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
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.
Domain Decomposition for Total Variation Minimization
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
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