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Spherical Demons: Fast Diffeomorphic LandmarkFree Surface Registration
 IEEE TRANSACTIONS ON MEDICAL IMAGING. 29(3):650–668, 2010
, 2010
"... We present the Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline interpolation theory, we show that a large class of regularizors for the modified Demons objective function can be efficiently approximated on the sphere using iterative smoothing. B ..."
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Cited by 25 (5 self)
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We present the Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline interpolation theory, we show that a large class of regularizors for the modified Demons objective function can be efficiently approximated on the sphere using iterative smoothing. Based on one parameter subgroups of diffeomorphisms, the resulting registration is diffeomorphic and fast. The Spherical Demons algorithm can also be modified to register a given spherical image to a probabilistic atlas. We demonstrate two variants of the algorithm corresponding to warping the atlas or warping the subject. Registration of a cortical surface mesh to an atlas mesh, both with more than 160k nodes requires less than 5 minutes when warping the atlas and less than 3 minutes when warping the subject on a Xeon 3.2GHz single processor machine. This is comparable to the fastest nondiffeomorphic landmarkfree surface registration algorithms. Furthermore, the accuracy of our method compares favorably to the popular FreeSurfer registration algorithm. We validate the technique in two different applications that use registration to transfer segmentation labels onto a new image: (1) parcellation of invivo cortical surfaces and (2) Brodmann area localization in exvivo cortical surfaces.
Shape modelling using markov random field restoration of point correspondences
 in Information Processing in Medical Imaging, LNCS 2732
, 2003
"... Abstract. A method for building statistical point distribution models is proposed. The novelty in this paper is the adaption of Markov random field regularization of the correspondence field over the set of shapes. The new approach leads to a generative model that produces highly homogeneous polygon ..."
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Abstract. A method for building statistical point distribution models is proposed. The novelty in this paper is the adaption of Markov random field regularization of the correspondence field over the set of shapes. The new approach leads to a generative model that produces highly homogeneous polygonized shapes and improves the capability of reconstruction of the training data. Furthermore, the method leads to an overall reduction in the total variance of the point distribution model. Thus, it finds correspondence between semilandmarks that are highly correlated in the shape tangent space. The method is demonstrated on a set of human ear canals extracted from 3Dlaser scans. 1
Leftinvariant Riemannian elasticity: a distance on shape diffeomorphisms
, 2006
"... Abstract. In intersubject registration, one often lacks a good model of the transformation variability to choose the optimal regularization. Some works attempt to model the variability in a statistical way, but the reintroduction in a registration algorithm is not easy. In [1], we interpreted the ..."
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Cited by 15 (5 self)
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Abstract. In intersubject registration, one often lacks a good model of the transformation variability to choose the optimal regularization. Some works attempt to model the variability in a statistical way, but the reintroduction in a registration algorithm is not easy. In [1], we interpreted the elastic energy as the distance of the GreenSt Venant strain tensor to the identity. By changing the Euclidean metric for a more suitable Riemannian one, we defined a consistent statistical framework to quantify the amount of deformation. In particular, the mean and the covariance matrix of the strain tensor could be efficiently computed from a population of nonlinear transformations and introduced as parameters in a Mahalanobis distance to measure the statistical deviation from the observed variability. This statistical Riemannian elasticity was able to handle anisotropic deformations but its isotropic stationary version was locally inverseconsistent. In this paper, we investigate how to modify the Riemannian elasticity to make it globally inverse consistent. This allows to define a leftinvariant ”distance ” between shape diffeomorphisms that we call the leftinvariant Riemannian elasticity. Such a closed form energy on diffeomorphisms can optimize it directly without relying on a time and memory consuming numerical optimization of the geodesic path. 1
Maximizing the Predictivity of Smooth Deformable Image Warps through CrossValidation
 J MATH IMAGING VIS
, 2008
"... Estimating smooth image warps from landmarks is an important problem in computer vision and medical image analysis. The standard paradigm is to find the model parameters by minimizing a compound energy including a data term and a smoother, balanced by a ‘smoothing parameter’ that is usually fixed b ..."
