Showing papers on "Phase correlation published in 2000"
Patent•
21 Jan 2000TL;DR: In this paper, a method for detecting a watermark signal in digital image data is presented, which includes the steps of computing a logpolar Fourier transform of the image data to obtain a log-polar-fourier spectrum; projecting the logp polar Fourier spectrum down to a lower dimensional space to obtain an extracted signal; comparing the extracted signal to a target watermark signals; and declaring the presence or absence of the target watermarks signal in image data based on the comparison.
Abstract: A method for detecting a watermark signal in digital image data. The detecting method includes the steps of: computing a log-polar Fourier transform of the image data to obtain a log-polar Fourier spectrum; projecting the log-polar Fourier spectrum down to a lower dimensional space to obtain an extracted signal; comparing the extracted signal to a target watermark signal; and declaring the presence or absence of the target watermark signal in the image data based on the comparison. Also provided is a method for inserting a watermark signal in digital image data to obtain a watermarked image. The inserting method includes the steps of: computing a log-polar Fourier transform of the image data to obtain a log-polar Fourier spectrum; projecting the log-polar Fourier spectrum down to a lower dimensional space to obtain an extracted signal; modifying the extracted signal such that it is similar to a target watermark; performing a one-to-many mapping of the modified signal back to log-polar Fourier transform space to obtain a set of watermarked coefficients; and performing an inverse log-polar Fourier transform on the set of watermarked coefficients to obtain a watermarked image.
77 citations
15 Oct 2000
TL;DR: The 3D-FRP as mentioned in this paper is based on a discretization of an inversion formula, so it is geometrically accurate for large oblique angles, and both methods involve reprojection of an initial image.
Abstract: The direct Fourier method (DFM) for three-dimensional (3-D) reconstruction of a 3-D volume is based on the relationship between the 3-D Fourier transform (FT) of the volume and the two-dimensional (2-D) FT of a parallel-ray projection of the volume. The direct Fourier method has the potential for very fast reconstruction, but a straightforward implementation of the method leads to unsatisfactory results. This paper presents an implementation of the direct Fourier method for fully 3-D positron emission tomography (PET) data with incomplete oblique projections (3D-FRP) that gives results as good as, or better than, those of a much slower 3-D filtered backprojection method (3DRP), and in the same time as a fast but less accurate method using Fourier rebinning (FORE) followed by slice-by-slice reconstruction. In common with 3DRP, 3D-FRP is based on a discretization of an inversion formula, so it is geometrically accurate for large oblique angles, and both methods involve reprojection of an initial image. The critical two steps in the 3D-FRP method are the estimations of the samples of the 3-D transform of the image from the samples of the 2-D transforms of the projections on the planes through the origin of Fourier space, and vice versa for reprojection. These steps use a gridding strategy, combined with new approaches for weighting in the transform and image domains. The authors' experimental results confirm that good image accuracy can be achieved together with a short reconstruction time.
67 citations
Patent•
15 Mar 2000TL;DR: In this article, a method for registering first and second images which are offset by an x and/or y displacement in sub-pixel locations is presented, which includes the steps of: multiplying the first image by a window function to create a first windowed image, transforming the first window image with a Fourier transform, multiplying the second image by the window function, and transforming the second windowing image with the Fourier transformation, and computing a collection of coordinate pairs from the two image Fourier transforms, such that at each coordinate pair the values of the first and the second
Abstract: Methods for registering first and second images which are offset by an x and/or y displacement in sub-pixel locations are provided. A preferred implementation of the methods includes the steps of: multiplying the first image by a window function to create a first windowed image; transforming the first windowed image with a Fourier transform to create a first image Fourier transform; multiplying the second image by the window function to create a second windowed image; transforming the second windowed image with a Fourier transform to create a second image Fourier transform; computing a collection of coordinate pairs from the first and second image Fourier transforms such that at each coordinate pair the values of the first and second image Fourier transforms are likely to have very little aliasing noise; computing an estimate of a linear Fourier phase relation between the-first and second image Fourier transforms using the Fourier phases of the first and second image Fourier transforms at the coordinate pairs in a minimum-least squares sense; and computing the displacements in the x and/or y directions from the linear Fourier phase relationship. Also provided are a computer program having computer readable program code and program storage device having a program of instructions for executing and performing the methods of the present invention, respectively.
