Showing papers on "Phase correlation published in 2017"

Fourier Phase Retrieval: Uniqueness and Algorithms

Abstract: The problem of recovering a signal from its phaseless Fourier transform measurements, called Fourier phase retrieval, arises in many applications in engineering and science Fourier phase retrieval poses fundamental theoretical and algorithmic challenges In general, there is no unique mapping between a one-dimensional signal and its Fourier magnitude, and therefore the problem is ill-posed Additionally, while almost all multidimensional signals are uniquely mapped to their Fourier magnitude, the performance of existing algorithms is generally not well-understood In this chapter we survey methods to guarantee uniqueness in Fourier phase retrieval We then present different algorithmic approaches to retrieve the signal in practice We conclude by outlining some of the main open questions in this field

AROSICS: An Automated and Robust Open-Source Image Co-Registration Software for Multi-Sensor Satellite Data

Abstract: Geospatial co-registration is a mandatory prerequisite when dealing with remote sensing data. Inter- or intra-sensoral misregistration will negatively affect any subsequent image analysis, specifically when processing multi-sensoral or multi-temporal data. In recent decades, many algorithms have been developed to enable manual, semi- or fully automatic displacement correction. Especially in the context of big data processing and the development of automated processing chains that aim to be applicable to different remote sensing systems, there is a strong need for efficient, accurate and generally usable co-registration. Here, we present AROSICS (Automated and Robust Open-Source Image Co-Registration Software), a Python-based open-source software including an easy-to-use user interface for automatic detection and correction of sub-pixel misalignments between various remote sensing datasets. It is independent of spatial or spectral characteristics and robust against high degrees of cloud coverage and spectral and temporal land cover dynamics. The co-registration is based on phase correlation for sub-pixel shift estimation in the frequency domain utilizing the Fourier shift theorem in a moving-window manner. A dense grid of spatial shift vectors can be created and automatically filtered by combining various validation and quality estimation metrics. Additionally, the software supports the masking of, e.g., clouds and cloud shadows to exclude such areas from spatial shift detection. The software has been tested on more than 9000 satellite images acquired by different sensors. The results are evaluated exemplarily for two inter-sensoral and two intra-sensoral use cases and show registration results in the sub-pixel range with root mean square error fits around 0.3 pixels and better.

Highly Accurate Time-of-Flight Measurement Technique Based on Phase-Correlation for Ultrasonic Ranging

Abstract: Ultrasonic-based distance measurements using time-of-flight (TOF) is a fundamental technique for different applications across a wide variety of fields. In general, cross correlation between a transmitted and received signal is considered to be the optimal TOF estimation technique, which produces a peak at the time delay between them. Cross correlation provides a superior performance in conjunction with a linear chirp. However, as its accuracy depends on the width of the peak, which is inversely proportional to the signal’s bandwidth, it can only be said to be highly accurate if the reflected signal at the receiver is separated in time by more than the width of the correlation peak; otherwise, errors are introduced into the system. To improve its accuracy, the bandwidth of the transmitted signal must be increased, which increases the system cost. In this paper, to solve this problem, a $\text {threshold-based}\,\,\text {phase-correlation}$ technique is proposed, which is able to provide a much narrower peak than cross correlation without increasing the signal’s physical bandwidth. To evaluate the proposed method, in a controlled environment, two experiments were performed under low and high multipath conditions. For an operational range of 600 mm (indoor), the root-mean-square errors were [0.10, 0.56] mm and [0.19, 1.19] mm for low and high multipath environments, respectively, which indicate that the proposed technique is precise enough to support high accuracy applications.

Automatic sub-pixel co-registration of Landsat-8 Operational Land Imager and Sentinel-2A Multi-Spectral Instrument images using phase correlation and machine learning based mapping

Abstract: This study investigates misregistration issues between Landsat-8/ Operational Land Imager and Sentinel-2A/ Multi-Spectral Instrument at 30 m resolution, and between multi-temporal Sentinel-2A images at 10 m resolution using a phase-correlation approach and multiple transformation functions. Co-registration of 45 Landsat-8 to Sentinel-2A pairs and 37 Sentinel-2A to Sentinel-2A pairs were analyzed. Phase correlation proved to be a robust approach that allowed us to identify hundreds and thousands of control points on images acquired more than 100 days apart. Overall, misregistration of up to 1.6 pixels at 30 m resolution between Landsat-8 and Sentinel-2A images, and 1.2 pixels and 2.8 pixels at 10 m resolution between multi-temporal Sentinel-2A images from the same and different orbits, respectively, were observed. The non-linear random forest regression used for constructing the mapping function showed best results in terms of root mean square error (RMSE), yielding an average RMSE error of 0.07 ± ...