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Cited by 9 (4 self)
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Estimating smooth image warps from landmarks is an important problem in computer vision and medical image analysis. The standard paradigm is to find the model parameters by minimizing a compound energy including a data term and a smoother, balanced by a ‘smoothing parameter’ that is usually fixed by trial and error. We point out that warp estimation is an instance of the general supervised machine learning problem of fitting a flexible model to data, and propose to learn the smoothing parameter while estimating the warp. The leading idea is to depart from the usual paradigm of minimizing the energy to the one of maximizing the predictivity of the warp, i.e. its ability to do well on the entire image, rather than only on the given landmarks. We use crossvalidation to measure predictivity, and propose a complete framework to solve for the desired warp. We point out that the wellknown noniterative closedform for the leaveoneout crossvalidation score is actually a good approximation to the true score and show that it extends to the warp estimation problem by replacing the usual vector twonorm by the matrix Frobenius norm. Experimental results on real data show that the procedure selects sensible smoothing parameters, very close to user selected ones.
Contributions au recalage d’images et a la reconstruction 3D de scènes rigides et déformables
, 2008
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Abstract Capturing intraoperative deformations: research experience at Brigham and WomenÕs hospital
, 2004
"... During neurosurgical procedures the objective of the neurosurgeon is to achieve the resection of as much diseased tissue as possible while achieving the preservation of healthy brain tissue. The restricted capacity of the conventional operating room to enable the surgeon to visualize critical health ..."
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During neurosurgical procedures the objective of the neurosurgeon is to achieve the resection of as much diseased tissue as possible while achieving the preservation of healthy brain tissue. The restricted capacity of the conventional operating room to enable the surgeon to visualize critical healthy brain structures and tumor margin has lead, over the past decade, to the development of sophisticated intraoperative imaging techniques to enhance visualization. However, both rigid motion due to patient placement and nonrigid deformations occurring as a consequence of the surgical intervention disrupt the correspondence between preoperative data used to plan surgery and the intraoperative configuration of the patientÕs brain. Similar challenges are faced in other interventional therapies, such as in cryoablation of the liver, or biopsy of the prostate. We have developed algorithms to model the motion of key anatomical structures and system implementations that enable us to estimate the deformation of the critical anatomy from sequences of volumetric images and to prepare updated fused visualizations of preoperative and intraoperative images at a rate compatible with surgical decision making. This paper reviews the experience at Brigham and WomenÕs Hospital through the process of developing and applying novel algorithms for capturing intraoperative deformations in support of image guided therapy. Ó 2004 Elsevier B.V. All rights reserved.
Localizing Structure and Function in the Cerebral Cortex
, 2010
"... In medical image analysis, registration is necessary to establish spatial correspondences across two or more images. Registration is rarely the endgoal, but instead, the results of image registration are used in other tasks, such as voxelbased morphometry, functional group analysis, image segmenta ..."
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In medical image analysis, registration is necessary to establish spatial correspondences across two or more images. Registration is rarely the endgoal, but instead, the results of image registration are used in other tasks, such as voxelbased morphometry, functional group analysis, image segmentation and tracking. In this thesis, we argue that the quality of image registration should be evaluated in the context of the application. Consequently, we develop a framework for learning registration cost functions optimized for specific tasks. We demonstrate that by taking into account the application, we not only achieve better registration, but also potentially resolve certain
UNIVERSITY OF COPENHAGEN
, 2008
"... A Brownian motion model in the group of diffeomorphisms has been introduced as inducing a least committed prior on warps. This prior is sourcedestination symmetric, fulfills a natural semigroup property for warps, and with probability 1 creates invertible warps. Using this as a least committed pri ..."
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A Brownian motion model in the group of diffeomorphisms has been introduced as inducing a least committed prior on warps. This prior is sourcedestination symmetric, fulfills a natural semigroup property for warps, and with probability 1 creates invertible warps. Using this as a least committed prior, we formulate a Partial Differential Equation for obtaining the maximally likely warp given matching constraints derived from the images. We solve for the free boundary conditions, and the bias toward smaller areas in the finite domain setting. Furthermore, we demonstrate the technique on 2D images, and show that the obtained warps are also in practice sourcedestination symmetric and in an example on Xray spine registration provides extrapolations from landmark point superior to those of spline solutions.