In this paper, we present a non-linear (multi-affine) registration algorithm based on a local polynomial expansion model. We generalize previous work using a quadratic polynomial expansion model. Local affine models are estimated using this generalized model analytically and iteratively, and combined to a deformable registration algorithm. Experiments show that the affine parameter calculations derived from this quadratic model are more accurate than using a linear model. Experiments further indicate that the multi-affine deformable registration method can handle complex non-linear deformation fields necessary for deformable registration, and a faster convergent rate is verified from our comparison experiment.

The inverse gradient problem, finding a scalar field f with a gradient near a given vector fieldgon some bounded and connected domain Ω ϵ R𝓃, can be solved by means of a Poisson equation with inhomogeneous Neumann boundary conditions. We present an elementary derivation of this partial differential equation and an efficient multigrid-based method to numerically compute the inverse gradient on non-rectangular domains. The utility of the method is demonstrated by a range of important medical applications such as phase unwrapping, pressure computation, inverse deformation fields, and fiber bundle tracking.

White matter fiber bundles in the human brain can be located by tracing the local water diffusion in diffusion weighted magnetic resonance imaging (MRI) images. In this paper, a novel Bayesian modeling approach for white matter tractography is presented. The uncertainty associated with estimated white matter fiber paths is investigated, and a method for calculating the probability of a connection between two areas in the brain is introduced. The main merits of the presented methodology are its simple implementation and its ability to handle noise in a theoretically justified way. Theory for estimating global connectivity is also presented, as well as a theorem that facilitates the estimation of the parameters in a constrained tensor model of the local water diffusion profile.

The paper makes a short presentation of three existing methods for estimation of orientation tensors, the so-called structure tensor, quadrature filter based techniques, and techniques based on approximating a local polynomial model. All three methods can be used for estimating an orientation tensor, which in the 3D case can be used for motion estimation. The methods are based on rather different approaches in terms of the underlying signal models. However, they produce more or less similar results, which indicates that there should be a common framework for estimation of the tensors. Such a framework is proposed, in terms of a second order mapping from signal to tensor with additional conditions on the mapping. It is also shown that the three methods in principle fall into this framework.

This contest involved the running and evaluation of computer vision and pattern recognition techniques on different data sets with known groundwidth. The contest included three areas; binary shape recognition, symbol recognition and image flow estimation. A package was made available for each area. Each package contained either real images with manual groundtruth or programs to generate data sets of ideal as well as noisy images with known groundtruth. They also contained programs to evaluate the results of an algorithm according to the given groundtruth. These evaluation criteria included the generation of confusion matrices, computation of the misdetection and false alarm rates and other performance measures suitable for the problems. The paper summarizes the data generation for each area and experimental results for a total of six participating algorithms.

Motion estimation in image sequences is an important step in many computer vision and image processing applications. Several methods for solving this problem have been proposed, but very few manage to achieve a high level of accuracy without sacrificing processing speed. This paper presents a novel motion estimation algorithm, which gives excellent results on both counts. The algorithm starts by computing 3D orientation tensors from the image sequence. These are combined under the constraints of a parametric motion model to produce velocity estimates. Evaluated on the well-known Yosemite sequence, the algorithm shows an accuracy substantially better than those obtained using previously published methods. Computationally, the algorithm is simple and can be implemented by means of separable convolutions, which also makes it fast.