Evaluating Fourier Cross-Correlation Sub-Pixel Registration in Landsat Images

Abstract: Multi-temporal analysis is one of the main applications of remote sensing, and Landsat imagery has been one of the main resources for many years. However, the moderate spatial resolution (30 m) restricts their use for high precision applications. In this paper, we simulate Landsat scenes to evaluate, by means of an exhaustive number of tests, a subpixel registration process based on phase correlation and the upsampling of the Fourier transform. From a high resolution image (0.5 m), two sets of 121 synthetic images of fixed translations are created to simulate Landsat scenes (30 m). In this sense, the use of the point spread function (PSF) of the Landsat TM (Thematic Mapper) sensor in the downsampling process improves the results compared to those obtained by simple averaging. In the process of obtaining sub-pixel accuracy by upsampling the cross correlation matrix by a certain factor, the limit of improvement is achieved at 0.1 pixels. We show that image size affects the cross correlation results, but for images equal or larger than 100 × 100 pixels similar accuracies are expected. The large dataset used in the tests allows us to describe the intra-pixel distribution of the errors obtained in the registration process and how they follow a waveform instead of random/stochastic behavior. The amplitude of this waveform, representing the highest expected error, is estimated at 1.88 m. Finally, a validation test is performed over a set of sub-pixel shorelines obtained from actual Landsat-5 TM, Landsat-7 ETM+ (Enhanced Thematic Mapper Plus) and Landsat-8 OLI (Operation Land Imager) scenes. The evaluation of the shoreline accuracy with respect to permanent seawalls, before and after the registration, shows the importance of the registering process and serves as a non-synthetic validation test that reinforce previous results.

Position detection method of linear motor mover based on extended phase correlation algorithm

Abstract: This study aims to explain the real-time and high-precision requirements of linear motor mover position detection. A new sub-pixel displacement estimation based on an extended phase correlation algorithm (PCA) is proposed and applied to measure the position of the linear motor mover. This extended PCA is on the basis of singular value decomposition (SVD), which is a novel application in position measurement of the linear motor mover. First, two adjacent stripe images are captured by a high-speed camera installed in the linear motor. Second, an improved Hanning (flap-top) window function is added to the input fence images to suppress the edge effect and spectral aliasing, before the discrete Fourier transform (DFT). Next, phase correlation matrix is acquired by PCA, and using SVD technique to calculate approximate rank-one matrix for subsequent phase unwrapping. Then, weighted-phase unwrap algorithm is applied to acquire the real horizontal phase data. Finally, least-squares method is utilised to linearly fit the real phase data and to obtain sub-pixel displacement of the linear motor mover. Experiments show that the detection accuracy is 1/100 pixel, and the position measurement of linear motor mover is fast and effective.

Enhancement of phase detection for autofocus

Abstract: Phase detection autofocus (PDAF) is a technique that uses sensors on left and right pixels to determine the relative position between the object and the focal plane. When an image is out of focus, a shift between the assembled left and right pixels is resulted, which can be used to determine the lens movement during the autofocus process. However, the presence of noise and blur often affects the accuracy of shift estimation and hence the performance of autofocus. In this paper, we propose a method to enhance phase detection for such sensors. A Gaussian filter is applied to overcome the adverse effect of image noise and blur. Experiments are conducted to show that the proposed method leads to a more accurate estimate of lens movement than the traditional phase correlation.

An image registration algorithm based on phase correlation and the classical Lucas–Kanade technique

Abstract: Image registration is defined as an important process in image processing in order to align two or more images. A new image registration algorithm for translated and rotated pairs of 2D images is presented in order to achieve subpixel accuracy and spend a small fraction of computation time. To achieve the accurate rotation estimation, we propose a two-step method. The first step uses the Fourier Mellin Transform and phase correlation technique to get the large rotation, then the second one uses the Fourier Mellin Transform combined with an enhance Lucas–Kanade technique to estimate the accurate rotation. For the subpixel translation estimation, the proposed algorithm suggests an improved Hanning window as a preprocessing task to reduce the noise in images then achieves a subpixel registration in two steps. The first step uses the spatial domain approach which consists of locating the peak of the cross-correlation surface, while the second uses the frequency domain approach, based on low-frequency (aliasing-free part) of aliased images. Experimental results presented in this work show that the proposed algorithm reduces the computational complexities with a better accuracy compared to other subpixel registration algorithms.

Robust Estimation of Similarity Transformation for Visual Object Tracking with Correlation Filters.

Abstract: Most of existing correlation filter-based tracking approaches only estimate simple axis-aligned bounding boxes, and very few of them is capable of recovering the underlying similarity transformation. To a large extent, such limitation restricts the applications of such trackers for a wide range of scenarios. In this paper, we propose a novel correlation filter-based tracker with robust estimation of similarity transformation on the large displacements to tackle this challenging problem. In order to efficiently search in such a large 4-DoF space in real-time, we formulate the problem into two 2-DoF sub-problems and apply an efficient Block Coordinates Descent solver to optimize the estimation result. Specifically, we employ an efficient phase correlation scheme to deal with both scale and rotation changes simultaneously in log-polar coordinates. Moreover, a fast variant of correlation filter is used to predict the translational motion individually. Our experimental results demonstrate that the proposed tracker achieves very promising prediction performance compared with the state-of-the-art visual object tracking methods while still retaining the advantages of efficiency and simplicity in conventional correlation filter-based tracking methods.

Solving sub-pixel image registration problems using phase correlation and Lucas-Kanade optical flow method

Abstract: Image registration plays a major role in many areas such as remote sensing, astronomy, biomedical imaging, and so on. Our main contribution in this paper is to present a new subpixel image registration that aligns translated of pair images. This algorithm combines well-known phase correlation technique with the differential methods of the optical flow field, especially the Locus-Kanade technique to register images. The experiment results show that our method not only enhances the precision of registration but also reduces time complexity.

Fourier–Mellin registration of two hyperspectral images

Abstract: Hyperspectral images contain a great amount of information which can be used to more robustly register such images. In this article, we present a phase correlation method to register two hyperspect...

Phase Correlation for Dense Visual Compass from Omnidirectional Camera-Robot Images

Abstract: In this paper, we present a new omnidirectional visual compass for a camera-robot, based on the phase correlation method in the 2-D Fourier domain. The proposed visual compass is accurate, robust to image noise, and frugal in the use of computational resources. Moreover, unlike the majority of existing ego-motion estimators, it does not rely on any geometric image primitive, and it only requires a minimal knowledge of the internal camera parameters. Extensive real-world experiments conducted with a hypercatadioptric camera mounted on the end-effector of a Staubli manipulator and on a Pioneer robot, show the effectiveness of our approach.

High-Accuracy Subpixel Image Registration With Large Displacements

Abstract: This paper aims to achieve computationally efficient and high-accuracy subpixel image registration with large displacements under the rotation–scale–translation model. This paper employs the classical phase correlation algorithm and the Lucas–Kanade (LK) algorithm in a two-stage coarse-to-fine framework, for which the motivation is from the observation that the two algorithms exhibit strong complementary property between convergence range and subpixel accuracy. In this framework, the LK algorithm will also become computationally efficient owing to the small residual displacement. On the other hand, this paper takes into account the residual model with respect to the compensation scheme explicitly, and deduces formulas for the final results combination, which is expected to be closer to the true displacement vector and thus further improve the estimation accuracy. Since the compensation can be applied to either the target image or the reference image, two algorithms are presented accordingly, and analysis as well as comparison are also performed. Finally, both simulations and real image experiments are performed to verify the motivation, and the results are consistent with the analysis.

Detecting Edges from Non-uniform Fourier Data Using Fourier Frames

Abstract: Edge detection plays an important role in identifying regions of interest in an underlying signal or image. In some applications, such as magnetic resonance imaging (MRI) or synthetic aperture radar (SAR), data are sampled in the Fourier domain. Many algorithms have been developed to efficiently extract edges of images when uniform Fourier data are acquired. However, in cases where the data are sampled non-uniformly, such as in non-Cartesian MRI or SAR, standard inverse Fourier transformation techniques are no longer suitable. Methods exist for handling these types of sampling patterns, but are often ill-equipped for cases where data are highly non-uniform or when the data are corrupted or otherwise not usable in certain parts of the frequency domain. This investigation further develops an existing approach to discontinuity detection, and involves the use of concentration factors. Previous research shows that the concentration factor technique can successfully determine jump discontinuities in non-uniform data. However, as the distribution diverges further away from uniformity so does the efficacy of the identification. Thus we propose a method that employs the finite Fourier approximation to specifically tailor the design of concentration factors. We also adapt the algorithm to incorporate appropriate smoothness assumptions in the piecewise smooth regions of the function. Numerical results indicate that our new design method produces concentration factors which can more precisely identify jump locations than those previously developed in both one and two dimensions.

Fast Fourier transform benchmark on X86 Xeon system for multimedia data processing

Abstract: I benchmarking the well-known Fast Fourier Transforms Library at X86 Xeon E5 2690 v3 system. Fourier transform image processing is an important tool that is used to decompose the image into sine and cosine components. If the input image represented by the equation in the spatial domain, output from the Fourier transform represents the image in the fourier or the frequency domain. Each point represents a particular frequency included in the spatial domain image in the Fourier domain image. Fourier transform is used widely for image analysis, image filtering, image compression and image reconstruction as a wide variety of applications. Fourier transform plays a important role in signal processing, image processing and speech recognition. It has been used in a wide range of sectors. For example, this is often a signal processing, is used in digital signal processing applications, such as voice recognition, image processing. The Discrete Fourier transform is a specific kind of Fourier transform. It maps the sequence over time to sequence over frequencies. If it implemented as a discrete Fourier transform, the time complexity is O (N2). It's actually not a better way to use. Alternatively, the Fast Fourier Transform is possible to easily perform a Discrete Fourier Transform of parallelism with only O (n log n) algorithm. Fast Fourier Transform is widely used in a variety of scientific computing program. If you are using the correct library can improve the performance of the program, without any additional effort. I have a well-known fast Fourier transform library was going to perform a benchmarking on X86 based Intel Xeon E5 2690 systems. In the machine's current Intel Xeon X86 Linux system. I have installed Intel IPP library, FFTW3 Library (West FFT), Kiss -FFT library and the numutils library on Intel X86 Xeon E5 based systems. The benchmark performed at C, and measuring the performance over a range of a transform size. It benchmarks both real and complex transforms in one dimension.

Features based image registration using cross correlation and Radon transform

Abstract: In many research fields, like Medical image analysis, pattern recognition, computer vision and remote sensed data processing, it is required to align the images. This article describes and compares two different methods to register images. In the first method, the Fourier Merlin transform based on the phase correlation of the two images in the Log-polar domain. However, it suffers from non-uniform sampling which makes it not suitable for applications causing losses in image information which will decrease the registration accuracy. The second method is to use the Radon transform proprieties to extract the rotation angle. Experiments show that the proposed method can detect the angle of rotation efficiently for different types of images without the SAR complex images.

Parallel Nonuniform Discrete Fourier Transform (P-NDFT) Over a Random Wireless Sensor Network

Abstract: Reduced execution time and increased power efficiency are important objectives in the distributed execution of collaborative signal processing tasks over wireless sensor networks (WSNs) Meanwhile, Fourier transforms are among the most widely used frequency analysis tools in WSNs for studying the behavior of sensed phenomena Several energy-efficient in-network Fourier transform computation algorithms have been proposed for WSNs Most of these works assume that the sensors are equally spaced over a one-dimensional (1D) region However, in practice, the sensors are usually randomly distributed over a two-dimensional (2D) plane Consequently, the conventional 2D Fast Fourier Transform (FFT) designed for data sampled on a uniform grid is not applicable in such environments We address this problem by designing a distributed hybrid structure consisting of local Non-equispaced Discrete Fourier Transform (NDFT) and global FFT computations First, the NDFT method is applied within suitably selected clusters to obtain the initial uniform Fourier coefficients within allowable estimation error bounds We investigate both classical linear and generalized interpolation methods for computing the NDFT coefficients within each cluster Second, a separable 2D FFT is applied over all clusters using our proposed energy-efficient 1D FFT computation method, which reduces communication costs by employing a novel binary representation mapping strategy for data exchanges between sensors The proposed techniques are implemented on the SIDnet-SWANS platform, and the tradeoffs between communication cost, execution time, and energy consumption are studied

