2D Discrete Fourier Transform Research Articles

Empirical mode decomposition and local binary pattern based feature extraction for face recognition

ABSTRACT Facial recognition is a challenging pattern recognition problem in computer vision. This paper proposes a face recognition system that uses Empirical Mode Decomposition (EMD) and Local Binary Pattern (LBP) based feature extraction for a robust face recognition system. This scheme initially decomposes the image into 2N number of IMF (Intrinsic Mode Function) images, where N numbers of IMF images are estimated in the X direction and N number of IMF images are estimated in the Y direction. From the 2N number of IMFs, the M number of best matching IMF image pairs is estimated using 2D Discrete Fourier Transform (DFT). The IMF pair is added to extract the IC-LBP (Intensity Compensated-Local Binary Pattern) features. The IC-LBP features are extracted from the IMF images such that the center intensity is adjusted based on an adaptive intensity threshold. The use of EMD and IC-LBP features uses the essential descriptors that best represent a facial image. The same process is repeated in the testing phase where the test image is categorized from the trained images using the Naïve Bayes algorithm. The performance evaluation was done using the Yale, MORPH, and FGNET using metrics such as time complexity and recognition rate on different types of test face images like partial faces, different lightning, and rotation. Results show that the proposed face recognition system outperforms the traditional algorithms. Results show that the proposed face recognition system outperforms the traditional algorithms.

Bespoke Fractal Sampling Patterns for Discrete Fourier Space via the Kaleidoscope Transform

Sampling strategies are important for sparse imaging methodologies, especially those employing the discrete Fourier transform (DFT). Chaotic sensing is one such methodology that employs deterministic, fractal sampling in conjunction with finite, iterative reconstruction schemes to form an image from limited samples. Using a sampling pattern constructed entirely from periodic lines in DFT space, chaotic sensing was found to outperform traditional compressed sensing for magnetic resonance imaging; however, only one such sampling pattern was presented and the reason for its fractal nature was not proven. Through the introduction of a novel image transform known as the kaleidoscope transform, which formalises and extends upon the concept of downsampling and concatenating an image with itself, this paper: (1) demonstrates a fundamental relationship between multiplication in modular arithmetic and downsampling; (2) provides a rigorous mathematical explanation for the fractal nature of the sampling pattern in the DFT; and (3) leverages this understanding to develop a collection of novel fractal sampling patterns for the 2D DFT with customisable properties. The ability to design tailor-made fractal sampling patterns expands the utility of the DFT in chaotic imaging and may form the basis for a bespoke chaotic sensing methodology, in which the fractal sampling matches the imaging task for improved reconstruction.

Image compression based on 2D Discrete Fourier Transform and matrix minimization algorithm

In the present era of the internet and multimedia, image compression techniques are essential to improve image and video performance in terms of storage space, network bandwidth usage, and secure transmission. A number of image compression methods are available with largely differing compression ratios and coding complexity. In this paper we propose a new method for compressing high-resolution images based on the Discrete Fourier Transform (DFT) and Matrix Minimization (MM) algorithm. The method consists of transforming an image by DFT yielding the real and imaginary components. A quantization process is applied to both components independently aiming at increasing the number of high frequency coefficients. The real component matrix is separated into Low Frequency Coefficients (LFC) and High Frequency Coefficients (HFC). Finally, the MM algorithm followed by arithmetic coding is applied to the LFC and HFC matrices. The decompression algorithm decodes the data in reverse order. A sequential search algorithm is used to decode the data from the MM matrix. Thereafter, all decoded LFC and HFC values are combined into one matrix followed by the inverse DFT. Results demonstrate that the proposed method yields high compression ratios over 98% for structured light images with good image reconstruction. Moreover, it is shown that the proposed method compares favorably with the JPEG technique based on compression ratios and image quality.

Discrete two dimensional Fourier transform in polar coordinates part II: numerical computation and approximation of the continuous transform.

