Abstract: This paper presents a fast algorithm for obtaining high-accuracy subpixel translation of low PSNR images. Instead of locating the maximum point on the upsampled images or fitting the peak of correlation surface, the proposed algorithm is based on the measurement of centroid on the cross correlation surface by Modified Moment method. Synthetic images, real solar images and standard testing images with white Gaussian noise added were tested, and the results show that the accuracies of our algorithm are comparable with other subpixel registration techniques and the processing speed is higher. The drawback is also discussed at the end of this paper.

Abstract: The Fourier transforms play a critical role in a broad range of image processing applications, including enhancement, analysis, restoration, and compression. Until recently, it was common to use the conventional methods to deal with colored images. These methods are based on RGB decomposition of the colored image by separating it into three separate scalar images and computing the Fourier transforms of these images separately. The computing of the Hypercomplex 2D Fourier transform of a color image as a whole unit has only recently been realized. This paper is concerned with frequency domain noise reduction of color images using quaternion Fourier transforms. The approach is based on obtaining quaternion Fourier transform of the color image and applying the Gaussian filter to it in the frequency domain. The filtered image is then obtained by calculating the inverse quaternion Fourier transforms.

Abstract: Copy-move is a common used forgeries in digital image tampering. In this paper, a non block-matching based fast method to detect image copy-move forgery is proposed exploiting phase correlation. Results of experiments indicate that the proposed method is valid in detecting the image region duplication and quite robust to additive noise and blurring.

Abstract: SUMMARY We present an analysis of four different algorithms used to register plantar pressure images: a first one based on the matching of the external contours of the feet, a second algorithm based on the technique of phase correlation, a third one based on the direct optimization of the cross-correlation (CC) and using the Fourier transform, and a fourth and last algorithm that is based on the iterative optimization of an intensity (dis)similarity measure. In terms of accuracy, the later algorithm achieved the best registration results; on the other hand, the algorithm based on the matching of contours was the fastest, but its accuracy was inferior to the accuracy of the remaining algorithms.

Abstract: In this paper, we propose a new observation model with optimizing particle filter framework for visual object tracking in the present of occlusion. Most of the existing algorithms are able to track the object only in predefined and well controlled environment. In computer vision research area, it is challenging task to track when objects get close and circle each others. Some algorithm doesn't even consider the optimization problem. In this work, we develop a robust phase correlation based observation model for particle filter framework and also introduce an optimization technique to improve the performance and accuracy of tracking. Phase correlation provides straight-forward estimation of rigid translational motion between two images. Phase correlation has the advantage that it is not affected by any intensity or contrast differences between two images. Therefore, we apply the phase correlation in particle filter framework for robust tracking. To solve the optimization problem every certain time, we calculate the variance of each weight values to estimate whether there is appeared or not the similar objects around the target object. Based on the estimation results we increase or decrease the number of particles for optimization rather than generate the constant number of particles. We obtained a surprising result with the propose algorithm. Experiments of propose tracker show that our system is robust against cluttered background and optimization problem.

Abstract: The traditional Fourier Mellin transform is applied to quaternion algebra in order to investigate quaternion Fourier transformation properties useful for color image registration in frequency domain. Combining with the quaternion phase correlation, we propose a method for color image registration based on the quaternion Fourier transform. The registration method, which processes color image in a holistic manner, is convenient to realign color images differing in translation, rotation, and scaling. Experimental results on different types of color images indicate that the proposed method not only obtains high accuracy in similarity transform in the image plane but also is computationally efficient.

Abstract: Here, we intend to introduce an invariant similarity registration method based on Analytical Fourier-Mellin Transform (AFMT) computed on the image functions. The well-known phase correlation method which estimates the geometrical transformation parameters between tow images from the corresponding Fourier-Mellin spectrums is compared to the proposed one. In order to illustrate the best performance of the geometric parameters estimation, we apply our method to the construction of Punic Panorama.

