We consider the problem of semi-supervised regression when the predictor variables are drawn from an unknown manifold. A simple approach to this problem is to first use both the labeled and unlabeled data to estimate the manifold geodesic distance between pairs of points, and then apply a k nearest neighbor regressor based on these distance estimates. We prove that given sufficiently many unlab...

This paper presents a method for 3D segmentation of kidneys from patients with autosomal dominant polycystic kidney disease (ADPKD) and severe renal insufficiency, using computed tomography (CT) data. ADPKD severely alters the shape of the kidneys due to non-uniform formation of cysts. As a consequence, fully automatic segmentation of such kidneys is very challenging. We present a segmentation ...

Principal Author’s Biography Shalini Gupta received a BE degree in Electronics and Electrical Communication Engineering from Punjab Engineering College, India. She received a MS degree in Electrical and Computer Engineering from the University of Texas at Austin, where she is currently a PhD student. During her masters, she developed techniques for computer aided diagnosis of breast cancer. She...

Geodesic regression generalizes linear regression to general Riemannian manifolds. Applied to images, it allows for a compact approximation of an image time-series through an initial image and an initial momentum. Geodesic regression requires the definition of a squared residual (squared distance) between the regression geodesic and the measurement images. In principle, this squared distance sh...

Combining sample plot and image data has been widely used to map forest carbon density at local, regional, national and global scales. When mapping is conducted using multiple spatial resolution images at different scales, field observations have to be collected at the corresponding resolutions to match image values in pixel sizes. Given a study area, however, to save time and cost, field obser...

We present a heuristic algorithm to compute approximate geodesic distances on a triangular manifold S containing n vertices with partially missing data. The proposed method computes an approximation of the geodesic distance between two vertices pi and pj on S and provides an upper bound of the geodesic distance that is shown to be optimal in the worst case. This yields a relative error bound of...

Abstract A conjecture of Burns and Knieper (1991) asks whether a 2-plane with metric without conjugate points, geodesic foliation whose lines are at bounded Hausdorff distance, is necessarily flat. We prove this in two cases: under the hypothesis that plane admits total curvature, visibility some point. Along way, we show all line foliations on Riemannian must be homeomorphic to standard one.