[Show abstract][Hide abstract] 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.
Full-text · Article · Dec 2010 · IEEE Transactions on Software Engineering
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: Ultrasound elastography is a promising technique for the detection of breast cancer. Despite being proven to be a useful method in clinical studies, no studies have looked at directly correlating information in in-vivo ultrasound elastography images with histopathology images (regarded as the gold standard) using image registration. In this paper, expert knowledge from clinicians is utilised as constraints to register 2D elastography and histopathology images based on corresponding features identified by clinicians such as tumours and fibrous structures. The recently proposed coherent point drift (CPD) algorithm by Myronenko and Song was applied to align the corresponding feature points and the thin-plate splines method of Bookstein is then used to warp the images. The registered images were then overlaid. It was found that in elastography images, the stiffness of malignant tumours tend to extend beyond the tumour boundaries identified in the histopathology images, and there were many stiff areas indicated in the elastography images where no corresponding features could be identified in the histopathology images. The study thus provides some new insight into the relationship of elastography and histopathology as well as suggests further work is needed to better understand how to interpret patterns in elastography images.
[Show abstract][Hide abstract] ABSTRACT: To compute left ventricular (LV) twist from 3-dimensional (3D) echocardiography.
LV twist is a sensitive index of cardiac performance. Conventional 2-dimensional based methods of computing LV twist are cumbersome and subject to errors.
We studied 10 adult open-chest pigs. The pre-load to the heart was altered by temporary controlled occlusion of the inferior vena cava, and myocardial ischemia was produced by ligating the left anterior descending coronary artery. Full-volume 3D loops were reconstructed by stitching of pyramidal volumes acquired from 7 consecutive heart beats with electrocardiography gating on a Philips IE33 system (Philips Medical Systems, Andover, Massachusetts) at baseline and other steady states. Polar coordinate data of the 3D images were entered into an envelope detection program implemented in MatLab (The MathWorks, Inc., Natick, Massachusetts), and speckle motion was tracked using nonrigid image registration with spline-based transformation parameterization. The 3D displacement field was obtained, and rotation at apical and basal planes was computed. LV twist was derived as the net difference of apical and basal rotation. Sonomicrometry data of cardiac motion were also acquired from crystals anchored to epicardium in apical and basal planes at all states.
The 3D dense tracking slightly overestimated the LV twist, but detected changes in LV twist at different states and showed good correlation (r = 0.89) when compared with sonomicrometry-derived twist at all steady states. In open chest pigs, peak cardiac twist was increased with reduction of pre-load from inferior vena cava occlusion from 6.25 degrees +/- 1.65 degrees to 9.45 degrees +/- 1.95 degrees . With myocardial ischemia from left anterior descending coronary artery ligation, twist was decreased to 4.90 degrees +/- 0.85 degrees (r = 0.8759).
Despite lower spatiotemporal resolution of 3D echocardiography, LV twist and torsion can be computed accurately.
Full-text · Article · Mar 2010 · JACC. Cardiovascular imaging
[Show abstract][Hide abstract] ABSTRACT: The criterion for the correct spatial alignment is a key component in image registration. We formulate the registration problem as one that finds the spatial and intensity mappings of minimal complexity that make images exactly equal. We do not assume any parametric forms of these functions, and estimate them within variational calculus. We analytically solve for non-stationary intensity mapping, eliminate it from the objective function and arrive with a new similarity measure. We name it the mapping complexity (MC) similarity measure, because it achieves the optimum when intensity and spatial mappings are of minimal complexity. Due to its general formulation, the similarity measure works both for complex intensity relationships (e.g. multimodal registration) and for spatially-varying intensity distortions. Our similarity measure can be interpreted as the one that favors one image to lie mostly within a span of the leading eigenvectors of the kernel matrix, where the kernel matrix is constructed from the second image. We introduce a fast algorithm to compute the similarity measure. In particular, we introduce a fast kernel vector product (FKVP) algorithm, which is of general interest in computer vision. We demonstrate the accuracy of the new similarity measure on several mono- and multi-modal examples with complex intensity non-uniformities.
[Show abstract][Hide abstract] ABSTRACT: 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 ldquocover all image areasrdquo 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.