Abstract: It is a well-known fact that scanning electron microscopic (SEM) image acquisition is mainly affected by nonlinearities and instabilities of the column and probe-specimen interaction; in turn, producing a shift in the image points with respect to many parameters and time, in particular. Even though this drift is comparatively less in modern SEMs, it is still an important factor to consider in most of the SEM-based applications. In this airticle, a simple and real-time method is proposed to estimate the global drift from a set of target images using image phase correlation, and to model its evolution by using the recursive equations of time and magnification. Based on the developed model, it is opted to use a Kalman filter in real time for accurate estimation and removal of the drift from the images. The developed method is tested using the images from a tungsten filament gun SEM (Jeol JSM 820) and a field effect gun SEM (FEI Quanta 200). The derived results show the effectiveness of the developed algorith...

Abstract: The key point of super resolution process is the accurate measuring of sub-pixel shift. Any tiny error in measuring such shift leads to an incorrect image focusing. In this paper, methodology of measuring sub-pixel shift using Phase correlation (PC) are evaluated using different window functions, then modified version of (PC) method using high pass filter (HPF) is introduced . Comprehensive analysis and assessment of (PC) methods shows that different natural features yield different shift measurements. It is concluded that there is no universal window function for measuring shift; it mainly depends on the features in the satellite images. Even the question of which window is optimal of particular feature is generally remains open. This paper presents the design of a method for obtaining high accuracy sub pixel shift phase correlation using (HPF).The proposed method makes the change in the different locations that lack of edges easy.

Abstract: This paper presents an efficient Phase Correlation based Image Analysis System (PCIAS) for high quality DEM generation. A multi-resolution phase correlation based disparity estimation and refinement algorithm has been implemented in PCIAS. It can easily cope with the precise disparity estimation from sub-pixel to very large disparity range with varying baseline/distance ratio in vertical or slightly oblique view stereo imaging. The PCIAS is now a fully operational, professional C++ software package equipped with a robust phase correlation engine, which is among the most advanced technology for sub-pixel image feature shift analysis, and is able to achieve <1/50th pixel accuracy in dense disparity map estimation. Our experiment indicates PCIAS can generate high quality DEM from very narrow baseline satellite image pairs with view angle difference as small as just 1 degree.

Abstract: Systems and methods of image reconstruction that can reduce the number of Fourier transform measurements required to obtain an exact or stable reconstruction of target images, using prior edge information obtained from a reference image. Full-sampled, 2 or 3-dimensional Fourier transform measurements are obtained for the reference image prior to performing a time series study. Based on the reference image sharing similar edge information with a time series of sparse-gradient images, the number of Fourier transform measurements required to reconstruct the target images can be reduced by using compressed sensing techniques to obtain the sparse-gradient images, and combining the edge information for the sparse-gradient images with the reduced number of Fourier transform measurements to obtain the exact or stable reconstruction of the target images, thereby permitting improved temporal resolution and/or extent of tissue coverage over the use of full sampling and conventional image reconstruction methods.

Abstract: Image registration or stabilization is a task that has been focused on in many fields in image processing. Many methods are available for registering two images, but when dealing with wide area motion imagery, registration of the full scene can be taxing computationally. The proposed algorithm is an application utilizing two existing registration methods to stabilize a specific region of interest in an aerial image database. The registration tools implemented during this application are a phase correlation method and the efficient second-order minimization method. The combination of both registration functions act as a coarse-to-fine image registration algorithm. The goal of this application is to output a set of registered smaller sized images from the larger dataset for the use in detection and tracking of objects in wide area imagery. Experiments performed on several image streams show that the proposed technique is effective and gives high registration accuracy.

Abstract: The measurement of translational shifts has an impact on applications in medical imaging, remote sensing and structural health monitoring. Phase correlation (PC) is a well-known method to measure displacement. However, the PC matrix is often degraded by phase noise and aliasing. Presented is a robust PC method based on adaptive masking and essentially non-oscillatory smoothing to reduce phase noise and aliasing. With this approach, translational shifts can be measured with an accuracy of 1/300 of a pixel as shown in the experimental results.

