Showing papers on "Phase correlation published in 1993"

Fast Fourier transforms for symmetric groups : theory and implementation

Abstract: Recently, it has been proved that a Fourier transform for the symmetric group S, based on Young's seminormal form can be evaluated in less than 0.5(n3 + n2)n! arithmetic operations. We look at this algorithm in more detail and show that it allows an efficient software implementation using appropriate data structures. We also describe a similarly efficient algorithm for the inverse Fourier transform. We compare the time and memory requirements of our program to those of other existing implementations.

Contrast performance of pure phase correlation

Abstract: The properties of the pure phase correlation method applied to pattern recognition are presented. Digital analysis of contrast performance of pure phase correlation function of binary and graytone segmented input scenes is realized. The results are compared with those obtained by using the matched spatial filter method and phase-only filtering.

Fourier transforms of fractional order and their optical interpretation

Abstract: Fourier transforms of fractional order a are defined in a manner such that the common Fourier transform is a special case with order a = 1. An optical interpretation is provided in terms of quadratic graded index media and discussed from both wave and ray viewpoints. Fractional Fourier transforms can extend the range of spatial filtering operations.

Two-dimensional image reconstruction from Fourier coefficients computed directly from zero crossings

Abstract: Two-dimensional image reconstruction using Fourier coefficients that are computed directly from the sampled representation of zero crossings is demonstrated. A two-dimensional image of dimensions Nx × Ny is interpreted as a set of Ny independent x-space lines (in gray-scale format) that are arranged uniquely along the y direction. Each line has Nx elements. Reconstruction is achieved first by computing the entire set of Ny one-dimensional Fourier transforms from the measured zero crossings using Newton’s formula. Each Nyth line spectra has Nx Fourier coefficients. The inverse Fourier transform is then applied to each of the line spectra to obtain a set of Ny reconstructed x-space lines. The reconstructed image is obtained by arranging the reconstructed lines properly along the y direction.

Speckle Displacement Analysis by Phase Correlation Using a SLM-based Processor

Abstract: A new approach of speckle displacement analysis by phase correlation measurement is described. An optical implementation of the method based on one focal length correlator architecture using a liquid crystal light valve is proposed.

Optoelectronic implementation of quasi phase-correlation-based processor

Abstract: We present a new optoelectronic quasi phase processor based on a conventional joint transform correlator architecture and using a liquid crystal SLM. The phase information is extracted from a joint transform spectrum producing a good correlation performance in terms of noise tolerances and peak sharpness. Several characteristics of the used SLM improving the correlation function are investigated. Computer simulations of the correlator performances and experimental results of an application on tool recognition are presented and discussed.

Application of an automatic phase unwrapping method for the quantitative extraction of information from high-resolution interferometric and photo-elastic data

Abstract: This paper describes the application of digital Fourier transform to phase encoded intensity distribution. Attention is drawn to a method of extracting quantitative information automatically from the interferometric fringe data. To achieve this a set of carrier fringes has been added to interferometric fringe data. This has made it possible to form a phase map using a FFT (Fast Fourier Transform) algorithm. A Minimum Spanning Tree (MST) phase unwrapping strategy has been used to create a contiguous map of the whole fringe field. Finally, the measurement parameter related to the fringe field has been calculated from one single image. Experimental results are given for the burner flames, a compressible flow, and photoelastic fringe data.

A complete translation and rotation invariant algorithm for pattern recognition

Abstract: This paper introduces a new complete translation and rotation invariant algorithm. Applying this algorithm to a target image produces two transformed images which are invariant under translation and rotation to the original target image. This algorithm is complete; that is, the object in the original image can be completely recovered from the resultant images except for its position and orientation. The algorithm begins by taking a two dimensional Fourier transform of the target image, resulting in two 2-D images: the Fourier phase and magnitude. The Fourier magnitude is translation invariant. In order to make the magnitude also be rotation invariant, a circular Fourier transform is taken. Applying the TR-Taylor invariant operation to the resultant image produces the first translation and rotation invariant image. Under the Hessian-Taylor invariant, the phase image is transformed into a Hessian matrix which is translation invariant. A complete derivation of the algorithm leading to the final invariant images is given. Simulations applying the algorithm to test images are shown. >

Segmentation of range images using phase Fourier transform

Abstract: We introduce a method for segmentation of planes and quadrics of a three-dimensional range image using the phase Fourier transform. We extend our previous method for contour determination and simultaneous detection of edges and quadrics. We consider optical and electronic implementations. Using the phase Fourier transform, we address the issue of invariant pattern recognition for segmented and non-segmented three-dimensional images. We show results obtained with a parallel computer.