The theory of the continuous two-dimensional (2D) Fourier Transform in polar coordinates has been recently developed but no discrete counterpart exists to date. In the first part of this two-paper series, we proposed and evaluated the theory of the 2D Discrete Fourier Transform (DFT) in polar coordinates. The theory of the actual manipulated quantities was shown, including the standard set of shift, modulation, multiplication, and convolution rules. In this second part of the series, we address the computational aspects of the 2D DFT in polar coordinates. Specifically, we demonstrate how the decomposition of the 2D DFT as a DFT, Discrete Hankel Transform and inverse DFT sequence can be exploited for coding. We also demonstrate how the proposed 2D DFT can be used to approximate the continuous forward and inverse Fourier transform in polar coordinates in the same manner that the 1D DFT can be used to approximate its continuous counterpart.

Discrete Two-Dimensional Fourier Transform in Polar Coordinates Part I: Theory and Operational Rules

The theory of the continuous two-dimensional (2D) Fourier transform in polar coordinates has been recently developed but no discrete counterpart exists to date. In this paper, we propose and evaluate the theory of the 2D discrete Fourier transform (DFT) in polar coordinates. This discrete theory is shown to arise from discretization schemes that have been previously employed with the 1D DFT and the discrete Hankel transform (DHT). The proposed transform possesses orthogonality properties, which leads to invertibility of the transform. In the first part of this two-part paper, the theory of the actual manipulated quantities is shown, including the standard set of shift, modulation, multiplication, and convolution rules. Parseval and modified Parseval relationships are shown, depending on which choice of kernel is used. Similar to its continuous counterpart, the 2D DFT in polar coordinates is shown to consist of a 1D DFT, DHT and 1D inverse DFT.

Algorithm and Architecture Optimization for 2D Discrete Fourier Transforms with Simultaneous Edge Artifact Removal

Two-dimensional discrete Fourier transform (DFT) is an extensively used and computationally intensive algorithm, with a plethora of applications. 2D images are, in general, nonperiodic but are assumed to be periodic while calculating their DFTs. This leads to cross-shaped artifacts in the frequency domain due to spectral leakage. These artifacts can have critical consequences if the DFTs are being used for further processing, specifically for biomedical applications. In this paper we present a novel FPGA-based solution to calculate 2D DFTs with simultaneous edge artifact removal for high-performance applications. Standard approaches for removing these artifacts, using apodization functions or mirroring, either involve removing critical frequencies or necessitate a surge in computation by significantly increasing the image size. We use a periodic plus smooth decomposition-based approach that was optimized to reduce DRAM access and to decrease 1D FFT invocations. 2D FFTs on FPGAs also suffer from the so-called “intermediate storage” or “memory wall” problem, which is due to limited on-chip memory, increasingly large image sizes, and strided column-wise external memory access. We propose a “tile-hopping” memory mapping scheme that significantly improves the bandwidth of the external memory for column-wise reads and can reduce the energy consumption up to 53%. We tested our proposed optimizations on a PXIe-based Xilinx Kintex 7 FPGA system communicating with a host PC, which gives us the advantage of further expanding the design for biomedical applications such as electron microscopy and tomography. We demonstrate that our proposed optimizations can lead to 2.8× reduced FPGA and DRAM energy consumption when calculating high-throughput 4096×4096 2D FFTs with simultaneous edge artifact removal. We also used our high-performance 2D FFT implementation to accelerate filtered back-projection for reconstructing tomographic data.

Discrete Fourier Transform-Based Multivariate Image Analysis: Application to Modeling of Aromatase Inhibitory Activity.