[Show abstract][Hide abstract] ABSTRACT: We introduce an adaptive regularization approach. In contrast to conventional Tikhonov regularization, which specifies a fixed regularization operator, we estimate it simultaneously with parameters. From a Bayesian perspective we estimate the prior distribution on parameters assuming that it is close to some given model distribution. We constrain the prior distribution to be a Gauss-Markov random field (GMRF), which allows us to solve for the prior distribution analytically and provides a fast optimization algorithm. We apply our approach to non-rigid image registration to estimate the spatial transformation between two images. Our evaluation shows that the adaptive regularization approach significantly outperforms standard variational methods.
[Show abstract][Hide abstract] ABSTRACT: Automated motion tracking of the myocardium from 3D echocardiography provides insight into heart’s architecture and function.
We present a method for 3D cardiac motion tracking using non-rigid image registration. Our contribution is two-fold. We introduce
a new similarity measure derived from a maximum likelihood perspective taking into account physical properties of ultrasound
image acquisition and formation. Second, we use envelope-detected 3D echo images in the raw spherical coordinates format,
which preserves speckle statistics and represents a compromise between signal detail and data complexity. We derive mechanical
measures such as strain and twist, and validate using sonomicrometry in open-chest piglets. The results demonstrate the accuracy
and feasibility of our method for studying cardiac motion.
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: We show the closed-form solution to the maximization of trace(A'R), where A is given and R is unknown rotation matrix. This problem occurs in many computer vision tasks involving optimal rotation matrix estimation. The solution has been continuously reinvented in different fields as part of specific problems. We summarize the historical evolution of the problem and present the general proof of the solution. We contribute to the proof by considering the degenerate cases of A and discuss the uniqueness of R.
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: 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 rela- tively low spatial and temporal resolution of 3D echocar- diography. To ensure accurate and robust tracking, high level spatial and temporal constraints need to be incorpo- rated. 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 con- straint, in conjunction with a dynamic model for the speck- les. This method is validated on in vivo porcine hearts, and is proved to be accurate and robust.
[Show abstract][Hide abstract] ABSTRACT: Automated motion reconstruction of the left ventricle (LV) from 3D echocardiography provides insight into myocardium architecture and function. Low image quality and artifacts make 3D ultrasound image processing a challenging problem. We introduce a LV tracking method, which combines textural and structural information to overcome the image quality limitations. Our method automatically reconstructs the motion of the LV contour (endocardium and epicardium) from a sequence of 3D ultrasound images.
[Show abstract][Hide abstract] ABSTRACT: We introduce a novel approach for non-parametric non-rigid image registration using generalized elastic nets. The concept behind the algorithm is to adapt an elastic net in spatial-intensity space of one image to fit the second image. The resulting configuration of the net, when it achieves its minimum energy state, directly represents correspondence between images in a probabilistic sense and recovers underlying image deformation, which can be arbitrary. Representation of elastic net in the spatial-intensity space with specific priors that enforce natural elastic deformation is introduced. Efficient algorithm for optimization of elastic net energy is developed. The accuracy and effectiveness of the method is demonstrated on different medical image registration examples with locally non-linear underlying deformations.
[Show abstract][Hide abstract] ABSTRACT: This paper explores the use of deformable mesh for registration of microscopic iris image sequences. The registration, as an effort for stabilizing and rectifying images corrupted by motion artifacts, is a crucial step toward leukocyte tracking and motion characterization for the study of immune systems. The image sequences are characterized by locally nonlinear deformations, where an accurate analytical expression can not be derived through modeling of image formation. We generalize the existing deformable mesh and formulate it in a probabilistic framework, which allows us to conveniently introduce local image similarity measures, to model image dynamics and to maintain a well-defined mesh structure and smooth deformation through appropriate regularization. Experimental results demonstrate the effectiveness and accuracy of the algorithm.
Full-text · Article · Feb 2006 · Lecture Notes in Computer Science
[Show abstract][Hide abstract] ABSTRACT: We introduce Coherent Point Drift (CPD), a novel probabilistic method for non- rigid registration of point sets. The registration is treated as a Maximum Like- lihood (ML) estimation problem with motion coherence constraint over the ve- locity eld 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 nds 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 coher- ence. 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.