Statistical Computing on Non-Linear Spaces for Computational Anatomy

Pennec, Xavier; Fillard, Pierre

doi:10.1007/978-0-387-09749-7_8

Cited by 3 publications

(2 citation statements)

References 67 publications

(75 reference statements)

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“…Diffeomorphic registration methods compute smooth and invertible forward and backward transformations between the images. These transformations have become fundamental inputs in computational anatomy applications since they belong to spaces endowed with a strong mathematical setting for the computation of statistics (Fletcher et al 2004, Pennec 2006, Durrleman et al 2008, Pennec and Fillard 2009, Lorenzi and Pennec 2013b. Diffeomorphisms have been used in the construction of statistical population models (Miller et al 1997, Thompson and Toga 1997, Miller 2004, Ma et al 2008, Durrleman et al 2009, Fletcher et al 2009, Durrleman et al 2011, Vialard et al 2012b, Lombaert et al 2014, Zhang and Fletcher 2015.…”

Section: Introductionmentioning

confidence: 99%

Primal-dual convex optimization in large deformation diffeomorphic metric mapping: LDDMM meets robust regularizers

Hernández

2017

Phys. Med. Biol.

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This paper proposes a method for primal-dual convex optimization in variational large deformation diffeomorphic metric mapping problems formulated with robust regularizers and robust image similarity metrics. The method is based on Chambolle and Pock primal-dual algorithm for solving general convex optimization problems. Diagonal preconditioning is used to ensure the convergence of the algorithm to the global minimum. We consider three robust regularizers liable to provide acceptable results in diffeomorphic registration: Huber, V-Huber and total generalized variation. The Huber norm is used in the image similarity term. The primal-dual equations are derived for the stationary and the non-stationary parameterizations of diffeomorphisms. The resulting algorithms have been implemented for running in the GPU using Cuda. For the most memory consuming methods, we have developed a multi-GPU implementation. The GPU implementations allowed us to perform an exhaustive evaluation study in NIREP and LPBA40 databases. The experiments showed that, for all the considered regularizers, the proposed method converges to diffeomorphic solutions while better preserving discontinuities at the boundaries of the objects compared to baseline diffeomorphic registration methods. In most cases, the evaluation showed a competitive performance for the robust regularizers, close to the performance of the baseline diffeomorphic registration methods.

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Section: Introductionmentioning

confidence: 99%

Primal-dual convex optimization in large deformation diffeomorphic metric mapping: LDDMM meets robust regularizers

Hernández

2017

Phys. Med. Biol.

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“…Shape is encoded by the spatial transformations existing between anatomical images and a template image selected as reference (Grenander 1994). Some particular groups of diffeomorphisms are well suited to represent these spatial transformations since these groups provide a strong mathematical setting for the computation of statistics (Fletcher et al 2004, Pennec 2006, Durrleman et al 2008, Pennec and Fillard 2009, Lorenzi and Pennec 2013b.…”

Section: Introductionmentioning

confidence: 99%

Gauss–Newton inspired preconditioned optimization in large deformation diffeomorphic metric mapping

Hernández

2014

Phys. Med. Biol.

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In this work, we propose a novel preconditioned optimization method in the paradigm of Large Deformation Diffeomorphic Metric Mapping (LDDMM). The preconditioned update scheme is formulated for the non-stationary and the stationary parameterizations of diffeomorphisms, yielding three different LDDMM methods. The preconditioning matrices are inspired in the Hessian approximation used in Gauss-Newton method. The derivatives are computed using Frechet differentials. Thus, optimization is performed in a Sobolev space, in contrast to optimization in L(2) commonly used in non-rigid registration literature. The proposed LDDMM methods have been evaluated and compared with their respective implementations of gradient descent optimization. Evaluation has been performed using real and simulated images from the Non-rigid Image Registration Evaluation Project (NIREP). The experiments conducted in this work reported that our preconditioned LDDMM methods achieved a performance similar or superior to well-established-in-literature gradient descent non-stationary LDDMM in the great majority of cases. Moreover, preconditioned optimization showed a substantial reduction in the execution time with an affordable increase of the memory usage per iteration. Additional experiments reported that optimization using Frechet differentials should be preferable to optimization using L(2) differentials.

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3D Statistical Shape Models Incorporating Landmark-Wise Random Regression Forests for Omni-Directional Landmark Detection

Norajitra

Maier‐Hein

2017

IEEE Trans. Med. Imaging

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3D Statistical Shape Models (3D-SSM) are widely used for medical image segmentation. However, during segmentation, they typically perform a very limited unidirectional search for suitable landmark positions in the image, relying on weak learners or use-case specific appearance models that solely take local image information into account. As a consequence, segmentation errors arise, and results in general depend on the accuracy of a previous model initialization. Furthermore, these methods become subject to a tedious and use-case dependent parameter tuning in order to obtain optimized results. To overcome these limitations, we propose an extension of 3D-SSM by landmark-wise random regression forests that perform an enhanced omni-directional search for landmark positions, thereby taking rich non-local image information into account. In addition, we provide a long distance model fitting based on a multi-scale approach, that allows an accurate and reproducible segmentation even from distant image positions, thus enabling an application without model initialization. Finally, translation of the proposed method to different organs is straightforward and requires no adaptation of the training process. In segmentation experiments on 45 clinical CT volumes, the proposed omni-directional search significantly increased accuracy and displayed great precision regardless of model initialization. Furthermore, for liver, spleen and kidney segmentation in a competitive multi-organ labeling challenge on publicly available data, the proposed method achieved similar or better results than the state of the art. Finally, liver segmentation results were obtained that successfully compete with specialized state-of-the-art methods from the well-known liver segmentation challenge SLIVER.

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Statistical Computing on Non-Linear Spaces for Computational Anatomy

Cited by 3 publications

References 67 publications

Primal-dual convex optimization in large deformation diffeomorphic metric mapping: LDDMM meets robust regularizers

Primal-dual convex optimization in large deformation diffeomorphic metric mapping: LDDMM meets robust regularizers

Gauss–Newton inspired preconditioned optimization in large deformation diffeomorphic metric mapping

3D Statistical Shape Models Incorporating Landmark-Wise Random Regression Forests for Omni-Directional Landmark Detection

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