Fourier-Mellin Transform Research Articles

Robust watermarking method based on the Analytical Clifford Fourier Mellin Transform

Robust watermarking method based on the Analytical Clifford Fourier Mellin Transform

Change Detection in VHR Imagery With Severe Co-Registration Errors Using Deep Learning: A Comparative Study

Change detection (CD) through Earth observation techniques can offer very significant information for monitoring tasks in a time-efficient manner. Very high-resolution (VHR) images can display objects in fine detail, thus making it possible to rapidly perceive isolated changes. However, this is a challenging task because of the increased within-class variance and geometric registration errors caused by different satellite view directions and angles. Lately, deep learning (DL) CD methods have proven very appealing for the CD problem because of their flexibility to combine and process different types of information along with the increased availability of higher processing power systems. Even though previous research has developed several notable DL methodologies, it has mostly focused on images with minor co-registration errors. Based on that, the goal of this study is to evaluate the performance of five state-of-the-art DL CD methods, two unsupervised and three supervised, on VHR images with severe co-registration errors. The methods are implemented on four urban European areas of versatile morphology. In addition, before applying the CD process, four popular automatic co-registration methods were evaluated because of the importance of this pre-processing step for the successful output of the CD problem. It was shown that phase correlation used on the Fourier-Mellin Transform produced the most satisfactory co-registration results and STANet detected building-related changes most successfully. Its success can be attributed to its particular attention mechanism and its training dataset. The rest of the co-registration and CD methods showed low performance.

Three Dimensional Fractional Fourier-Mellin Transform, and its Applications

The main objective of the paper is to study the three-dimensional fractional Fourier Mellin transforms (3DFRFMT), their basic properties and applicability due to mainly use in the radar system, reconstruction of grayscale images, in the detection of the human face, etc. Only the fractional Fourier transform is based on time-frequency distribution, whereas only the fractional Mellin transform is on scale covariant transformation. Both transforms can discover action in the definite assortment. The fractional Fourier transform is applicable for controlling the range of shift, whereas the fractional Mellin transform is accustomed to managing the range of rotation and scaling of the function. So, combining both transformations, we get an elegant expression for 3DFRFMT, which can be used in several fields. The paper introduces the concept of three-dimensional fractional Fourier Mellin transforms and their applications. Modulation property is the most useful concept in the signal system, radar technology, pattern reorganization, and many more in the integral transform. Parseval's identity applies to the conservation of energy in the universe. Thus we establish the modulation theorem, Parseval's theorem, scaling theorem, analytic theorem for three-dimensional fractional Fourier Mellin transform. We also give some examples of three-dimensional fractional Fourier-Mellin transform on some functions. Finally, we provide three-dimensional fractional Fourier-Mellin transform applications for solving homogeneous and non-homogeneous Mboctara partial differential equations that we can apply with advantages to solve the different types of problems in signal processing systems. The transform is beneficial in a maritime strategy as a co-realtor to control moments in any specific three-dimensional space. The concept is the most powerful tool to deal with any information system problems. After obtaining the generalization, we can explore many more ideas in applying three-dimensional fractional Fourier-Mellin transformations in many real word problems.

Rethinking the Fourier-Mellin Transform: Multiple Depths in the Camera’s View

Remote sensing and robotics often rely on visual odometry (VO) for localization. Many standard approaches for VO use feature detection. However, these methods will meet challenges if the environments are feature-deprived or highly repetitive. Fourier-Mellin Transform (FMT) is an alternative VO approach that has been shown to show superior performance in these scenarios and is often used in remote sensing. One limitation of FMT is that it requires an environment that is equidistant to the camera, i.e., single-depth. To extend the applications of FMT to multi-depth environments, this paper presents the extended Fourier-Mellin Transform (eFMT), which maintains the advantages of FMT with respect to feature-deprived scenarios. To show the robustness and accuracy of eFMT, we implement an eFMT-based visual odometry framework and test it in toy examples and a large-scale drone dataset. All these experiments are performed on data collected in challenging scenarios, such as, trees, wooden boards and featureless roofs. The results show that eFMT performs better than FMT in the multi-depth settings. Moreover, eFMT also outperforms state-of-the-art VO algorithms, such as ORB-SLAM3, SVO and DSO, in our experiments.

