In this paper we introduce a novel and efficient approach to dense image registration, which does not require a derivative of the employed cost function. In such a context the registration problem is formulated using a discrete Markov Random Field objective function. First, towards dimensionality reduction on the variables we assume that the dense deformation field can be expressed using a small number of control points (registration grid) and an interpolation strategy. Then, the registration cost is expressed using a discrete sum over image costs (using an arbitrary similarity measure) projected on the control points, and a smoothness term that penalizes local deviations on the deformation field according to a neighborhood system on the grid. Towards a discrete approach the search space is quantized resulting in a fully discrete model. In order to account for large deformations and produce results on a high resolution level a multi-scale incremental approach is considered where the optimal solution is iteratively updated. This is done through successive morphings of the source towards the target image. Efficient linear programming using the primal dual principles is considered to recover the lowest potential of the cost function. Very promising results using synthetic data with known deformations and real data demonstrate the potentials of our approach.

Modern morphometric studies use non-linear image registration to compare anatomies and perform group analysis. Recently, log-Euclidean approaches have contributed to promote the use of such computational anatomy tools by permitting simple computations of statistics on a rather large class of invertible spatial transformations. In this work, we propose a non-linear registration algorithm perfectly fit for log-Euclidean statistics on diffeomorphisms. Our algorithm works completely in the log-domain, i.e. it uses a stationary velocity field. This implies that we guarantee the invertibility of the deformation and have access to the true inverse transformation. This also means that our output can be directly used for log-Euclidean statistics without relying on the heavy computation of the log of the spatial transformation. As it is often desirable, our algorithm is symmetric with respect to the order of the input images. Furthermore, we use an alternate optimization approach related to Thirion’s demons algorithm to provide a fast non-linear registration algorithm. First results show that our algorithm outperforms both the demons algorithm and the recently proposed diffeomorphic demons algorithm in terms of accuracy of the transformation while remaining computationally efficient.

Multi-subject non-rigid registration algorithms using dense deformation fields often encounter cases where the transformation to be estimated has a large spatial variability. In these cases, linear stationary regularization methods are not su#cient. In this paper, we present an algorithm that uses a priori information about the nature of imaged objects in order to adapt the regularization of the deformations. We also present a robustness improvement that gives higher weight to those points in images that contain more information. Finally, a fast parallel implementation using networked personal computers is presented. In order to improve the usability of the parallel software by a clinical user, we have implemented it as a grid service that can be controlled by a graphics workstation embedded in the clinical environment. Results on inter-subject pairs of images show that our method can take into account the large variability of most brain structures. The registration time for images 124 is 5 minutes on 15 standard PCs. A comparison of our non-stationary visco-elastic smoothing versus solely elastic or fluid regularizations shows that our algorithm converges faster towards a more optimal solution in terms of accuracy and transformation regularity.

We propose an efficient non-parametric diffeomorphic image registration algorithm based on Thirion’s demons algorithm. In the first part of this paper, we show that Thirion’s demons algorithm can be seen as an optimization procedure on the entire space of displacement fields. We provide strong theoretical roots to the different variants of Thirion’s demons algorithm. This analysis predicts a theoretical advantage for the symmetric forces variant of the demons algorithm. We show on controlled experiments that this advantage is confirmed in practice and yields a faster convergence. In the second part of this paper, we adapt the optimization procedure underlying the demons algorithm to a space of diffeomorphic transformations. In contrast to many diffeomorphic registration algorithms, our solution is computationally efficient since in practice it only replaces an addition of displacement fields by a few compositions. Our experiments show that in addition to being diffeomorphic, our algorithm provides results that are similar to the ones from the demons algorithm but with transformations that are much smoother and closer to the gold standard, available in controlled experiments, in terms of Jacobians.

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We propose a learning method which introduces explicit knowledge to the object correspondence problem. Our approach uses an a priori learning set to compute a dense correspondence field between two objects, where the characteristics of the field bear close resemblance to those in the learning set. We introduce a new local shape measure we call the "observed transport measure", whose properties make it particularly amenable to the matching problem. From the values of our measure obtained at every point of the objects to be matched, we compute a distance matrix which embeds the correspondence problem in a highly expressive and redundant construct and facilitates its manipulation. We present two learning strategies that rely on the distance matrix and discuss their applications to the matching of a variety of 1-D, 2-D and 3-D objects, including the corpus callosum and ventricular surfaces.

We propose a non-parametric diffeomorphic image registration algorithm based on Thirion’s demons algorithm. The demons algorithm can be seen as an optimization procedure on the entire space of displacement fields. The main idea of our algorithm is to adapt this procedure to a space of diffeomorphic transformations. In contrast to many diffeomorphic registration algorithms, our solution is computationally efficient since in practice it only replaces an addition of free form deformations by a few compositions. Our experiments show that in addition to being diffeomorphic, our algorithm provides results that are similar to the ones from the demons algorithm but with transformations that are much smoother and closer to the true ones in terms of Jacobians.

Abstract—In this paper, we propose the DT-REFinD algorithm for the diffeomorphic nonlinear registration of diffusion tensor images. Unlike scalar images, deforming tensor images requires choosing both a reorientation strategy and an interpolation scheme. Current diffusion tensor registration algorithms that use full tensor information face difficulties in computing the differential of the tensor reorientation strategy and consequently, these methods often approximate the gradient of the objective function. In the case of the finite-strain (FS) reorientation strategy, we borrow results from the pose estimation literature in computer vision to derive an analytical gradient of the registration objective function. By utilizing the closed-form gradient and the velocity field representation of one parameter subgroups of diffeomorphisms, the resulting registration algorithm is diffeomorphic and fast. We contrast the algorithm with a traditional FS alternative

Stereotactic neurosurgery for Parkinson's disease consists of stimulating deep nuclei of the brain. Although target coordinates are calculated with high precision on the pre-operative images, cerebrospinal fluid (CSF) leakage during the procedure can lead to a brain deformation and cause potential error with respect to the surgical planning.

As image registration becomes more and more central to many biomedical imaging applications, the efficiency of the algorithms becomes a key issue. Image registration is classically performed by optimizing a similarity criterion over a given spatial transformation space. Even if this problem is considered as almost solved for linear registration, we show in this paper that some tools that have recently been developed in the field of vision-based robot control can outperform classical solutions. The adequacy of these tools for linear image registration leads us to revisit non-linear registration and allows us to provide interesting theoretical roots to the different variants of Thirion’s demons algorithm. This analysis predicts a theoretical advantage to the symmetric forces variant of the demons algorithm. We show that, on controlled experiments, this advantage is confirmed, and yields a faster convergence.