Reliability-Driven, Spatially-Adaptive Regularization for Deformable Registration

Tang, Lisa; Hamarneh, Ghassan; Abugharbieh, Rafeef

doi:10.1007/978-3-642-14366-3_16

Cited by 19 publications

(15 citation statements)

References 28 publications

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“…There are few formulations of the traditional MRF for solving the discrete registration problem. When the smoothing term Ψ ij is a metric, the MRF energy can efficiently be optimized using graph cuts [10,8]. For more complex interaction terms, Glocker et al [9] use a linear programming method (based on the primal-dual principle).…”

Section: Discrete Formulation For the Random Walker Algorithmmentioning

confidence: 99%

“…One other way of imposing regularization is to restrict the space of deformations to a Sobolev space [6]. Some effort has been made to adapt the regularization of deformations to local image content [7,8]. This is particularly important considering that different tissue deform differently and parts of the image might contain an abnormality that does not match the atlas.…”

Section: Introductionmentioning

confidence: 99%

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Random Walks for Deformable Image Registration

Cobzaş

Sen

2011

Lecture Notes in Computer Science

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Abstract. We introduce a novel discrete optimization method for nonrigid image registration based on the random walker algorithm. We discretize the space of deformations and formulate registration using a Gaussian MRF where continuous labels correspond to the probability of a point having a certain discrete deformation. The interaction (regularization) term of the corresponding MRF energy is convex and image dependent, thus being able to accommodate different types of tissue elasticity. This formulation results in a fast algorithm that can easily accommodate a large number of displacement labels, has provable robustness to noise and a close to global solution. We experimentally demonstrate the validity of our formulation on synthetic and real medical data.

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Section: Discrete Formulation For the Random Walker Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Random Walks for Deformable Image Registration

Cobzaş

Sen

2011

Lecture Notes in Computer Science

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“…Recently, registration approaches that represent transformations in the discrete domain have arisen [5,3,12,13]. In discrete approaches every pixel (or voxel) is assigned a displacement vector from a predefined set, referred to as a discrete transformation, allowing the image registration energy to be formulated as a Markov random field (MRF) and well established optimization techniques such as graph cuts [2] to be utilized.…”

Section: Introductionmentioning

confidence: 99%

“…A useful feature of RWIR is that it seamlessly allows for spatially adaptive regularization weights, which have been shown to improve registration accuracy compared to a constant regularization weight [12]. However, it is not clear a priori how much regularization is required in RWIR to ensure topology preservation.…”

Section: Introductionmentioning

confidence: 99%

Topology Preservation and Anatomical Feasibility in Random Walker Image Registration

Andrews

Tang

Hamarneh

2014

Medical Image Computing and Computer-Assisted Intervention – MICCAI 2014

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Abstract. The random walker image registration (RWIR) method is a powerful tool for aligning medical images that also provides useful uncertainty information. However, it is difficult to ensure topology preservation in RWIR, which is an important property in medical image registration as it is often necessary for the anatomical feasibility of an alignment. In this paper, we introduce a technique for determining spatially adaptive regularization weights for RWIR that ensure an anatomically feasible transformation. This technique only increases the run time of the RWIR algorithm by about 10%, and avoids over-smoothing by only increasing regularization in specific image regions. Our results show that our technique ensures topology preservation and improves registration accuracy.

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“…In rigid registration, the influence of mismatching regions can be drastically reduced by cropping the image distance function, e.g., by using Tukey's biweight instead of squared error as an instance of robust statistics [17]. In non-rigid registration, one can estimate a local measure of image data reliability to spatially adapt the strength of regularization [18], while in atlas-based registration this information can equally be derived from atlas statistics.…”

Section: Introductionmentioning

confidence: 99%

Geodesic Active Fields—A Geometric Framework for Image Registration

Zosso

Bresson

Thiran

2011

IEEE Trans. on Image Process.

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Abstract-In this paper we present a novel geometric framework called geodesic active fields for general image registration. In image registration, one looks for the underlying deformation field that best maps one image onto another. This is a classic ill-posed inverse problem, which is usually solved by adding a regularization term. Here, we propose a multiplicative coupling between the registration term and the regularization term, which turns out to be equivalent to embed the deformation field in a weighted minimal surface problem. Then, the deformation field is driven by a minimization flow toward a harmonic map corresponding to the solution of the registration problem. This proposed approach for registration shares close similarities with the well-known geodesic active contours model in image segmentation, where the segmentation term (the edge detector function) is coupled with the regularization term (the length functional) via multiplication as well. As a matter of fact, our proposed geometric model is actually the exact mathematical generalization to vector fields of the weighted length problem for curves and surfaces introduced by Caselles-Kimmel-Sapiro [1]. The energy of the deformation field is measured with the Polyakov energy weighted by a suitable image distance, borrowed from standard registration models. We investigate three different weighting functions, the squared error and the approximated absolute error for monomodal images, and the local joint entropy for multimodal images. As compared to specialized state-of-theart methods tailored for specific applications, our geometric framework involves important contributions. Firstly, our general formulation for registration works on any parametrizable, smooth and differentiable surface, including non-flat and multiscale images. In the latter case, multiscale images are registered at all scales simultaneously, and the relations between space and scale are intrinsically being accounted for. Secondly, this method is, to the best of our knowledge, the first re-parametrization invariant registration method introduced in the literature. Thirdly, the multiplicative coupling between the registration term, i.e. local image discrepancy, and the regularization term naturally results in a data-dependent tuning of the regularization strength. Finally, by choosing the metric on the deformation field one can freely interpolate between classic Gaussian and more interesting anisotropic, TV-like regularization.

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Reliability-Driven, Spatially-Adaptive Regularization for Deformable Registration

Cited by 19 publications

References 28 publications

Random Walks for Deformable Image Registration

Random Walks for Deformable Image Registration

Topology Preservation and Anatomical Feasibility in Random Walker Image Registration

Geodesic Active Fields—A Geometric Framework for Image Registration

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