An Improved Fourier-Mellin Transform-Based Registration Used in TDI-CMOS

Time-delayed integration (TDI) is a common imaging mode used in airborne cameras to compensate for image motion. The paper presents an improved Fourier-Mellin transform (FMT)-based registration method, which can be used to realize the registration-based TDI. It first analyzes the noise influences on the FMT spectrum by comparing the curve changes in the standard-deviation versus column plots under the various intensity of noise, then designs a special filter called WCSDF according to the amount of variation of each column in the FMT spectrum, which can reduce the noise affection on registration process to the larger extent. And an improved FMT-based registration method is finally proposed to form a framework of registration-based TDI. In computer simulations, the proposed method shows a significant improvement in robustness to noise (noise level up to 40). Compared with the existing method, its low computational complexity makes the method easy to be implemented in hardware and can estimate the larger relative shifts among dim noisy images, moreover, the TDI images generated by the proposed framework have higher quality in the index of information entropy, average gradient, and spatial frequency response.

A hybrid copy-move image forgery detection technique based on Fourier-Mellin and scale invariant feature transforms

In digital images, the most common forgery is copy-move image forgery in which some region(s) of an image is replicated within the image. The copy-move forgery detection (CMFD) techniques fall under two categories; keypoint-based and block-based. The keypoint-based techniques perform well under rotation and scaling but show very poor performance in the case of smooth images. On the contrary, the block-based techniques perform better in smooth images but are comparatively more time demanding. In this paper, a hybrid technique has been proposed by combining the block-based technique using Fourier-Mellin Transform (FMT) and a keypoint-based technique using Scale Invariant Feature Transform (SIFT). In this technique, the input image to be checked for forgery is first divided into texture and smooth regions. Then the keypoints are extracted from the texture part of the image using the SIFT descriptor, and the FMT is applied on the smooth part of the image. Extracted features are then matched to detect the duplicated regions of the image. The experimental results illustrate that the proposed technique performs better in comparison to other state-of-the-art CMFD techniques under various geometric transformations and post-processing operations in reasonable time.

Quasi Fourier-Mellin Transform for Affine Invariant Features.

Fourier-Mellin transform (FMT) has been widely used for the extraction of rotation- and scale-invariant features. However, affine transform is a more reasonable approximation model for real viewpoint change. Due to shearing, the integral along the angular direction in the calculation of FMT cannot be used to extract the inherent features of an image undergoing affine transform. To eliminate the effect of shearing, whitening transform should be conducted on the integral along the radial direction. FMT can hardly be modified by conventional whitening-based methods with low computational cost due to additional processes. In this paper, two factors are constructed and embedded into FMT. Quasi Fourier-Mellin transform (QFMT) is proposed. The embedding of these factors is equivalent to whitening transform and can eliminate the effect of shearing in the affine transform. In particular, QFMT can also be calculated by integrating along the radial direction followed by integrating along the angular direction, as in FMT. Based on QFMT, the quasi Fourier-Mellin descriptor (QFMD) is constructed for the extraction of affine invariant features. Some experiments have also been conducted to test the performance of the proposed method.

Target recognition method with frequency features on retina-like laser detection and range images.

A target-recognition method for retina-like laser detection and range images is proposed. A log-polar (LP) frequency descriptor (LPHFM) is constructed using Fourier-Mellin transformation combined with a high-pass filter for LP range images. The target-recognition result can be obtained via the maximum energy from the phase correlation spectrum. The LPHFM feature with LP images is explored, and examples are used to demonstrate the validity and capability of the proposed method. Finally, important conclusions are drawn as follows: (I) Applying frequency features with the LP process is valid; (II) LPHFM feature extraction is easily accomplished when the technique is directly applied to LP images after high-pass filtering; (III) The accuracy of the proposed solution agrees well with theoretical values when angle and scale variants are used. Thus, the proposed recognition solution may be used in various applications involving space-variant image processing.

A robust and forensic transform for copy move digital image forgery detection based on dense depth block matching

ABSTRACTCopy-move forgery is one of the most popular tampering artefacts in digital images. However, tampering effect in digital images makes the authentication of the processing as untrustworthy. In this paper, a combination of Fourier-Mellin and Zernike moments (FMZM) Transform is proposed which detects the copy-move region with high-speed and low-computational complexity. Here, initially an image is segmented into various blocks using marker controlled watershed management and from that proposed FMZM feature extraction is used which detects duplication. The detected regions are matched with the Dense Depth Reconstruction based lexicographically sorting. Finally, tampered outliers presented at the data are removed through RANSAC (RANdom Sample Consensus) algorithm, in which removed false matches are verified with the morphological operators. The efficiency of proposed method is measured by various performance metrics and this method earned up to 97.56%, 99.98%, and 97.12% for precision, recall, and F1-score performance, respectively.

