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: email@example.com
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
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
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