Abstract: The automatic extraction of objects from airborne laser scanner data and images has been a topic of research for decades. Laser scanner data have proven to be a powerful source for a wide range of 2D–3D geographic information system object tasks. This paper presents the Fourier transform as an image enhancement tool for determination of buildings from the images generated by laser signal. Spatial and frequency domain filtering techniques have been utilized for extraction of building from enhanced images. While Gaussian and Wiener filterings were selected in frequency domain, Sobel and Unsharp were selected for the spatial domain. The boundaries of buildings have been delineated from the generated images, which were obtained from inverse Fourier transform, by using edge detectors, such as Canny, Sobel, and Prewitt. Frequency domain filters using Fourier transformation were compared with spatial domain filters in the way of kernel function and windows. The reason for doing the filtering in the frequency domain is that it is computationally faster to perform two-dimensional Fourier transforms and a filter is more applicable than to perform a convolution in the spatial domain. Results showed that using Fourier transformation has a great advantage in enhancing images and detecting the buildings on images. Filtering in the frequency domain is more efficient computationally than spatial domain filtering when the filter size is big. The conclusion proved that Fourier transformation can be used as an image enhancement tool to detect and extract buildings automatically.

Abstract: The invention discloses a time frequency domain image rectification method of fractional order Fourier transform (FRFT) expressed by employing polar log coordinate. According to the invention, a signal is expressed on a fractional order Fourier domain, simultaneously, information of the signal at a time domain and a frequency domain is fused, phase correlation technology is employed, a reference image and an image to be rectified are subjected to the FRFT transform, a translation parameter is determined, and rectification parameters of rotation, zooming and the like are obtained through log-polar coordinate transformation. According to the invention, a frequency characteristic of the signal with time change can be comprehensively reflected.

Abstract: A novel invariant region-shape descriptor based on Fourier transform is proposed in this paper.In this method,a shape pixel-matrix is firstly generated by image re-sampling using polar raster.Two times of 1D Fourier transforms and a correcting operator of phase are then conducted against the shape pixel matrix.The resulting matrix formed by the Fourier coefficients of low frequency is used to describe the region shape.The obtained shape descriptor not only preserves the phase information of the Fourier coefficients,but also achieves invariance to translation,scale and rotation.The experimental results show that the proposed method outperforms the existing Fourier region-shape descriptor and Zernike moment descriptor.

Abstract: By adopting a concept from signal processing, instead of starting from the correlation functions which are even, one considers the causal correlation functions whose Fourier transforms become complex. Their real and imaginary parts multiplied by 2 are the Fourier transforms of the original correlations and the subsequent Hilbert transforms, respectively. Thus, by taking this step one can complete the two previously needed transforms. However, to obviate performing the Cauchy principal integrations required in the Hilbert transforms is the greatest advantage. Meanwhile, because the causal correlations are well-bounded within the time domain and band limited in the frequency domain, one can replace their Fourier transforms by the discrete Fourier transforms and the latter can be carried out with the FFT algorithm. This replacement is justified by sampling theory because the Fourier transforms can be derived from the discrete Fourier transforms with the Nyquis rate without any distortions. We apply this method in calculating pressure induced shifts of H2O lines and obtain more reliable values. By comparing the calculated shifts with those in HITRAN 2008 and by screening both of them with the pair identity and the smooth variation rules, one can conclude many of shift values in HITRAN are not correct.

Abstract: The Fourier transform method is an analytical method for interferograms with a spatial linear carrier. Interferograms with a spatial linear carrier are analyzed to obtain the phase, by eliminating the noise from the shape components of the interferograms in the Fourier domain. However, when the noise and shape components overlap in the Fourier domain, it is difficult to eliminate only the overlapped noise components using conventional filtering techniques, such as bandpass filtering. Accordingly, a method is proposed to solve this problem using two interferograms with slightly different carrier frequencies. In this method, the Fourier transforms of two interferograms with slightly different carrier frequencies are separately calculated. Both of the spectra resulting from the Fourier transforms of the interferograms contain the same noise components; however, the locations of these components differ slightly for the two spectra. By subtracting the two Fourier spectra, the noise components are removed, and the main components are generated, because the frequency difference between the two components is small. We have named the proposed method the “two-step Fourier transpose method”. The validity of the proposed filtering method is confirmed by experiments in which two color fringes are projected simultaneously onto a scatter object. Images of the color fringes are acquired via a CCD camera under the slow deformation of the scatter object. The images are then analyzed via the proposed method.