FAST PAIRWISE COARSE REGISTRATION BETWEEN POINT CLOUDS OF CONSTRUCTION SITES USING 2D PROJECTION BASED PHASE CORRELATION

Abstract. For conducting change detection using 3D scans of a construction site, the registration between point clouds at different acquisition times is normally necessary. However, due to the complexity of constructing areas, the automatic registration of temporal scans is a challenging problem. In this work, we propose a fast and maker-free method for coarse registration between point clouds by converting the 3D matching problem into a 2D correlation problem, taking the special properties of building structures into consideration. Our proposed method consists of two major steps: the conversion from 3D points to 2D image data and the estimation of transformation parameters between 2D images in the frequency domain. In the conversion step, the point cloud of each scan is projected into a 2D grey image, by which the ground footprint of the point cloud is obtained. In the following step, we represent the 2D image in frequency-domain and estimate the horizontal transformation parameters by using Fourier-Mellin transformation. A real application is performed to validate the feasibility and effectiveness of our workflow using photogrammetric point clouds of a construction site in two different acquisition time. Regarding the real application of coarse registration of point clouds, our proposed method can achieve a registration error of less than 1 degree and more efficient than the classical baseline methods for the fast orientation between scans.

Phase-Only Rotation Invariant Correlation Using Synthesized Phase Objects.

We present a development of the method of synthesized phase objects (SPO-method) (P. V. Yezhov, et al. Opt. Exp. 20, 29854 (2012)) for the phase-only rotation invariant pattern recognition. It has been performed a comparison of correlation signals for a set of amplitude objects under their rotation by using the standard and SPO methods, by applying the Fourier-Mellin transformation. The results of both calculation and optical experiments carried out using an optical-digital correlator with SLM in the Fourier plane have been presented.

快速高精度Fourier-Mellin变换图像配准方法

快速高精度Fourier-Mellin变换图像配准方法

CMF-iteMS: An automatic threshold selection for detection of copy-move forgery

Taking into consideration that the prior CMF detection methods rely on several fixed threshold values in the filtering process, we propose an efficient CMF detection method with an automatic threshold selection, named as CMF-iteMS. The CMF-iteMS recommends a PatchMatch-based CMF detection method that adapts Fourier-Mellin Transform (FMT) as the feature extraction technique while a new automatic threshold selection based on iterative means of regions size (iteMS) procedure is introduced to have flexibility in changing the threshold value for various characteristics (quality, sizes, and attacks) in each input image. To ensure the reliability of the proposed CMF-iteMS, the method is compared with four state-of-the-art CMF detection methods based on Scale Invariant Feature Transform (SIFT), patch matching, multi-scale analysis and symmetry techniques using three available datasets that cover the variety of characteristics in CMF images. The results show that the F-score of the CMF-iteMS outperformed existing CMF detection methods by exceeding an average of 90% F-score values for image-level evaluation and 82% of F-score value for pixel-level evaluation for all datasets in original size. As special attention is given to the image resizing attack, the method is able to maintain the highest performance even if the images in the datasets are resized to 0.25 parameter.

Fourier Mellin transform characterisation in the automotive environment

This paper discusses the problem of reliably estimating motion in video sequences. A core issue in this application is the registration of successive images in an image sequence of a dynamic scene. The paper examines the core characteristics of the Fourier Mellin transform (FMT) when applied to this task in the automotive environment. Of particular interest are the transformational, scale and rotational invariances of the transform. The objective of the paper is to examine the behaviour of the algorithm under wide variations in these three parameters. Images from a range of automotive scenarios are considered in this evaluation. Our main contributions are the experimental evaluations carried out on various images with a range of known translations, rotations and scale changes. The results of the experimental process allow the determination of the relationship between the transformation of image patches, and the resulting level of error in motion estimation. This helps to inform the application of the FMT, when it is effective, and where its limitations occur. The results of the experimental process described in this paper may be applied in several ways in practice. The applicability of the method may be extended through the addition of environmental variables from external sensors, i.e. CAN bus data, GPS or spatial feature ego-motion. This allows adaptive execution of the transform.

A two-stage localization for copy-move forgery detection

A two-stage localization for copy-move forgery detection (CMFD) is proposed in this paper. In the first stage, rough localization, Simple Linear Iterative Clustering (SLIC) is employed to segment the image into meaningful patches (superpixels). Subsequently, the Weber Local Descriptor (WLD) is proposed to calculate and extract the feature from each superpixel. Then, based on an experimental analysis, a matching threshold is employed to obtain the superpixel matches. Finally, Euclidean distance is employed to filter out the weak features of the superpixels and obtain the rough suspected matches. In the second stage, precise localization, circular blocks with different radii are slid over the above rough suspected regions to extract the block features by employing the Discrete Analytic Fourier–Mellin Transform (DAFMT). Then, Locality-Sensitive Hashing (LSH) is employed to match the candidate circular block matches. Post-processing is applied to further filter out the weak matches and obtain the detected regions. Geometric morphological operations are employed to remove the isolated regions and indicate the final detected regions. The comprehensive experimental results demonstrate that the proposed method performs better on public benchmark databases than do other state-of-the-art CMFD schemes.

