Fast no ground truth image registration accuracy evaluation: Comparison of bootstrap and Hessian approaches

Image registration algorithms provide a displacement field between two images. We consider the problem of estimating accuracy of the calculated displacement field from the input images only and without assuming any specific model for the deformation. We compare two algorithms: the first is based on bootstrap resampling, the second, new method, uses an estimate of the criterion Hessian matrix. We also present a block matching strategy using multiple window sizes where the final result is obtained by fusion of partial results controlled by the accuracy estimates for the blocks involved. Both accuracy estimation methods and the new registration strategy are experimentally compared on synthetic as well as real medical ultrasound data

Cortical mapping by Laplace-Cauchy transmission using a boundary element method.

International audienceThe Laplace-Cauchy problem of propagating Dirichlet and Neumann data from a portion to the rest of the boundary is an ill-posed inverse problem. Many regularizing algorithms have been recently proposed, in order to stabilize the solution with respect to noisy or incomplete data. Our main application is in electro-encephalography (EEG) where potential measurements available at part of the scalp are used to reconstruct the potential and the current on the inner skull surface. This problem, known as cortical mapping, and other applications --- in fields such as nondestructive testing, or biomedical engineering --- require to solve the problem in realistic, three-dimensional geometry. The goal of this article is to present a new boundary element based method for solving the Laplace-Cauchy problem in three dimensions, in a multilayer geometry. We validate the method experimentally on simulated data

Bootstrap Optical Flow Confidence and Uncertainty Measure

We address the problem of estimating the uncertainty of optical flow algorithm results. Our method estimates the error magnitude at all points in the image. It can be used as a confidence measure. It is based on bootstrap resampling, which is a computational statistical inference technique based on repeating the optical flow calculation several times for different randomly chosen subsets of pixel contributions. As few as ten repetitions are enough to obtain useful estimates of geometrical and angular errors. For demonstration, we use the combined local-global optical flow method (CLG) which generalizes both Lucas-Kanade and Horn-Schunck type methods. However, the bootstrap method is very general and can be applied to almost any optical flow algorithm that can be formulated as a pixel-based minimization problem. We show experimentally on synthetic as well as real video sequences with known ground truth that the bootstrap method performs better than all other confidence measures tested

Elastic image registration using parametric deformation models

The main topic of this thesis is elastic image registration for biomedical applications. We start with an overview and classification of existing registration techniques. We revisit the landmark interpolation which appears in the landmark-based registration techniques and add some generalizations. We develop a general elastic image registration algorithm. It uses a grid of uniform B-splines to describe the deformation. It also uses B-splines for image interpolation. Multiresolution in both image and deformation model spaces yields robustness and speed. First we describe a version of this algorithm targeted at finding unidirectional deformation in EPI magnetic resonance images. Then we present the enhanced and generalized version of this algorithm which is significantly faster and capable of treating multidimensional deformations. We apply this algorithm to the registration of SPECT data and to the motion estimation in ultrasound image sequences. A semi-automatic version of the registration algorithm is capable of accepting expert hints in the form of soft landmark constraints. Much fewer landmarks are needed and the results are far superior compared to pure landmark registration. In the second part of this thesis, we deal with the problem of generalized sampling and variational reconstruction. We explain how to reconstruct an object starting from several measurements using arbitrary linear operators. This comprises the case of traditional as well as generalized sampling. Among all possible reconstructions, we choose the one minimizing an a priori given quadratic variational criterion. We give an overview of the method and present several examples of applications. We also provide the mathematical details of the theory and discuss the choice of the variational criterion to be used

Fast Multipole Method for the Symmetric Boundary Element Method in MEG/EEG

The accurate solution of the forward electrostatic problem is an essential first step before solving the inverse problem of magneto- and electro-encephalography (MEG/EEG). The symmetric Galerkin boundary element method is accurate but is difficule to use for very large problems because of its computational complexity and memory requirements. We describe a fast multipole-based acceleration for the symmetric BEM with complexity. It creates a hierarchical structure of the elements and approximates far interactions using spherical harmonics expansions. The accelerated method is shown to be as accurate as the direct method, yet for large problems it is both faster and more economical in terms of memory consumption

Parallel integral projection transform for straight electrode localization in 3-D ultrasound images

In surgical practice, small metallic instruments are frequently used to perform various tasks inside the human body. We address the problem of their accurate localization in the tissue. Recent experiments using medical ultrasound have shown that this modality is suitable for real-time visualization of anatomical structures as well as the position of surgical instruments. We propose an image- processing algorithm that permits automatic estimation of the position of a line-segment-shaped object. This method was applied to the localization of a thin metallic electrode in biological tissue. We show that the electrode axis can be found through maximizing the parallel integral projection transform that is a form of the Radon transform. To accelerate this step, hierarchical mesh-grid algorithm is implemented. Once the axis position is known, localization of the electrode tip is performed. The method was tested on simulated images, on ultrasound images of a tissue mimicking phantom containing a metallic electrode, and on real ultrasound images from breast biopsy. The results indicate that the algorithm is robust with respect to variations in electrode position and speckle noise. Localization accuracy is of the order of hundreds of micrometers and is comparable to the ultrasound system axial resolution

Consistent and elastic registration of histological sections using vector-spline regularization

The final publication is available at Springer via http://dx.doi.org/10.1007/11889762_8Revised Papers on Second International ECCV Workshop, CVAMIA 2006 Graz, Austria, May 12, 2006Here we present a new image registration algorithm for the alignment of histological sections that combines the ideas of B-spline based elastic registration and consistent image registration, to allow simultaneous registration of images in two directions (direct and inverse). In principle, deformations based on B-splines are not invertible. The consistency term overcomes this limitation and allows registration of two images in a completely symmetric way. This extension of the elastic registration method simplifies the search for the optimum deformation and allows registering with no information about landmarks or deformation regularization. This approach can also be used as the first step to solve the problem of group-wise registration.Ignacio Arganda-Carreras is being supported by a predoctoral FPI-CAM fellow- ship since October 2003. Carlos Ortiz-de-Solorzano is supported by a Ramon y Cajal (Spanish Ministry of Education and Science ryc-2004-002353) and a Marie Curie International Reintegration Grant (FP6-518688). Jan Kybic was sponsored by the Czech Ministery of Education under project number MSM210000012. Par- tial support is acknowledged to Comunidad de Madrid through grant GR/SAL/0234, to Instituto de Salud Carlos III-Fondo de Investigaciones Sanitarias (FIS) through the IM3 Network and grant 040683 and to the Plan Nacional de Investigación Científica, Desarrollo e Innovación Tecnológica (I+D+I)

Integral Formulations for the EEG Problem

The forward electro-encephalography (EEG) problem involves finding a potential V from the Poisson equation (V)=f, in which f represents electrical sources in the brain, and the conductivity of the head tissues. In the piecewise constant conductivity head model, this can be accomplished by the Boundary Element Method (BEM) using a suitable integral formulation. Most previous work is based on the same integral formulation, based on a double-lay- er potential. In this article we detail several alternative possibilities. We present a dual approach which involves a single-layer potential. Finally, we propose a symmetric formulation, which combines single and double-layer potentials, and which is new to the field of EEG, although it has been applied to other problems in electromagnetism. The three methods have been evaluated numerically using a semi-realistic geometry with known analytical solution, and the symmetric method achieves a significantly higher accuracy