Determining the velocity of a moving object from a series of photon-limited frames using a temporal Fourier transform

Abstract: We propose a technique to obtain directly from a series of photon-limited frames, the spectrum of an object moving with constant velocity. Instead os averaging statistical functions as the auto or triple correlations or their Fourier transforms, our method averages the series of frame spectra once the phase factor due to the movement has been removed. Two different procedures to obtain this phase factor are studied: the temporal derivative of the spectrum logarithm and the temporal Fourier transform of the series of spatial spectra. The latter method involves a larger number of calculations but it produces much better results, especially when only a small number of frames are available. Finally, the recovery technique is checked for a simulated experiment in which a one-dimensional object is reconstructed from a short series of photon-limited frames.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Optical Fourier analysis of biological cell patterns

Abstract: This paper presents the optical Fourier analysis of human corneal endothelial cell patterns. The quantitative analysis of human corneal endothelial cells patterns is analyzed with Fourier transform methods. The optical Fourier transform of the pattern of endothelial cell borders is analyzed to yield the average cell area and the coefficient of variation of the average cell area. The advantage of the Fourier transform analysis is the parallel processing of the optical Fourier transform and the potential development of a hybrid digital-optical device for the rapid analysis of large numbers of endothelial specular photomicrographs. The intensity distribution of the Fourier transform of binary images of endothelial cell patterns is detected with a wedge- ring detector. The radial and the angular distribution of intensity is analyzed and related to the cell size distribution in the input image.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Lensless 2D correlation experiments

Abstract: Converging light is used for a reference beam in constructing the Fourier transform of a filter for use in a 2-D correlator. This eliminates the need for the inverse Fourier transform lens used for performing correlation. We analyze this approach and demonstrate correct performance with optical experiments. Further, we propose a compact optical correlator system that uses only one curved element for both constructing filters and performing correlation.

Multi-dimensional information encoding and holo-spectrum display of two-dimensional image

Abstract: The multi-dimensional information encoding is introduced as a means of displaying Fourier spectrums of signal, and an information encoding and displaying algorithm is proposed in this paper. It can be used in Fourier spectrum display and analysis of two-dimensional (2-D) image, and a 4-D hole-spectrum, i.e. first spatial frequency, second spatial frequency, magnitude and phase plot, of 2-D image is obtained. An experimental display system is developed, and the hole-spectrums of the 2-D images based on the multi-dimensional information encoding are analyzed. The results show that the hole-spectrum of the 2-D image based on the multi-dimensional information encoding are able to represent the details of the 2-D image magnitude and phase characteristics in the spatial frequency domain. >

Three-dimensional object tracking from range images using sine wave coding and Fourier transform

Abstract: An efficient method for tracking the attitude and translation of an object from a sequence of dense range images is demonstrated. The range data is sine encoded and then Fourier transformed. By this process, planar surfaces in the image produce distinctive peaks in the FT plane; the position of a peak provides a direct measure of the normal of the plane. By tracking the position of these peaks, the orientation of a known object can be tracked directly. The Fourier transform can also be used for segmentation. After computing and undoing the rotation, the translation is obtained by measuring the centroid of the segmented planar surfaces. The object must present at least three planar surfaces, for determining absolute orientation and translation. All computations are closed form. The integrative nature of the Fourier transform is very effective in attenuating the effect of noise and outliers. Results of tracking an object in a simulated range image sequence show high accuracy potential (0.2 deg. in orientation and 0.5% rms error in translation with respect to the dimension of the object). The method promises real-time (video rate) performance with the addition of accelerator hardware for computing the Fourier transform. The approach is well suited for dynamic robotic vision applications. Furthermore, the translation invariance of the Fourier transform essentially decouples the rotational and translational components of the motion, this contributes to the tracking performance.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

APL-implemented compact and generalized program for fast Fourier and Hadamard transforms

Abstract: Generalized program for selecting Fourier and Hadamard transforms has been developed in APL2 language. It is advantageous that this makes the program compact and the algorithm clear.