Math 290J (section 2) current literature in applied mathematics
Mathematical models in image processing and analysis

Organizer: Luminita Vese. E-mail: lvese@math.ucla.edu

Time: Friday, 12:00pm-1:00pm.

Location: MS 5128.

Presentations, Time and Location:
Please note that some meetings will be at a different time and location. All meetings will be announced by email.

Format: Graduate students give presentations from current literature in the field.

  • Friday, October 1st: Rami Mohieddine (UCLA Mathematics), Open curve evolution for Mumford-Shah segmentation models and motion of junctions.
    Preparatory references:
    - A Variational Level Set Approach to Multiphase Motion (Zhao, Chan, Merriman, Osher); http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.25.3048
    - Motion of multiple junctions (Merriman, Bence, Osher); http://www.math.lsa.umich.edu/~psmereka/LEVELSET/LSPAPERS/zzmbo.pdf
    - Optimal approximations by piecewise-smooth functions and associated variational problems (Mumford-Shah) http://www.dfmf.uned.es/~daniel/www-imagen-dhp/biblio/mumford-shah-original.pdf
    - Spiral Crystal Growth (Smereka) http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.37.4928
    - A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model (Chan-Vese) http://www.math.ucla.edu/~lvese/PAPERS/IJCV2002.pdf

  • Friday, October 8: Ming Yan (UCLA Mathematics and CDSC), EM+TV method for image reconstruction in computerized tomography
    Preparatory references:

  • Friday, October 15: Guest speaker, Hemant Tagare, Yale University: The Geometry of Non-rigid Registration
    Abstract: Computational procedures for rigid and non-rigid registration are widely used, but a conceptual and theoretical framework for understanding these procedures has been scarce. Such a framework is critical for designing a new generation of registration algorithms - algorithms with guaranteed (i.e. provable) properties. Research presented in this talk suggests that viewing registration algorithms from a geometric point-of-view provides a basis for understanding registration. In this framework, intra- and inter-modality registration appear on common ground and the fundamental role of the geometric volume form becomes clear. Different volume forms give registration algorithms with different properties. Four properties of registration objective functions are identified as useful, and a unique volume form is shown to impart these properties. Experimental results confirm that the theoretical results hold in practice even in the presence of noise in the images.
    Preparatory references:
    Symmetric Non-rigid Registration: A Geometric Theory and Some Numerical Techniques (Tagare et al) http://www.springerlink.com/content/577652v3320822m0/fulltext.pdf

  • Friday, October 22: Egil Bae, visiting student from University of Bergen and IPAM, Global optimization methods for interphase problems in image processing
    Preparatory references:

  • Friday, October 29 (Guest speaker): Xue-Cheng Tai (University of Bergen, Norway), on Augmented Lagrangian Method for Generalized TV-Stokes Model
    Abstract. In this paper, we propose a general form of TV-Stokes models and provide an efficient and fast numerical algorithm based on the augmented Lagrangian method. The proposed model and numerical algorithm can be used for a number of applications such as image inpainting, image decomposition, surface reconstruction from sparse gradient, direction denoising, and image denoising. Comparing with properties of different norms in regularity term and fidelity term, various results are investigated in applications. We numerically show that the proposed model recovers jump discontinuities.
    Preparatory references: UCLA CAM Report 10-30, link ftp://ftp.math.ucla.edu/pub/camreport/cam10-30.pdf

  • Friday, November 5: TBA
    Preparatory references:

  • Friday, November 12: Guest speaker, Igor Yanovsky, JPL
    Title: Inverse Problems in Remote Sensing
    Abstract: Remote sensing is the science of deriving information about objects from images acquired by remote instruments. Nonlinear model of radiative transfer, which describes physical phenomenon of energy transfer in the form of electromagnetic radiation, is used for constructing forward models for obtaining radiances by instruments onboard spacecraft. We describe the forward model for the Earth Observing System (EOS) Microwave Limb Sounder (MLS) onboard Aura satellite. We then describe the analytic computation of Jacobians and the inverse method for estimating the atmospheric composition from radiances. The approach is based on Bayesian formulation, and an associated energy function is minimized using nonlinear estimation methods.

  • Friday, November 19: TBA
    Preparatory references:

  • Friday, November 26 (no meeting due to Thanksgiving Holiday)

  • Friday, December 3rd: TBA
    Preparatory references: