Math 290J/2: current literature in applied mathematics, in conjunction with IPAM and LONI, CCB.

Organizer: Luminita Vese.

Topics: variational models, image analysis, medical imaging.

Schedule of talks:

Tuesday, April 8, 11am-12pm, location MS 7619.
Speaker: Igor Yanovsky
Title: Unbiased Nonlinear Image Registration
Abstract: We present a novel unbiased nonlinear image registration technique. The unbiased framework generates theoretically and intuitively correct deformation maps, and is compatible with large-deformation models. We apply information theory to quantify the magnitude of deformations and examine the statistical distributions of Jacobian maps in the logarithmic space. To demonstrate the power of the proposed framework, we generalize the well known large-deformation viscous fluid registration model to compute unbiased deformations. We show that unbiased fluid registration method generates more accurate maps compared to those generated with the viscous fluid registration model. We also propose a large-deformation image registration model based on nonlinear elastic regularization and unbiased registration. The new model is written in a unified variational form and is minimized using gradient descent on the corresponding Euler-Lagrange equations. The new unbiased nonlinear elastic registration model is computationally efficient and easy to implement. Furthermore, we examine the reproducibility and the power to detect real changes of different computational techniques. It is the first work to systematically investigate the reproducibility and variability of different registration methods in tensor based morphometry. In particular, we compare different matching functionals, as well as large deformation registration schemes using serial magnetic resonance imaging scans. Our results show that the unbiased methods have higher reproducibility than the conventional registration models. The unbiased methods are less likely to produce changes in the absence of any real physiological change. Moreover, they are also better in detecting biological deformations by penalizing any bias in the corresponding statistical maps. Finally, we extend the idea of the unbiased registration to simultaneously registering and tracking deforming objects in a sequence of two or more images. A level set based Chan-Vese multiphase segmentation model is generalized to consider Jacobian fields while segmenting regions of growth and shrinkage in deformations. Deforming objects are thus classified based on magnitude of homogeneous deformation.

Wednesday Apr 09, 4-5pm, MS 6229
Speaker: visiting graduate student George Papandreou, National Technical University of Athens.
Title: Multi-resolution techniques for efficient image analysis: Multigrid solution of PDEs and wavelet-domain modeling for image segmentation and inpainting
Abstract: Multi-resolution analysis is a powerful framework, both for modeling and for efficiently solving image analysis problems. In the first part of the talk we will discuss how popular PDE-based models can be efficiently handled using multigrid methods. The techniques developed can be used to numerically solve a wide range of level-set-based geometric active contour models and total variation/anisotropic diffusion PDE models at nearly interactive speeds. We demonstrate corresponding applications in image segmentation, image denoising, and image inpainting. In the second part of the talk we will discuss multi-resolution modeling in the wavelet domain, focusing on the probabilistic description of the wavelet coefficients of natural images using sparse and structured hierarchical models. We will present a recently proposed technique for image inpainting under such a wavelet-domain model.

Thursday, April 24th, 3.00pm, location IPAM 1200
Speaker: Carola Schoenlieb from Cambridge University, UK.
Title: Domain Decomposition for Total Variation Minimization
Abstract: We are interested in the application of domain decomposition methods to the minimization of functionals with total variation (TV) constraints. The main challenge of domain decomposition methods for TV minimization is that interesting solutions may be discontinuous, e.g., along curves in 2D. These discontinuities may cross the interfaces of the domain decomposition patches. These discontinuities may cross the interfaces of the domain decomposition patches. Hence, the crucial difficulty lies in the proper treatment of interfaces: we need both the preservation of crossing discontinuities and correct patching where the solution is continuous. In this talk we will present recent results on this task using an iterative proximity-map algorithm which is implemented via the so called oblique thresholding. Specifically, we will discuss its application for TV-image inpainting.

Future talks by:
Yunho Kim
Mi-Youn Jung
Tungyou Lin
Pascal Getreuer