64 citations
Proceedings Article•
1 Sep 2000TL;DR: This paper shows that hypercomplex 2D Fourier transforms may be implemented by decomposition into two independent complex Fourier transform and may thus be implementation by building upon existing complex code.
Abstract: Hypercomplex 2D Fourier transforms have been proposed by several authors with applications in image processing of both grayscale and colour images. Previously published works on hypercomplex Fourier transforms have utilized direct evaluation of a Fast Fourier transform using hypercomplex arithmetic. This paper shows that such transforms may be implemented by decomposition into two independent complex Fourier transforms and may thus be implemented by building upon existing complex code. This is a significant step because it makes available to researchers using hypercomplex Fourier transforms all the investment made by others in efficient complex fft implementations, and requires substantially less effort than coding hypercomplex versions of existing code.
46 citations
1 Sep 2000
TL;DR: A new technique for recognising Arabic cursive words from scanned images of text based on a normalised Euclidean distance from templates, which tolerates variations in size and rotation of displacement.
Abstract: We present a new technique for recognising Arabic cursive words from scanned images of text. The approach is segmentation-free, and is applied to four different Arabic typeface, where ligatures and overlaps pose challenges to segmentation-based methods. We first transform each word into a normalised polar image, then we apply a two dimensional Fourier transform to the polar image. The resultant spectrum tolerates variations in size and rotation of displacement. Each word is represented by a template that includes a set of Fourier coefficients. The recognition is based on a normalised Euclidean distance from those templates.
41 citations
TL;DR: A novel algorithm for the detection of cuts in video sequences is proposed that uses phase correlation to obtain a measure of content similarity for temporally adjacent frames and responds very well to scene cuts.
Abstract: A novel algorithm for the detection of cuts in video sequences is proposed. The algorithm uses phase correlation to obtain a measure of content similarity for temporally adjacent frames and responds very well to scene cuts. The algorithm is insensitive to the presence of global illumination changes and noise and outperforms established methods for cut detection. As the proposed scheme is implemented in the frequency domain, the availability of fast hardware makes the scheme attractive for interactive and on-line applications.
41 citations
Patent•
23 Aug 2000
TL;DR: In this paper, a cardiac triggered, fast gradient-recalled echo pulse sequence is used to acquire a partial Fourier image data set during a single breath-hold and a velocity image is produced by zero-filling and Fourier transforming the zero-filled data set.
Abstract: A cardiac triggered, fast gradient-recalled echo pulse sequence is used to acquire a partial Fourier image data set during a single breath-hold. The image data is velocity encoded and a velocity image is produced by zero-filling and Fourier transforming the zero-filled data set. A separate magnitude image is produced by performing a homodyne reconstruction on the partial Fourier image data set. Anatomic information, such as artery size, is obtained from the magnitude image and combined with velocity information from the velocity image to measure blood flowing through an artery.
31 citations
TL;DR: In this article, a quasi-Born approximation of the Lippman-Schwinger equation is proposed to handle strong scattering accurately and efficiently, which can efficiently produce good-quality images of complex structures with strong lateral perturbations of slowness.
Abstract: Summary
The Born approximation of the Lippman–Schwinger equation has recently been used to implement a recursive method for seismic migration of pressure wavefields. This Born-based method is stable only when the scattering from heterogeneities within an extrapolation depth interval is weak. To handle strong scattering accurately and efficiently, we propose a quasi-Born approximation of the Lippman–Schwinger equation to extrapolate pressure wavefields downwards recursively. We assume that the scattered wavefield is linearly related to the incident wavefield by a scalar function that varies slowly with lateral position within an extrapolation depth interval. The extrapolation is implemented as a dual-doma in procedure in the frequency–space and frequency–wavenumber domains. Fast Fourier transforms are used to transform data between these two domains. The quasi-Born-based depth-migration algorithm is termed the quasi-Born Fourier method. It can efficiently produce good-quality images of complex structures with strong lateral perturbations of slowness. It is stable for strong scattering and can accurately handle scattering and wave propagation along directions at large angles from the main propagation direction. Image quality obtained using the new method is similar to that of a dual-domain migration method that uses the Rytov approximation within each extrapolation depth interval, but the computational speed of the new method is approximately 27 per cent faster than the latter method for pre-stack migration of an industry standard data set—the Marmousi data set. Compared to the Born-based migration method, the quasi-Born Fourier method is slightly less efficient because it requires an additional multiplication and an additional division for each lateral gridpoint in each step of wavefield extrapolation. For weak scattering, the quasi-Born Fourier method converges to the Born-based method. To improve the efficiency of the quasi-Born Fourier method further without losing its accuracy, we propose a hybrid Born/quasi-Born Fourier method in which the Born-based method is used when the scattering within an extrapolation depth interval is weak, and the quasi-Born Fourier method is used for other cases. This hybrid method is approximately 32 per cent faster than the Rytov-based method for the pre-stack depth migration of the Marmousi data set, while the images obtained using both methods have almost the same quality.
