Projection-Slice Theorem as a Tool for Mathematical Representation of Diffraction

Cataloged from PDF version of article.Although the impulse (Dirac delta) function has been widely used as a tool in signal processing, its more complicated counterpart, the impulse function over higher dimensional manifolds in R-N, did not get such a widespread utilization. Based on carefully made definitions of such functions, it is shown that many higher dimensional signal processing problems can be better formulated, yielding more insight and flexibility, using these tools. The well-known projection-slice theorem is revisited using these impulse functions. As a demonstration of the utility of the projection-slice formulation using impulse functions over hyperplanes, the scalar optical diffraction is reformulated in a more general context

Sampling of the diffraction field

Cataloged from PDF version of article.When optical signals, like diffraction patterns, are processed by digital means the choice of sampling density and geometry is important during analog-to-digital conversion. Continuous band-limited signals can be sampled and recovered from their samples in accord with the Nyquist sampling criteria. The specific form of the convolution kernel that describes the Fresnel diffraction allows another, alternative, full-reconstruction procedure of an object from the samples of its diffraction pattern when the object is space limited. This alternative procedure is applicable and yields full reconstruction even when the diffraction pattern is undersampled and the Nyquist criteria are severely violated. Application of the new procedure to practical diffraction-related phenomena, like in-line holography, improves the processing efficiency without creating any associated artifacts on the reconstructed-object pattern. (C) 2000 Optical Society of America. OCIS codes: 050.1940, 070.6020, 090.1760, 100.2000

Utilization of the recursive shortest spanning tree algorithm for video-object segmentation by 2-D affine motion modeling

Cataloged from PDF version of article.A novel video-object segmentation algorithm is proposed, which takes the previously estimated 2-D dense motion vector field as input and uses the generalized recursive shortest spanning tree method to approximate each component of the motion vector field as a piecewise planar function. The algorithm is successful in capturing 3-D planar objects in the scene correctly, with acceptable accuracy at the boundaries. The proposed algorithm is fast and requires no initial guess about the segmentation mask. Moreover, it is a hierarchical scheme which gives finest to coarsest segmentation results. The only external parameter needed by the algorithm is the number of segmented regions that essentially control the level at which the coarseness the algorithm would stop. The proposed algorithm improves the “analysis model” developed in the European COST211 framework

Introduction to the Special Section on 3DTV

Cataloged from PDF version of article.The set of six papers that we invited to this part of the Special Section present extensive reviews of the state-of-the-art in functional building blocks of 3DTV systems

Integral imaging based 3D display of holographic data

Cataloged from PDF version of article.We propose a method and present applications of this method that converts a diffraction pattern into an elemental image set in order to display them on an integral imaging based display setup. We generate elemental images based on diffraction calculations as an alternative to commonly used ray tracing methods. Ray tracing methods do not accommodate the interference and diffraction phenomena. Our proposed method enables us to obtain elemental images from a holographic recording of a 3D object/scene. The diffraction pattern can be either numerically generated data or digitally acquired optical data. The method shows the connection between a hologram (diffraction pattern) and an elemental image set of the same 3D object. We showed three examples, one of which is the digitally captured optical diffraction tomography data of an epithelium cell. We obtained optical reconstructions with our integral imaging display setup where we used a digital lenslet array. We also obtained numerical reconstructions, again by using the diffraction calculations, for comparison. The digital and optical reconstruction results are in good agreement. © 2012 Optical Society of America

On a parameter estimation method for Gibbs-Markov random fields

Cataloged from PDF version of article.This correspondence is about a Gibbs-Markov random field (GMRF) parameter estimation technique proposed by Derin and Elliott. We will refer to this technique as the histogramming (H) method. First, the relation of the H method to the (conditional) maximum likelihood (ML) method is considered. Second, a bias-reduction based modification of the H method is proposed to improve its performance, especially in the case of small amounts of image data

A class of adaptive directional image smoothing filters

Cataloged from PDF version of article.The gray level distribution around a pixel of an image usually tends to be more coherent in some directions compared to other directions. The idea of adaptive directional filtering is to estimate the direction of higher coherence around each pixel location and then to employ a window which approximates aline segment in that direction. Hence, the details of the image may be preserved while maintaining a satisfactory level of noise suppression performance. In this paper we describe a class of adaptive directional image smoothing filters based on generalized Gaussian distributions. We propose a measure of spread for the pixel values based on the maximum likelihood estimate of a scale parameter involved in the generalized Gaussian distribution. Several experimental results indicate a significant improvement compared to some standard filters. Copyright (C) 1996 Pattern Recognition Society