Abstract: A new image forensics algorithm based on phase correlation is proposed to detect image copy-move forgery Phase correlation is computed to obtain the typical distribution of correlation value and then minimum variance method is applied to determine the pulse diagram The spatial offset between copied portion and pasted portion is estimated according to the pulse position, thus the copy-move region can be quickly located Experimental results indicate that this method is not only implemented easily, but also achieve an effective and accurate location for small tampered areas With this method, detection accuracy is guaranteed and application scope of the algorithm is extended simultaneously

Abstract: Astronomical images are characterized by their smooth features, low level of Signal to Noise Ratio (SNR), and their extreme sensitivity to the motion of platform. Due to the low SNR, it is necessary to collect a large number of frames and consider the average. However, it is a common occurrence to have unregistered frames in the sequence. Frame registration using feature-based approach fails due to low contrast. Also, area-based approaches such as template matching and phase correlation methods, although accurate, suffer from computational inefficiency as a result of the large size and number of image frames in a sequence. This paper introduces a novel two-stage algorithm to accelerate the process of registration. The first stage projects the direction of movement as a cluster of parallel streaks and determines the angle of motion, using Linear Hough Transform. The next stage utilizes Normalized Cross Correlation only in the estimated direction to find the exact amount of displacement. Experimental results have been tabulated to illustrate superior computational efficiency of the proposed algorithm versus phase correlation, as well as robustness of the procedure in the presence of the noise.

Abstract: Digital image stabilisation for mobile devices based on real-time phase correlation with support for the SIMD data path is presented. By using sub-image projection, the phase correlation process can be fitted within the real-time criteria. The proposed method acquires a global motion vector from a sub-image at the centre of the viewport, which is projected onto the x- and y-axes on which the phase correlation is performed. The projection stage and the FFT calculations are accelerated using the Neon SIMD engine that is facilitated in the ARM CPU. With this acceleration, the global motion vector for each image frame can be calculated in<20 ms on the Samsung Galaxy S smartphone running at 1.0 GHz.

Abstract: Nowadays the interpretation of the images acquired by wireless endoscopy system is a tedious job for doctors. A viable solution is to construct a map, which is the 2D representation of gastrointestinal (GI) tract to reduce the redundancy of images and improve the understandability of them. The work reported in this paper addresses the problem of the 2D representation of GI tract based on a new wireless Micro-Ball endoscopy system with multiple image sensors. This paper firstly models the problem of constructing the map, and then discusses mainly on the issues of perspective distortion correction, image preprocessing and image registration, which lie in the whole problem. The perspective distortion correction algorithm is realized based on attitude angles, while the image registration is based on phase correlation method (PCM) and scale invariant feature transform (SIFT) combined with particular image preprocessing methods. Based on R channels of images, the algorithm can deal with 26.3% to 100% of image registration when the ratio of overlap varies from 25% to 80%. The performance and effectiveness of the algorithms are verified by experiments.

Abstract: In recent years, a number of methods have been proposed in the literature for the encryption of two-dimensional information by use of the fractional Fourier transform, but most of their encryptions are complex value and need digital hologram technique to record information, which is inconvenience for digital transmission. In this paper, we propose a new approach for image encryption based on the real-value and decorrelation property of the reality-preserving multiple-parameter fractional Fourier transform in order to meet the requirements of the secure image transmission. In the proposed scheme, the original and encrypted images are respectively in the spatial domain and the reality-preserving multiple-parameter fractional Fourier transformed domain determined by the encryption keys. Numerical simulations are performed to demonstrate that the proposed method is reliable and more robust to blind decryption than several existing methods.

Abstract: We outline a method that brings the elegant, unifying geometry of orthogonal function expansions to the teaching of Fourier Analysis in our gateway course on Signals and Systems at UC Berkeley. Our approach starts with discrete-time periodic signals. Their straightforward representation as finite-dimensional Cartesian vectors provides a gentle ingress into the more abstract Euclidean vector spaces that inform the Fourier decompositions of richer signal types. As we describe how a signal fragments into its elemental frequencies, we are careful with the mathematics but we do not let rigor eclipse clarity; plausible reasoning often suffices. We sequence the topics and develop the theory to reduce algebraic clutter and promote geometric insight into the progressively nuanced world of frequency decompositions nestled in the beautiful heart of Fourier Analysis.