23 citations
TL;DR: In this article, the authors introduce the colour as a third dimension of images and extend the definition of Fourier transform to these three variable light distributions, paying special attention to the properties of the colour variable transformation.
17 citations
5 Jun 2000
TL;DR: A novel method for classifying an image into one of predefined classes in a data bank by applying mutual information to a representation of the Fourier amplitude domain, which adequately preserves edges even at lower resolutions while permitting at the same time, a reduction in the computational burden.
Abstract: This paper presents a novel method for classifying an image into one of predefined classes in a data bank by applying mutual information to a representation of the Fourier amplitude domain. Template and test images are made translation and rotation invariant through the Fourier-Mellin transform. While mutual information could be employed here, we choose instead to apply it to the lower dimension phase spectrum generated by the complex multiresolution wreath product transform of the Fourier-Mellin amplitude spectrum. The phase information of this transform adequately preserves edges even at lower resolutions while permitting at the same time, a reduction in the computational burden. Brodatz textures and ORL faces are used to demonstrate the capability of this algorithm.
14 citations
TL;DR: In this paper, path difference dependent misalignments, such as those due to imperfect mechanical movement of the scanning mirror, can be modelled as path difference-dependent apodisation and phase errors.
Patent•
16 Feb 2000TL;DR: In this article, the Fourier transform or frequency domain representation is modified by phase shift terms corresponding to image shifts in the spatial domain with sub-unity distances matching the locations where the image values need to be restored.
Abstract: A method for interpolating digital images is provided. An original digital image in the spatial domain is transformed into a frequency domain representation via a Fourier transform. The Fourier transform or frequency domain representation is then modified by phase shift terms corresponding to image shifts in the spatial domain with sub-unity distances matching the locations where the image values need to be restored. The original and the shifted images are then interspersed together, yielding an interpolated image. The method is particularly useful for two and three-dimensional computer tomography (CT) and magnetic resonance imaging (MRI) images, as well as other medical and non-medical digital images.
TL;DR: In this paper, it was shown that the classes of Fourier coefficients defined by Fomin and furthermore by C. V. Stanojevic and V. B. Stranojevevic are identical.
Abstract: It is shown that the classes of Fourier coefficients defined by Fomin, furthermore by C. V. Stanojevic and V. B. Stanojevic are identical. Mathematics subject classification (1991): 26D15, 42A10.
Patent•
25 Feb 2000
TL;DR: Fractional Fourier transform properties inherent in lens systems and other light and particle-beam environments may be exploited to correct misfocus effects in photographs, digital files, video, and other types of images as discussed by the authors.
Abstract: Fractional Fourier transform properties inherent in lens systems and other light and particle-beam environments may be exploited to correct misfocus effects in photographs, digital files, video, and other types of images. Small corrections may utilize fractional Fourier transform approximations around the reflection operator. The fractional Fourier transform and approximations can be rendered by optical or numerical methods, alone or in combination, directly or though use of a conventional discrete Fourier transform in combination with multiplying phase “chirps.” The corrective fractional Fourier transform power may be determined automatically or by human operator. The image correction can be applied to lens-systems or other systems obeying fractional Fourier optics, including integrated optics, optical computing, particle beams, radiation accelerators, and astronomical observation, and may be incorporated into film processing machines, desktop photo editing software, photo editing websites, VCRs, camcorders, video editing systems, video surveillance systems, video conferencing systems, and other types of products and service facilities.
