Math 290J (section 2) current literature in applied mathematics
Mathematical models for image processing and medical imaging
(joint with the activity group SIG-PDE from the Center for Computational Biology)

Organizer: Luminita Vese. E-mail:

Location: MS 6118.

Presentations, Time and Location:

  • Wednesday, April 8, time 3-4pm (MS 6227)
    Speaker: Michael Moeller, visting student from Germany.
    Title: A Variational Approach for Sharpening High Dimensional Images.
    Abstract: Many earth observing satellites not only take ordinary red-green-blue (RGB) images but further include bands from the near-infrared and infrared spectrum and provide so called multispectral images. The additional bands greatly help in classification and identification tasks, but the drawback of the additional spectral information is that each spectral band has rather low spatial resolution. Therefore, many multispectral satellites such as Quickbird or the Landsat7 satellite include a panchromatic image at high spatial resolution.
    Pan-sharpening is the process of fusing a low resolution multispectral image with a high resolution panchromatic image to obtain a high resolution multispectral image. We propose a new pan-sharpening method called Variational Wavelet Pan-sharpening (VWP) that combines wavelet fusion and alligning the isocontours of each multipectral band with the panchromatic image as an energy minimization problem. Furthermore, we introduce additional energy terms to explicitly preserve the color information within each band and the correlation between bands.
    In this talk we present the VWP model, show numerical results and extend the model to sharpening hyperspectral images (with up to 210 bands) with the help of screenshots from Google Maps.

  • Wednesday, April 15, time 3-4pm
    Speaker: Rongjie Lai
    Title: Laplace-Beltrami Nodal Counts: a new signature for 3D shape analysis.
    Abstract: The analysis of 3D shapes is an important problem in medical imaging. By studying shapes, we can obtain detailed information about morphometry changes of anatomical structures. Recently there has been increasing interests in using the eigenvalues of the Laplace-Beltrami operators to study shapes. Features based on eigenvalues, however, have limitations in resolving isospectral shapes. To overcome this difficulty, we propose in this work a new signature derived from the nodal counts of eigenfunctions and demonstrate its advantage in classifying medical shapes.

  • Wednesday, April 22, time 3-4pm
    Speaker: Jian Liu
    Title: Controlling the Dynamics of Recurrent Neural Networks with Synaptic Learning Rule
    Abstract: The synaptic learning rules underlying the creation of stable propagation and reproducible neural trajectories within recurrent networks remains a fundamental problem in theoretical neuroscience. Here, we examine different synaptic learning rules, and find that the homeostatic presynaptic-dependent scaling (PSD) can achieve the above goal. By connecting the recurrent neurons to a output layer, it is possible to generate arbitrary spatiotemporal output motor patterns. To quantify the degree of network recurrence, we develop a recurrence index, which reveals that a functionally feed-forward network is shaped by learning with a single stimulus. However, learning with multiple stimuli establishes that: (1) multiple nonoverlapping stable trajectories can be embedded in the network; and (2) the recurrence index progressively increases as a function of the number of training stimuli. In addition we show that PSD and spike-timing-dependent plasticity together improve the ability of the network to incorporate multiple and less variable trajectories. Together these results establish a means to embed multiple trajectories within a spiking neural network in a self-organizing manner.

  • Wednesday, April 29, time 3-4pm

  • Wednesday, May 6, time 3-4pm
    Speaker: Yunho Kim

  • Wednesday, May 13, time 4-5pm, MS 6229 (note place and time changed)
    Invited speaker: Gilad Lerman, University of Minnesota
    Title: Multi-Manifold Data Modeling Via Spectral Curvature Clustering
    Abstract: We propose a fast multi-way spectral clustering algorithm for multi-manifold data modeling, i.e., modeling data by mixtures of manifolds (possibly intersecting). We describe the supporting theory as well as the practical choices guided by it. We first develop the case of hybrid linear modeling, i.e., when the underlying manifolds are affine subspaces in a Euclidean space, and then we extend this setting to more general manifolds. We exemplify the practical use of the algorithm by demonstrating its successful application to problems of motion segmentation.

  • Wednesday, May 20, time 3-4pm

  • Wednesday, May 27, time 3-4pm
    Speaker: Pascal Getreuer

  • Wednesday, June 3rd, time 3-4pm

  • Wednesday, June 10, time 3-4pm