivo porcine hearts, and is proved to be accurate and robust.

We introduce Coherent Point Drift (CPD), a novel probabilistic method for nonrigid registration of point sets. The registration is treated as a Maximum Likelihood (ML) estimation problem with motion coherence constraint over the velocity field such that one point set moves coherently to align with the second set. We formulate the motion coherence constraint and derive a solution of regularized ML estimation through the variational approach, which leads to an elegant kernel form. We also derive the EM algorithm for the penalized ML optimization with deterministic annealing. The CPD method simultaneously finds both the non-rigid transformation and the correspondence between two point sets without making any prior assumption of the transformation model except that of motion coherence. This method can estimate complex non-linear non-rigid transformations, and is shown to be accurate on 2D and 3D examples and robust in the presence of outliers and missing points.

We describe a novel adaptive method that achieves robustness in pattern classification by combining a large number of weak classifiers. The individual classifiers are trained on subsets of features of the training samples and the output classification is obtained by a weighted sum of the individual weak classifiers. When the classifier is applied to the test set, the combination weights are adaptively adjusted in accordance with the agreement among the individual classifiers. We evaluated the performances of several different combination methods using simulated data and the results proved to be robust.