AISEM series provide a unique opportunity for both new and returning students to interact with groups of the UW Artificial Intelligence community (including machine learning, bioinformatics, computer vision etc.) and hear about their research. Each seminar will feature a unique group. The seminar includes several short talks given by students in that group and a social time which the PI will be present. **Refreshments** are provided.

In this seminar, we will introduce Prof. Vikas Singh’s lab. Singh lab focuses on problems motivated from image data with a distinct optimization and/or geometric flavor in the field of Computer Vision, Medical Image Analysis, and Machine Learning. Three members of this lab, Maxwell Collins, Won Hwa Kim and Deepti Pachauri will present their work.

*Title* Random Walks based Multi-Image Segmentation: Quasiconvexity Results and GPU-based Solutions

*Speaker* Maxwell Collins

*Abstract* We recast the Cosegmentation problem using Random Walker (RW) segmentation as the core segmentation algorithm, rather than the traditional MRF approach adopted in the literature so far. Our formulation is similar to previous approaches in the sense that it also permits Cosegmentation constraints (which impose consistency between the extracted objects from ≥ 2 images) using a nonparametric model. However, several previous nonparametric cosegmentation methods have the serious limitation that they require adding one auxiliary node (or variable) for every pair of pixels that are similar (which effectively limits such methods to describing only those objects that have high entropy appearance models). In contrast, our proposed model completely eliminates this restrictive dependence — the resulting improvements are quite significant. Our model further allows an optimization scheme exploiting quasiconvexity for model-based segmentation with no dependence on the scale of the segmented foreground. Finally, we show that the optimization can be expressed in terms of linear algebra operations on sparse matrices which are easily mapped to GPU architecture. We provide a highly specialized CUDA library for Cosegmentation exploiting this special structure, and report experimental results showing these advantages.

*Title* Wavelet based multi-scale shape features on arbitrary surfaces for cortical thickness discrimination

*Speaker* Won Hwa Kim

*Abstract* Hypothesis testing on signals defined on surfaces (such as the cortical surface) is a fundamental component of a variety of studies in Neuroscience. The goal here is to identify regions that exhibit changes as a function of the clinical condition under study. As the clinical questions of interest move towards identifying very early signs of diseases, the corresponding statistical differences at the group level invariably become weaker and increasingly hard to identify. Indeed, after a multiple comparisons correction is adopted (to account for correlated statistical tests over all surface points), very few regions may survive. In contrast to hypothesis tests on point-wise measurements, in this paper, we make the case for performing statistical analysis on multi-scale shape descriptors that characterize the local topological context of the signal around each surface vertex. Our descriptors are based on recent results from harmonic analysis, that show how wavelet theory extends to non-Euclidean settings (i.e., irregular weighted graphs). We provide strong evidence that these descriptors successfully pick up group-wise differences, where traditional methods either fail or yield unsatisfactory results. Other than this primary application, we show how the framework allows performing cortical surface smoothing in the native space without mappint to a unit sphere.

*Title* Incorporating Domain Knowledge in Matching Problems via Harmonic Analysis

*Speaker* Deepti Pachauri

*Abstract* Matching one set of objects to another is a ubiquitous task in machine learning and com-
puter vision that often reduces to some form of the quadratic assignment problem (QAP).
The QAP is known to be notoriously hard, both in theory and in practice. Here, we in-
vestigate if this difficulty can be mitigated when some additional piece of information is
available: (a) that all QAP instances of interest come from the same application, and (b)
the correct solution for a set of such QAP instances is given. We propose a new approach
to accelerate the solution of QAPs based on learning parameters for a modified objective
function from prior QAP instances. A key feature of our approach is that it takes ad-
vantage of the algebraic structure of permutations, in conjunction with special methods
for optimizing functions over the symmetric group Sn in Fourier space. Experiments show
that in practical domains the new method can outperform existing approaches.