TL;DR: The phase correlation algorithm is extended to the case of multi-component images such as RGB and multi-spectral images, allowing for translations between monochromatic and color images.
Abstract: Phase correlation is a very robust technique to estimate image translations, but it works only for monochromatic images. If the input image is a color image, it must be first converted to monochrome, wasting part of the input information. In this work we extend the phase correlation algorithm to the case of multi-component images such as RGB and multi-spectral images.
TL;DR: This column closely follows the discussion of motion blur in [4] and remarks that the Fourier transform of an argument array results in another array, typically a complex valued array.
Abstract: F AST FOultIElt TII.ANSFOILMS make it possible to convert back and forth between image space and frequency space. It is amazing that it is possible to remove of some of the blur caused by motion or improper focus [5]. J offers a powerful add-on packageffl'w based on work of Frigo and Johnson [2], that makes it easy to combine fast Fourier transforms with other array processing. This column closely follows the discussion of motion blur in [4]. We will not discuss the mathematics of computing the Fourier transform. However, we remark that the Fourier transform of an argument array results in another array. While the input array is ordinarily a real array representing an image, any complex valued array is allowed. The result, typically a complex valued array, can be thought of as giving a real and imaginary part for each entry. Or, more important for applications, we can think of those complex entries as a magnitude and phase. Images of the magnitude essentially give diffraction patterns [1,3]. Thefl~o add-on package can be downloaded from wzow.jsoftware.com. We load the ffkw add-on package, create a small example and compute the. Fourier transform of that array as follows: require 'system\\packages\\fftw\\fftw' ]a=:
5 Jun 2000
TL;DR: A sinusoidal signal analysis technique is extended to frequency determination and enables a closed form solution to the discrete-time Fourier transform of a Kaiser-Bessel window in computational order 1.
Abstract: A sinusoidal signal analysis technique is extended to frequency determination. It improves upon previously reported maximum-likelihood methods by reducing computational order per iteration from N to 1, where N is the number of data points. Subject to a noise floor, there is no limit to achievable accuracy or discrimination. The proposed extension accommodates any window whose continuous-time Fourier transform is known. It is illustrated here with the Kaiser-Bessel window, a near-optimum window with full design parameterization. To achieve reduced computational order, an approach is proposed for the fast computation of discrete-time Fourier transforms when corresponding continuous-time Fourier transforms are known. Its computational order is generally superior to that of an FFT. Furthermore, it enables a closed form solution to the discrete-time Fourier transform of a Kaiser-Bessel window in computational order 1. The exceptional performance is demonstrated through A/D converter performance analysis.
TL;DR: Based on optical Fourier transform, the online measurement of the sizes of standard wire sieves is described in this article, which has more advantages than other traditional methods, such as operating efficiently and precisely on line and in real time.
Abstract: Based on optical Fourier transform, the online measurement
of the sizes of standard wire sieves is described. Compared with other
traditional methods, this system has more advantages, such as operating
efficiently and precisely on line and in real time. The measuring system,
composed of a laser, an optical Fourier transform system, a CCD
camera, an image acquisition system, and a personal computer, can
offer averaged sizes and percentage of apertures exceeding the specified
size of standard wire sieves in two-dimensional directions. The experimental
results are also presented.
2 Nov 2000
TL;DR: In this paper, the authors describe a hybrid electronic/photonic correlator which exploits recent developments in both electronics and photonics to provide a fast, compact and rugged processor, which is demonstrated operating at 10,500 correlations/sec.
Abstract: We describe the principles and performance of a novel form of hybrid electronic/photonic correlator which exploits recent developments in both electronics and photonics to provide a fast, compact and rugged processor. In the earlier Vander Lugt correlator the input image is Fourier Transformed optically and multiplied optically with the conjugate Fourier Transform of a reference pattern; the required correlation function is completed by taking the inverse Fourier Transform of the product optically. The correlator described here is similar, but performs the initial Fourier Transforms and multiplication electronically. In this scheme the Fourier Transforms of both the input scene and reference pattern are reduced to a binary phase-only format, when the multiplication process simplifies to a simple Boolean logic XOR function. The output of this XOR gate is displayed on a state-of-the-art Fast Bit Plane Spatial Light Modulator (FBPSLM). This device is electrically addressed, and employs a ferroelectric liquid crystal so its operation is inherently binary and fast. A consequence of the use of binary phase-only data is the appearance of a second (unwanted) peak in the output plane, but we demonstrate its elimination through the introduction of a chirp function. The complete correlator is demonstrated operating at 10,500 correlations/sec.© (2000) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
Journal Article•
TL;DR: A method for improving the measuring accuracy by applying a frame of gray image to Fourier transform profilometry is proposed and it can achieve the effect of π phase shift.