THE IMAGE REGISTRATION OF FOURIER-MELLIN BASED ON THE COMBINATION OF PROJECTION AND GRADIENT PREPROCESSING

Abstract. Image registration is one of the most important applications in the field of image processing. The method of Fourier Merlin transform, which has the advantages of high precision and good robustness to change in light and shade, partial blocking, noise influence and so on, is widely used. However, not only this method can’t obtain the unique mutual power pulse function for non-parallel image pairs, even part of image pairs also can’t get the mutual power function pulse. In this paper, an image registration method based on Fourier-Mellin transformation in the view of projection-gradient preprocessing is proposed. According to the projection conformational equation, the method calculates the matrix of image projection transformation to correct the tilt image; then, gradient preprocessing and Fourier-Mellin transformation are performed on the corrected image to obtain the registration parameters. Eventually, the experiment results show that the method makes the image registration of Fourier-Mellin transformation not only applicable to the registration of the parallel image pairs, but also to the registration of non-parallel image pairs. What’s more, the better registration effect can be obtained

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

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.

Classification of footwear outsole patterns using Fourier transform and local interest points

Successful classification of questioned footwear has tremendous evidentiary value; the result can minimize the potential suspect pool and link a suspect to a victim, a crime scene, or even multiple crime scenes to each other. With this in mind, several different automated and semi-automated classification models have been applied to the forensic footwear recognition problem, with superior performance commonly associated with two different approaches: correlation of image power (magnitude) or phase, and the use of local interest points transformed using the Scale Invariant Feature Transform (SIFT) and compared using Random Sample Consensus (RANSAC). Despite the distinction associated with each of these methods, all three have not been cross-compared using a single dataset, of limited quality (i.e., characteristic of crime scene-like imagery), and created using a wide combination of image inputs. To address this question, the research presented here examines the classification performance of the Fourier–Mellin transform (FMT), phase-only correlation (POC), and local interest points (transformed using SIFT and compared using RANSAC), as a function of inputs that include mixed media (blood and dust), transfer mechanisms (gel lifters), enhancement techniques (digital and chemical) and variations in print substrate (ceramic tiles, vinyl tiles and paper). Results indicate that POC outperforms both FMT and SIFT+RANSAC, regardless of image input (type, quality and totality), and that the difference in stochastic dominance detected for POC is significant across all image comparison scenarios evaluated in this study.

Low-quality fingerprint recognition using a limited ellipse-band-based matching method.

Current fingerprint recognition technologies are based mostly on the minutia algorithms, which cannot recognize fingerprint images in low-quality conditions. This paper proposes a novel recognition algorithm using a limited ellipse-band-based matching method. It uses the Fourier-Mellin transformation method to improve the limitation of the original algorithm, which cannot resist rotation changes. Furthermore, an ellipse band on the frequency amplitude is used to suppress noise that is introduced by the high-frequency parts of images. Finally, the recognition result is obtained by considering both the contrast and position correlation peaks. The experimental results show that the proposed algorithm can increase the recognition accuracy, particularly of images in low-quality conditions.

Measurement of fluid rotation, dilation, and displacement in particle image velocimetry using a Fourier–Mellin cross-correlation

Traditional particle image velocimetry (PIV) uses discrete Cartesian cross correlations (CCs) to estimate the displacements of groups of tracer particles within small subregions of sequentially captured images. However, these CCs fail in regions with large velocity gradients or high rates of rotation. In this paper, we propose a new PIV correlation method based on the Fourier–Mellin transformation (FMT) that enables direct measurement of the rotation and dilation of particle image patterns. In previously unresolvable regions of large rotation, our algorithm significantly improves the velocity estimates compared to traditional correlations by aligning the rotated and stretched particle patterns prior to performing Cartesian correlations to estimate their displacements. Our algorithm, which we term Fourier–Mellin correlation (FMC), reliably measures particle pattern displacement between pairs of interrogation regions with up to ±180° of angular misalignment, compared to 6–8° for traditional correlations, and dilation/compression factors of 0.5–2.0, compared to 0.9–1.1 for a single iteration of traditional correlations.We apply our FMC algorithm to synthetic computer-generated PIV images with known velocity and vorticity fields, and to an experimentally measured flow field. Our results show that combining FMC with discrete window offset (DWO) or iterative image deformation (IID) algorithms decreases the mean and variance of displacement and vorticity errors compared to traditional correlations, and that FMC accelerates the convergence of IID.