Preface 1. Background in linear algebra 2. Discretization of partial differential equations 3. Sparse matrices 4. Basic iterative methods 5. Projection methods 6. Krylov subspace methods Part I 7. Krylov subspace methods Part II 8. Methods related to the normal equations 9. Preconditioned iterations 10. Preconditioning techniques 11. Parallel implementations 12. Parallel preconditioners 13. Multigrid methods 14. Domain decomposition methods Bibliography Index.

/pdf/iterative-methods-for-sparse-linear-systems-34ozhpwq89.pdf

Iterative Methods for Sparse Linear Systems

We propose a new model for active contours to detect objects in a given image, based on techniques of curve evolution, Mumford-Shah (1989) functional for segmentation and level sets. Our model can detect objects whose boundaries are not necessarily defined by the gradient. We minimize an energy which can be seen as a particular case of the minimal partition problem. In the level set formulation, the problem becomes a "mean-curvature flow"-like evolving the active contour, which will stop on the desired boundary. However, the stopping term does not depend on the gradient of the image, as in the classical active contour models, but is instead related to a particular segmentation of the image. We give a numerical algorithm using finite differences. Finally, we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable. Also, the initial curve can be anywhere in the image, and interior contours are automatically detected.

/pdf/active-contours-without-edges-2tt3qz9lq0.pdf

Active contours without edges

Co-Planar Stereotaxic Atlas of the Human Brain—3-Dimensional Proportional System: An Approach to Cerebral Imaging, J. Talairach, P. Tournoux. Georg Thieme Verlag, New York (1988), 122 pp., 130 figs. DM 268

Data Mining - Concepts and Techniques.

https://hal.archives-ouvertes.fr/hal-00417283/document

Independent component analysis, a new concept?

Inpainting refers to the task of filling in missing or damaged regions of an image. In this paper we are interested in the inpainting problem where the missing regions are so large that local inpainting methods fail. As an alternative to the local principle, we make use of other images with related global information to enable a reasonable inpainting. Our method has roughly three phases: landmark matching, interpolation, and copying. The experimental results obtained are promising.

Inpainting from multiple views

We study the problem of reconstructing a high-resolution image from multiple undersampled, shifted, degraded frames with subpixel displacement errors. The corresponding reconstruction operators H is a spatially variant operator. In this paper, instead of using the usual zero boundary condition, the Neumann boundary condition is imposed on the images. The resulting discretization matrix of H is a block-Toeplitz-Toeplitz-block-like matrix. We apply the preconditioned conjugate gradient (PCG) method with cosine transform preconditioner to solve the discrete problems. Preliminary results how that the image model under the Neumann boundary condition gives better reconstructed high-resolution images than that under the zero boundary condition, and the PCG method converges very fast.

/pdf/preconditioned-iterative-methods-for-high-resolution-image-3j855mlv78.pdf

Preconditioned iterative methods for high-resolution image reconstruction with multisensors

A logic framework for active contours on multi-channel images

We developed a general method for global conformal parameterizations based on the structure of the cohomology group of holomorphic one-forms with or without boundaries. 1, 2 For genus zero surfaces, our algorithm can find a unique mapping between any two genus zero manifolds by minimizing the harmonic energy of the map. In this paper, we apply the algorithm to the cortical surface matching problem. We use a mesh structure to represent the brain surface. Further constraints are added to ensure that the conformal map is unique. Empirical tests on MRI data show that the mappings preserve angular relationships, are stable in MRIs acquired at different times, and are robust to differences in data triangulation, and resolution. Compared with other brain surface conformal mapping algorithms, our algorithm is more stable and has good extensibility.

/pdf/intrinsic-brain-surface-conformal-mapping-using-a-bryqgpqs76.pdf

Intrinsic Brain Surface Conformal Mapping using a Variational Method

Publisher Summary This chapter discusses the numerical solution of mildly nonlinear problems by augmented Lagrangian methods. It partly carries on the work of CHAN-GLOWINSKI and extends the algorithmic part of it, in particular the part dealing with approximation by finite element methods and with the use of quadrature formulas. It is also seen how, by a judicious choice of the functional spaces and of the decomposition, one can obtain hybrid finite element methods and solve the corresponding approximate problems by augmented Lagrangian methods. This chapter presents some numerical results illustrating the potentialities of the methods described and one shall show the close links which exist between these algorithms and the alternating direction methods of Peaceman-Rachford and Douglas-Rachford.

Tony F. Chan

Papers

Inpainting from multiple views

Preconditioned iterative methods for high-resolution image reconstruction with multisensors

A logic framework for active contours on multi-channel images

Intrinsic Brain Surface Conformal Mapping using a Variational Method

Chapter IV Numerical Solution Of Mildly Nonlinear Problems By Augmented Lagrangian Methods