Abstract: In Fourier transform profilometry,π phase shift is often used to eliminate zero frequency for avoiding spectral mixing and overlapping,thus the measuring accuracy can be improved.But a phase shift device is included in the measuring system and the system complexity is increased.However,people often ignore the functions of information included in gray image in Fourier transform profilometry.A method for improving the measuring accuracy by applying a frame of gray image to Fourier transform profilometry is proposed in the paper.The constitution of the measuring device for this method is simple and it can achieve the effect of π phase shift.It is significant in the practical Fourier transform profilometry.
TL;DR: A least-squares estimation method in the frequency domain that allows wavefront recovery from two orthogonal shearing fringe patterns when a large shear is applied is presented.
Abstract: Electronic speckle-shearing pattern interferometry offers the possibility of analyzing out-of-plane and in-plane deformations in experimental mechanics. However, to obtain high-contrast fringes this technique must introduce large shears into the speckle patterns. Several techniques have recently been proposed to recover the phase from these data, but they all suffer limitations due to the slow convergence of the proposed algorithms or to the low precision of the recovered phase. This paper presents a least-squares estimation method in the frequency domain that allows wavefront recovery from two orthogonal shearing fringe patterns when a large shear is applied. This method is based on the application of a single Fourier filter using the fast Fourier transform process. The experimental results obtained by using electronic speckleshearing pattern interferometry for the analysis of a finite circular plate deformed at the center illustrate the advantages of the proposed technique.
1 Jan 2000
TL;DR: In this article, a phase shifting method using Fourier transform was proposed to analyze the phase at each pixel point by calculating the argument of the phase shifted brightness at the pixel point, which is applied to the analysis of fringe patterns obtained by a Twyman-Green interferometer and photo-elastic fringe patterns using a linear polariscope.
Abstract: Phase analysis methods provide accurate results of fringe pattern analysis. A phase shifting method using Fourier transform uses many images obtained by changing the phases of fringe patterns. The phase at each pixel point is analyzed by calculating the argument using Fourier transform of the phase shifted brightness at the pixel point. It is applied to the analysis of fringe patterns obtained by a Twyman-Green interferometer and photoelastic fringe patterns obtained by a linear polariscope. Furthermore it is extended to a phase shifting method using correlation with rectangular functions to measure a 3-D shape by a grating projection method.
3 Sep 2000
TL;DR: The colour is introduced as the third dimension of images and the definition of Fourier transform and correlation to these signals are extended and extended and the pattern recognition method is extended based in correlation toThese signals.
Abstract: Image processing is carried out in general with monochromatic information. So it does not consider the colour information of the objects. However, the human visual system is very sensitive to the colour information, so it seems logical to introduce this information to increase the capacity of computer-based systems. Obtaining all the spectral information for each pixel of an image could between expensive but the image acquisition systems may provide several images each one corresponding to a special sub-band. In this paper we introduce the colour as the third dimension of images and extend the definition of Fourier transform and correlation to these signals. Firstly, we study the Fourier transform properties of these 3D images, paying special attention to the third dimension, which contains the colour information. Then, the correlation operation is studied. As an application, we extend the pattern recognition method based in correlation to these signals and we show the advantages of introducing the colour information.
1 Jan 2000
TL;DR: In this article, the Fourier transform of the 3D intensity function is used to estimate planar rotations of the Madonna of Donatello in the Basilica of St. Anthony in Padua.