We recently generalized the formerly alignment-dependent multivariate image analysis applied to quantitative structure-activity relationships (MIA-QSAR) method through the application of the discrete Fourier transform (DFT), allowing for its application to noncongruent and structurally diverse chemical compound data sets. Here we report the first practical application of this method in the screening of molecular entities of therapeutic interest, with human aromatase inhibitory activity as the case study. We developed an ensemble classification model based on the two-dimensional (2D) DFT MIA-QSAR descriptors, with which we screened the NCI Diversity Set V (1593 compounds) and obtained 34 chemical compounds with possible aromatase inhibitory activity. These compounds were docked into the aromatase active site, and the 10 most promising compounds were selected for in vitro experimental validation. Of these compounds, 7419 (nonsteroidal) and 89 201 (steroidal) demonstrated satisfactory antiproliferative and aromatase inhibitory activities. The obtained results suggest that the 2D-DFT MIA-QSAR method may be useful in ligand-based virtual screening of new molecular entities of therapeutic utility.

Cell shape characterization and classification with discrete Fourier transforms and self-organizing maps.

Cells in their natural environment often exhibit complex kinetic behavior and radical adjustments of their shapes. This enables them to accommodate to short- and long-term changes in their surroundings under physiological and pathological conditions. Intravital multi-photon microscopy is a powerful tool to record this complex behavior. Traditionally, cell behavior is characterized by tracking the cells' movements, which yields numerous parameters describing the spatiotemporal characteristics of cells. Cells can be classified according to their tracking behavior using all or a subset of these kinetic parameters. This categorization can be supported by the a priori knowledge of experts. While such an approach provides an excellent starting point for analyzing complex intravital imaging data, faster methods are required for automated and unbiased characterization. In addition to their kinetic behavior, the 3D shape of these cells also provide essential clues about the cells' status and functionality. New approaches that include the study of cell shapes as well may also allow the discovery of correlations amongst the track- and shape-describing parameters. In the current study, we examine the applicability of a set of Fourier components produced by Discrete Fourier Transform (DFT) as a tool for more efficient and less biased classification of complex cell shapes. By carrying out a number of 3D-to-2D projections of surface-rendered cells, the applied method reduces the more complex 3D shape characterization to a series of 2D DFTs. The resulting shape factors are used to train a Self-Organizing Map (SOM), which provides an unbiased estimate for the best clustering of the data, thereby characterizing groups of cells according to their shape. We propose and demonstrate that such shape characterization is a powerful addition to, or a replacement for kinetic analysis. This would make it especially useful in situations where live kinetic imaging is less practical or not possible at all. © 2017 International Society for Advancement of Cytometry.

OTFS(Orthogonal Time Frequency Space) 변조를 사용하는 MIMO(Multiple Input Multiple Output) 시스템 설계와 성능 평가

In this paper, we have evaluated and analyzed OTFS(Orthogonal Time Frequency Space) modulation and OTFS-MIMO(Multiple Input Multiple Output) system. OTFS modulation can concisely compensate delay-Doppler spreading effect by using 2D(2-Dimension) iDFT (inverse Discrete Fourier Transform) and DFT(Discrete Fourier Transform) operation. It enables OTFS system to transmit high-speed data. Especially, OTFS-MIMO system can transmit all data streams without performance degradation on high Doppler frequency channel. As simulation results, we have confirmed that 1×1 OTFS system’s achievable rate is a similar to each stream of 2×2 OTFS-MIMO system. That is, we have also confirmed that 2×2 MIMO system can completely achieve double achievable rate in comparison with OTFS system on high Doppler frequency channel.

Comparison of Discrete Cosine Transforms (DCT), Discrete Fourier Transforms (DFT), and Discrete Wavelet Transforms (DWT) in Digital Image Watermarking

Digital Image Watermarking is used recently to secure the image by embedding another digital image. It is typically used to identify ownership of the copyright of the signal. Frequency domain transformation methods used widely in Digital Image Compression and Digital Image Watermarking. They reduce the weakness of classics digital image watermarking such as Least Significant Bit (LSB) methods which is more noise-tolerant. Popular transformation method used are Two Dimensional Discrete Cosine Transform (2D DCT), Two Dimensional Discrete Fourier Transforms (2D DFT), and Two Dimensional Discrete Wavelet Transform (2D DWT). This paper will show the comparison result of those three transformation method. The experiments are comparison analysis of image watermark quality using Peak Signal to Noise Ratio (PSNR), color converting, image resizing, image optical scanning and the noise-tolerant of the image watermarked by giving Gaussian noise.

