The authors develop consistent nonparametric estimation techniques for the directional mixing density. Classical spherical harmonics are used to adapt Euclidean techniques to this directional environment. Minimax rates of convergence are obtained for rotationally invariant densities verifying various smoothness conditions. It is found that the difference in smoothness between the Laplace, the G...

We consider the problem of constructing of binary space partitions (BSP) for a set S of n hyperrectangles in arbitrary dimensional space. If the set S fulfills the low directional density condition defined in this paper then the resultant BSP has O(n) size and it can be constructed in O(n log n) time in R. The low directional density condition defines a new class of objects which we are able to...

This paper develops approximation techniques for directional densities by nite dimensional exponential densities. The methodology is to use expansions with respect to classical spherical harmonics followed by estimating the unknown parameters by maximum likelihood. The advantage of this approach is that one estimates directional probability densities by probability densities while at the same t...

Standard approaches to evaluate scar formation within histological sections rely on qualitative evaluations and scoring, which limits our understanding of the remodelling process. We have recently developed an image analysis technique for the rapid quantification of fibre alignment at each pixel location. The goal of this study was to evaluate its application for quantitatively mapping scar for...

We consider the problem of constructing of binary space partitions (BSP) for a set S of n hyperrectangles in arbitrary dimensional space. If the set S fulllls the low directional density condition deened in this paper then the resultant BSP has O(n) size and it can be constructed in O(n log 2 n) time in R 3. The low directional density condition deenes a new class of objects which we are able t...

The most common solutions to the light transport problem rely on either Monte Carlo (MC) integration or density estimation methods, such as uni& bi-directional path tracing or photon mapping. Recent gradient-domain extensions of MC approaches show great promise; here, gradients of the final image are estimated numerically (instead of the image intensities themselves) with coherent paths generat...

A procedure for estimating directional wave spectra from an array of wave probes based on the Maximum Entropy Method (MEM) is developed in the present paper. The MEM approach yields an angular spreading function at each frequency band consistent with the input crossspectral density matrix. The method is evaluated using numerical simulations of directional sea states. The MEM is also used to ana...

Our aim was to assess the integrity of the photoreceptors in the fovea, and to measure the optical density of the macular pigment and the eye lens in patients with diabetes mellitus, and to compare the results with those of a group of healthy subjects. The directional and spectral properties of the light reflected from a 1.9 deg field centered on the fovea were measured simultaneously, in a sin...