We study how the typical gradient and height of a random surface are modified by addition quenched disorder in form independent external field. The results provide quantitative estimates, sharp up to multiplicative constants, following cases. It is shown that for real-valued random-field surfaces $$\nabla \phi $$ type with uniformly convex interaction potential: (i) delocalizes dimensions $$1\l...

SEAN HO: Profile Scale Spaces for Statistical Image Match in Bayesian Segmentation (Under the direction of Guido Gerig, Ph.D.) Object boundaries in images often exhibit a complex greylevel appearance, and modeling of that greylevel appearance is important in Bayesian segmentation. Traditional image match models such as gradient magnitude or static templates are insufficient to model complex and...

Rainfall data are often collected at coarser spatial scales than required for input into hydrology and agricultural models. We therefore describe a spatio-temporal model which allows multiple imputation of rainfall at fine spatial resolutions, with a realistic dependence structure in both space and time and with the total rainfall at the coarse scale consistent with that observed. The method in...

The authors consider the problem of searching for activation in brain images obtained from functional magnetic resonance imaging and the corresponding functional signal detection problem. They develop a Bayesian procedure to detect signals existing within noisy images when the image is modeled as a scale space random field. Their procedure is based on the Radon–Nikodym derivative, which is used...

We present fixed domain asymptotic results that establish consistent estimates of the variance and scale parameters for a Gaussian random field with a geometric anisotropic Matérn autocovariance in dimension d > 4. When d < 4 this is impossible due to the mutual absolute continuity of Matérn Gaussian random fields with different scale and variance (see Zhang [J. Amer. Statist. Assoc. 99 (2004) ...

the aim of this paper is to establish random coincidence point results for weakly increasing random operators in the setting of ordered metric spaces by using generalized altering distance functions. our results present random versions and extensions of some well-known results in the current literature.

We present fixed domain asymptotic results that establish consistent estimates of the variance and scale parameters for a Gaussian random field with a geometric anisotropic Matérn autocovariance in dimension d > 4. When d < 4 this is impossible due to the mutual absolute continuity of Matérn Gaussian random fields with different scale and variance (see Zhang [33]). Informally, when d > 4, we sh...

This paper deals with the figure field, which is defined as the negative of the gradient vector field of the linear scale-space image. The scale-space hierarchy is obtained from the connectivity of stationary points determined by figure-field fluxes and trajectories of the stationary points in the scale space. A point at infinity plays an important role in this theory. The figure-field fluxes a...