Abstract: Phase correlation is one of the robustest methods for estimating planar translations: it is a global approach because it operates in the frequency domain using the whole image information and not just a selected subset of the image as the feature-based methods do. The good characteristics of phase correlation for estimating planar translations were found to be a strong motivation for its extension to the estimation of planar rotations. An original algorithm for estimating planar rotations inspired by phase correlation is presented in this work. Practical experimentation on real imagery confirm the expected robustness of the method. Furthermore, a natural extension of the proposed algorithm will be also presented for 3D shapes motion estimation. Free-form 3-D surfaces registration is a fundamental problem in 3-D imaging, tipically approached by extensions or variations of the ICP algorithm [2,10]. In this paper an alternative procedure for 3-D motion estimation wiil be suggested, based on the Fourier transform of the 3-D intensity function, implicitly described by the registered time-sequences of range data. As the proposed method is very suitable for 2D and 3D modeling of cultural heritages, some examples and results of its application to Madonna of Donatello, located in the Basilica of St. Anthony in Padua, will be also presented. 1. ESTIMATION OF PLANAR ROTATIONS BY MEANS OF PHASE CORRELATION
TL;DR: Based on the wavelength dependence of the optical fractional Fourier transform, it was shown in this paper that the scale and order of polychromatic FDF transforms can be adjusted independently if the transforms are implemented with an asymmetric optical system.
TL;DR: A novel interferometric optical Fourier-transform processor is presented that calculates the complex-valued Fourier transform of an image at preselected points on the spatial-frequency plane and is demonstrated in a moving-object trajectory estimation system.
Abstract: A novel interferometric optical Fourier-transform processor is presented that calculates the complex-valued Fourier transform of an image at preselected points on the spatial-frequency plane. The Fourier spectrum of an arbitrary input image is interfered with that of a reference image in a common-path interferometer. Both the real and the imaginary parts of the complex-valued spectrum are determined. The source and the reference images are easily matched to guarantee good fringe visibility. At least six interferograms are postprocessed to extract the real and the imaginary parts of the Fourier spectrum at preselected points. The proposed hybrid optical-digital technique is computationally appropriate when the number of desired spatial frequencies is small compared with the number of pixels in the image. When the number of desired points is comparable with the number of image pixels, a conventional or pruned two-dimensional fast Fourier transform is more appropriate. The number of digital operations required by the hybrid optical-digital Fourier processor is proportional to the number of desired spatial frequencies rather than the number of pixels in the image. The points may be regularly distributed over the spatial-frequency plane or concentrated in one or several irregularly shaped regions of interest. The interferometric optical Fourier processor is demonstrated in a moving-object trajectory estimation system. The system successfully estimates the trajectory of multiple objects moving over both stationary and white-noise backgrounds. A comparison of performance was made with all-digital computation. With everything else equal, our hybrid optical-digital calculation was more than 3 orders of magnitude faster.
26 Sep 2000
TL;DR: The results of this research show an acceptability of the suggested method for segmentation of low-contrast images by approximating the Fourier transform spectrum module of the image to approximately increase the contrast by 3.5 times.
Abstract: In the most analysis and interpretation problems, the segmentation procedure is the key one: it allows to separate an image into parts, which are informatively interpreted and correspond to different objects in the image analyzed It is shown that approximating the Fourier transform spectrum module of the image allows to approximately increase the contrast by 35 times The results of this research show an acceptability of the suggested method for segmentation of low-contrast images
23 Jul 2000
TL;DR: In this paper, two new approaches to longitudinal interpolation in single-slice helical CT volumes are described and evaluated, which represent a step toward the goal of achieving essentially isotropic resolution and noise properties.
Abstract: This paper describes and evaluates two new approaches to longitudinal interpolation in single-slice helical CT that represent a step toward the goal of achieving essentially isotropic resolution and noise properties in reconstructed helical CT volumes. Both approaches exploit the fast Fourier transform and the Fourier shift theorem to generate from the helical projection data a set of fan-beam sinograms corresponding to equispaced transverse slices. Slice-by-slice reconstruction is then performed by use of two-dimensional fan-beam algorithms. The first approach, called 360FT, makes use only of the directly measured projection data, but the second approach, called 180FT, exploits the redundancy of fan-beam data acquired over 360/spl deg/ to generate a second set of longitudinal samples at each projection angle and bin. These approaches, and particularly the 180FT approach, have been shown under certain conditions to produce reconstructed volumes with more isotropic resolution and aliasing properties than do existing approaches based on the use of linear interpolation. We present evidence that the approaches also have favorable noise uniformity properties relative to currently used approaches.