Automatic registering and fused splicing method of multiple images

Abstract: The invention relates to an automatic registering and fused splicing method of multiple images. The unordered images are enhanced in a multi-dimension Retinex method; the images match each other by utilizing a logarithm polar coordinate transformation improved phase correlation algorithm, zooming, rotation and translation parameters are calculated, an overlapped area among the images is estimated roughly, and an ordering rule is formulated according to energy peak values of an impulse function; an SUFR algorithm is used to extract characteristic points from the overlapped area to be registered, a random sampling consistent algorithm is improved to purify matching point pairs accurately, model parameters are optimized, a transformation matrix among the images is established, and sequential images are spliced successively; and an NSCT algorithm is utilized, a fusion strategy is made to further fuse spliced images, and a spliced image after fusion is output. The method of the invention can be used to reduce influence of difficult manual ordering, fuzzy image details, low resolution, high noise, nonuniform illumination and the like on image registration and splicing, provides help for reducing cost of imaging equipment and accurate diagnosis of medical staff, and has good application prospects in the medical image assisted field.

Phase retrieval using a conjugate symmetric reference

Abstract: It was recently shown that finding a compactly supported vector that solves the 1D Fourier phase retrieval problem in the least-squares sense can be computed in polynomial-time, although the solution is not unique. To resolve identifiability, we previously proposed adding a Kronecker delta reference with sufficiently large intensity to the signal before measuring its Fourier magnitude. In practice, however, it is difficult to add a reference that is both strong enough to meet the intensity requirement, and narrow enough to be considered a Kronecker delta after sampling. In this paper we propose a physically more accessible approach to correctly recover a signal from Fourier magnitude measurements, assuming we can 1) generate a reference that is conjugate symmetric (no specific requirement on the power), and 2) measure the Fourier intensity of both the desired signal alone and the signal plus the reference. Numerical simulations showcase the effectiveness of the proposed method in exact signal recovery, as well as noise robustness for certain choices of the references, which cannot be achieved by other methods under the same measuring settings.

Image matching method based on multiscale Fourier-Mellin transform

Abstract: The invention discloses an image matching method based on multiscale Fourier-Mellin transform. The method comprises the following steps of acquiring a reference image I1 and an image to be matched I2 respectively, determining a Gaussian kernel at a pixel position (x, y) in the I2, and calculating a scale space image pixel value L(x, y, t) at the pixel position (x, y) in the I2; further acquiring a scale space image L(t) of the image to be matched I2, and carrying out bilinear interpolation on the L(t) respectively so as to acquire simulation imaging S(t) after the bilinear interpolation; setting a blank image whose size is the same with the size of the L(t), embedding a gray value of each pixel position in the S(t) into the blank image respectively so as to acquire a multiscale image, and calculating a Fourier-Mellin invariant image of the I1 and a Fourier-Mellin invariant image of the multiscale image S'(t) respectively; and calculating a phase correlation matching image between the scale space images L(t) of the I1 and the I2, calculating a convergent-divergent scale estimation value of a pixel position in the I1 and a rotation angle estimation value of the pixel position in the I1 respectively and then acquiring an optimal matching image of the I2.

A Fast Algorithm of GNSS-R Signal Processing Based on DBZP

Abstract: An important observation of GNSS-R is Delay-Doppler mapping (DDM). According to the requirement of GNSS-R signal real-time processing, a fast processing algorithm of GNSS-R signal based on double block zero padding (DBZP) and frequency domain rotation transformation is proposed for DDM generation. The reflected data is blocked and then correlated, which avoids the FFT calculation with too long points. The block and zero padding operations not only guarantee the full search of the pseudo code phase, but also avoid the repetitive calculation. In the frequency domain, the correlation results at different Doppler frequencies are approximated by the rotation transformation method, which avoids a large number of carrier multiplication operations and effectively reduces the computational burden. The computational burden and computational loss of parallel code phase correlation algorithm and fast algorithm are analyzed. Finally, the UK-DMC satellite-borne reflected data are processed by two algorithms and the simulation time-consuming and processing results were compared. The results show that the fast algorithm greatly shortens the DDM generation time and the loss of the processing result is small.

