Coupled Harmonic Bases for Longitudinal Characterization of Brain Networks.

There is a great deal of interest in using large scale brain imaging studies to understand how brain connectivity evolves over time for an individual and how it varies over different levels/quantiles of cognitive function. To do so, one typically performs so-called tractography procedures on diffusion MR brain images and derives measures of brain connectivity expressed as graphs. The nodes correspond to distinct brain regions and the edges encode the strength of the connection.

A Projection free method for Generalized Eigenvalue Problem with a nonsmooth Regularizer.

Eigenvalue problems are ubiquitous in computer vision, covering a very broad spectrum of applications ranging from estimation problems in multi-view geometry to image segmentation. Few other linear algebra problems have a more mature set of numerical routines available and many computer vision libraries leverage such tools extensively. However, the ability to call the underlying solver only as a "black box" can often become restrictive.

Multivariate General Linear Models (MGLM) on Riemannian Manifolds with Applications to Statistical Analysis of Diffusion Weighted Images.

Linear regression is a parametric model which is ubiquitous in scientific analysis. The classical setup where the observations and responses, i.e.

Incorporating User Interaction and Topological Constraints within Contour Completion via Discrete Calculus.

We study the problem of interactive segmentation and contour completion for multiple objects. The form of constraints our model incorporates are those coming from user scribbles (interior or exterior constraints) as well as information regarding the topology of the 2-D space after partitioning (number of closed contours desired). We discuss how concepts from discrete calculus and a simple identity using the Euler characteristic of a planar graph can be utilized to derive a practical algorithm for this problem.

Random walks based multi-image segmentation: Quasiconvexity results and GPU-based solutions.

We recast the 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).

Analyzing the Subspace Structure of Related Images: Concurrent Segmentation of Image Sets.

We develop new algorithms to analyze and exploit the joint subspace structure of a set of related images to facilitate the process of concurrent segmentation of a large set of images. Most existing approaches for this problem are either limited to extracting a single similar object across the given image set or do not scale well to a large number of images containing multiple objects varying at different scales. One of the goals of this paper is to show that various desirable properties of such an algorithm (ability to handle images with objects showing scale variations) can be cast elegantly using simple constructs from linear algebra: this significantly extends the operating range of such methods.