An interpolation model is a necessary ingredient of intensity-based registration methods. The properties of such
a model depend entirely on its basis function, which has been traditionally characterized by features such as its
order of approximation and its support. However, as has been recently shown, these features are blind to the
amount of registration bias created by the interpolation process alone; an additional requirement that has been
named constant-variance interpolation is needed to remove this bias.
In this paper, we present a theoretical investigation of the role of the interpolation basis in a registration
context. Contrarily to published analyses, ours is deterministic; it nevertheless leads to the same conclusion,
which is that constant-variance interpolation is beneficial to image registration.
In addition, we propose a novel family of interpolation bases that can have any desired order of approximation
while maintaining the constant-variance property. Our family includes every constant-variance basis we know
of. It is described by an explicit formula that contains two free functional terms: an arbitrary 1-periodic binary
function that takes values from {-1, 1}, and another arbitrary function that must satisfy the partition of unity.
These degrees of freedom can be harnessed to build many family members for a given order of approximation
and a fixed support. We provide the example of a symmetric basis with two orders of approximation that is
supported over [-3/2, 3/2] this support is one unit shorter than a basis of identical order that had been previously
Assembling partial views is an attractive means to extend the field of view of microscope images. In this paper, we propose a semi-automated solution to achieve this goal. Its intended audience is the microscopist who desires to scan a large area while acquiring a series of partial views, but who does not wish to--or cannot--planify the path of the scan. In a first stage, this freedom is dealt with by interactive manipulation of the resulting partial views, or tiles. In a second stage, the position of the tiles is refined by a fully automatic pairwise registration process. The contribution of this paper is a strategy that determines which pairs of tiles to register, among all possible pairs.
The central tenet of our proposed strategy is that two tiles that happen to possess a large common area will register with higher accuracy than two tiles with a smaller overlap. Our strategy is then to minimize the number of pairwise registrations while maximizing the global amount of overlap, and while ensuring that the local registration efforts are sufficient to link all tiles together to yield a global mosaic. By stating this requirement in a graph-theoretic context, we are able to derive the optimal solution thanks to Kruskal's algorithm.
We have developed an algorithm for the rigid-body registration of a 3D CT to a set of C-arm images by matching them to computed cone-beam projections of the CT (DRRs). We precomputed rescaled versions (pyramid) of the CT volume and of the C-arm images. We perform the registration of the CT to the C-arm images starting from their coarsest resolution until we reach some finer resolution that offers a good compromise between time and accuracy. To achieve precision, we use a cubic-spline data model to compute the data pyramids, the DRRs, and the gradient and the Hessian of the cost function. We validate our algorithm on a 3D CT and on C-arm images of a cadaver spine using fiducial markers. When registering the CT to two C-arm images, our algorithm operates safely if the angle between the two image planes is larger than 10°. It achieves an accuracy with a mean and a standard deviation of approximately 2.0±1.0 mm.
We propose an algorithm for aligning a preoperative computed tomography (CT) volume and intraoperative C-arm images, with applications in computer-assisted spinal surgery. Our three-dimensional (3D)/two-dimensional (2D) registration algorithm is based on splines and is tuned to a multiresolution strategy. Its goal is to establish the mutual relations of locations in the real-world scene to locations in the 3D CT and in the 2D C-arm images. The principle of the solution is to simulate a series of C-arm images, using CT data only. Each numerical simulation of a C-arm image is defined by its pose. Our registration algorithm then adjusts this pose until the given C-arm projections and the simulated projections exhibit the greatest degree of similarity. We show the performance of the algorithm for the experiments in a controlled environment which allows for an objective validation of the quality of our algorithm. For each of 100 randomly generated disturbances around the optimum solution, the 3D/2D registration algorithm was successful and resulted in image registration with subpixel error.
KEYWORDS: Data modeling, Receptors, Positron emission tomography, Data processing, Spatial resolution, Convolution, In vivo imaging, Molecules, Plasma, Blood
The aim of this study is to obtain voxel-by-voxel images of binding parameters between [11C]-flumazenil and benzodiazepine receptors using positron emission tomography (PET). We estimate five local parameters (k1, k2, B'max, kon/VR, koff) by fitting a three- compartment ligand-receptor model for each voxel of a PET time series. It proves difficult to fit the ligand-receptor model to the data. We trade noise and spatial resolution to get better results. Our strategy is based on the use of a multiresolution pyramid. It is much easier to solve the problem at coarse resolution because there are fewer data to process. To increase resolution, we expand the parameter maps to the next finer level and use them as initial solution to further optimization, which then proceeds at a fast pace and is more likely to escape false local minima. For this approach to work optimally, the residue between data at a given pyramid level and data at the next level must be as small as possible. We satisfy this constraint by working with spline-based least- squares pyramids. To achieve speed, the optimizer must be efficient, particularly when it is nearing the solution. To that effect, we have developed a Marquardt-Levenberg algorithm that exhibits superlinear convergence properties.
Registration of images subject to non-linear warping has numerous practical applications. We present an algorithm based on double multiresolution structure of warp and image spaces. Tuning a so-called scale parameter controls the coarseness of the grid by which the deformation is described and also the amount of implicit regularization. The application of our algorithm deals with undoing unidirectional non-linear geometrical distortion of echo- planar images (EPI) caused by local magnetic field inhomogeneities induced mainly by the subject presence. The unwarping is based on registering the EPI images with corresponding undistorted anatomical MRI images. We present evaluation of our method using a wavelet-based random Sobolev-type deformation generator as well as other experimental examples.
One of the earliest models of stochastic growth was originally developed for simulating the appearance of various biological patterns; in particular, bacterial colonies. Although it received little attention from biologists, some twenty years later it was adopted by crystallographers, solid state researchers, other physicists and chemists. Because of the model's flexibility it is being used by them after modifications appropriate to the application, in order to simulate their physical study objects under a variety of conditions. Only within the last few years has there been any interest in using this and similar digital models to represent the possible products of biological processes. It is also worth noting that aside from its relevance to probabilistically influenced pattern formation, the model has possible use in image processing for image compression and as an information-lossless way to code, regions, contours, or line segments.
We propose a new optimizer for multiresolution image registration. It is adapted to a criterion known as mutual information and is well suited to inter-modality. Our iteration strategy is inspired by the Marquardt-Levenberg algorithm, even though the underlying problem is not least- squares. We develop a framework based on a continuous polynomial spline representation of images. Together with the use of Parzen histogram estimates, it allows for closed- form expressions of the gradient and Hessian of the criterion. Tremendous simplifications result from the choice of Parzen windows satisfying the partition of unity, also based on B-splines. We use this framework to compute an image pyramid and to set our optimizer in a multiresolution context. We perform several experiments and show that it is particularly well adapted to a coarse-to-fine optimization strategy. We compare our approach to the popular Powell algorithm and conclude that our proposed optimizer is faster, at no cost in robustness or precision.
We present examples of a new type of wavelet basis functions that are orthogonal across shifts, but not across scales. The analysis functions are low order splines while the synthesis functions are polynomial splines of higher degree n2. The approximation power of these representations is essentially as good as that of the corresponding Battle- Lemarie orthogonal wavelet transform, with the difference that the present wavelet synthesis filters have a much faster decay. This last property, together with the fact that these transformation s are almost orthogonal, may be useful for image coding and data compression.
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