Motion estimation of sequence image based on feature extraction of extended objects

Abstract: SIFT feature point extraction algorithm is commonly used in image matching which maintains invariance for scaling, rotation, and brightness changes. Phase correlation algorithm is less dependent on image information with relativity strong noise cancellation performance and high robustness. Based on the traditional phase correlation method, a subpixel accuracy motion estimation method based on interest region is proposed to achieve the high precision localization of the extended object. The paper choose feature blocks centered on feature points extracted from SIFT algorithm. Then the phase correlation operation is performed on the obtained feature blocks and the initial amount of translation is obtained. Then interpolate and implement cubic surface fitting on the neighborhood of the correlation peak, the accurate translation of adjacent images is obtained. The paper simulate the classical pictures applied to image processing. The accuracy of the method is verified by the ideal data.

Automatic Matching of Multi-Source Satellite Images: A Case Study on ZY-1-02C and ETM+

Abstract: The ever-growing number of applications for satellites is being compromised by their poor direct positioning precision. Existing orthoimages, such as enhanced thematic mapper (ETM+) orthoimages, can provide georeferences or improve the geo-referencing accuracy of satellite images, such ZY-1-02C images that have unsatisfactory positioning precision, thus enhancing their processing efficiency and application. In this paper, a feasible image matching approach using multi-source satellite images is proposed on the basis of an experiment carried out with ZY-1-02C Level 1 images and ETM+ orthoimages. The proposed approach overcame differences in rotation angle, scale, and translation between images. The rotation and scale variances were evaluated on the basis of rational polynomial coefficients. The translation vectors were generated after blocking the overall phase correlation. Then, normalized cross-correlation and least-squares matching were applied for matching. Finally, the gross errors of the corresponding points were eliminated by local statistic vectors in a TIN structure. Experimental results showed a matching precision of less than two pixels (root-mean-square error), and comparison results indicated that the proposed method outperforms Scale-Invariant Feature Transform (SIFT), Speeded Up Robust Features (SURF), and Affine-Scale Invariant Feature Transform (A-SIFT) in terms of reliability and efficiency.

Image registration with subpixel accuracy of DCT-sign phase correlation with real subpixel shifted images

Abstract: We evaluate the subpixel accuracy of Discrete Cosine Transform (DCT)-sign phase correlation (-SPC) for image registration. So far, the accuracy was evaluated using images captured by a commercial-off-the-shelf camera, which yields poor results. In the present paper, we use the subpixel-shifted images captured by an industry product camera in order to avoid the problems with a commercial-off-the-shelf camera. We demonstrate the DCT-SPC will be an alternative for phase correlation.

Aerial photographing sequential image automatic ordering method

Abstract: The invention discloses an aerial photographing sequential image automatic ordering method. The limitation of the conventional phase correlation method for the image size consistency can be broken through, and an improved image sequence automatic ordering algorithm scheme based on the phase correlation method is provided. According to the scheme, the relationship of two images to be matched is expressed by using a log polar coordinate mode, ordering models of rotation, translation and scale transformation are established, the head and tail images of the sequence are determined through the maximum degree of correlation and then translation parameters are determined by using the coordinates of the peak value, and the left and right positional relationship of the images is judged according to the given criteria so that artificial intervention can be avoided, the confusion problem of left and right translation can also be eliminated and the sequential images can be accurately ordered. Automatic ordering of translation, rotation, zooming and other complex relationship between the images cannot be completed by the conventional phase correlation method can be overcome so that the range of application of the algorithm can be enhanced, a certain foundation is laid for aerial photographing panoramic image splicing and thus the method has high practical value.

The application of random phase filter in the image recognition

Abstract: We define one kind of new correlation, i.e. random phase correlation, which based on the Random Fourier Transform (RFT). An optical pattern recognition system, random phase filtering, is given according to random phase correlation. Furthermore its electro-optical setup is given for the application in image recognition. By the numerical simulation on computer, when the, we have found the proposed random phase filter can recognize the small change of object image and has higher recognition capability comparing of other three conventional correlators, the classical marched filter, the phase-only filter and the pure phase correlator.