Vector Radix 2 × 2 Sliding Fast Fourier Transform

The two-dimensional (2D) discrete Fourier transform (DFT) in the sliding window scenario has been successfully used for numerous applications requiring consecutive spectrum analysis of input signals. However, the results of conventional sliding DFT algorithms are potentially unstable because of the accumulated numerical errors caused by recursive strategy. In this letter, a stable 2D sliding fast Fourier transform (FFT) algorithm based on the vector radix (VR) 2 × 2 FFT is presented. In the VR-2 × 2 FFT algorithm, each 2D DFT bin is hierarchically decomposed into four sub-DFT bins until the size of the sub-DFT bins is reduced to 2 × 2; the output DFT bins are calculated using the linear combination of the sub-DFT bins. Because the sub-DFT bins for the overlapped input signals between the previous and current window are the same, the proposed algorithm reduces the computational complexity of the VR-2 × 2 FFT algorithm by reusing previously calculated sub-DFT bins in the sliding window scenario. Moreover, because the resultant DFT bins are identical to those of the VR-2 × 2 FFT algorithm, numerical errors do not arise; therefore, unconditional stability is guaranteed. Theoretical analysis shows that the proposed algorithm has the lowest computational requirements among the existing stable sliding DFT algorithms.

Novel comparison of microscopy and diffraction techniques on the structure of iron oxide nanoparticle monolayers transferred by Langmuir-Schaefer method

Iron oxide nanoparticles undergo self-assembly into well-ordered monolayer films of macroscopic size at the air-water interface. This self-assembly process is the result of the van der Waals forces between the constituent particles. For roughly spherical particles, this monolayer is a 2D hexagonal close packed lattice. With Grazing Incidence X-Ray Diffraction (GID), one can obtain global statistical information about the film's spacing and correlation length. Herein, we demonstrate that comparable structural information can be obtained by a novel Fourier transform analysis method applied to Scanning Electron Microscopy (SEM) images taken of the film after it has been transferred to a silicon substrate. This consists of using numerical methods to isolate the lattice structure of the monolayer in the SEM image to which a 2D discrete Fourier Transform is applied and the result integrated. This results in Bragg peak information akin to that obtained from GID, whose structure shows the same hexagonal close packed lattice with similar spacing and of greater peak contrast. This analysis technique may prove to be a suitable alternative or compliment to GID for many applications.

2D-Discrete Fourier Transform: Generalization of the MIA-QSAR strategy in molecular modeling

Adequate alignment of chemical structure images with respect to the basic scaffold in a series of chemical compounds constitutes an indispensable requirement for constructing multivariate images (MVIs) and subsequent molecular modeling using the Multivariate Image Analysis applied to Quantitative Structure–Activity Relationship (MIA-QSAR) approach. However, up to the moment, this alignment procedure has been manually performed, based on subjective ocular precision. The 2D-Discrete Fourier Transform (2D-DFT) is introduced as a strategy for creating a common base to construct MVIs for chemical structures using their magnitude spectra. The utility of magnitude spectra in QSAR studies has been evaluated through models for the antimalarial, anticancer and trichomonicidal activity of a series of 2, 5-diaminobenzophenone, 4-phenylpyrrolocarbazole and benzimidazole derivatives, respectively, yielding satisfactory results comparable to superior to those reported in the literature. It is anticipated that this strategy should enable the application of the MIA-QSAR approach to structurally diverse datasets other than a series of congeneric datasets.

Implementation Oriened Phase based IRIS Recognition

Phase based image matching is one of the technique which is used for iris recognition. In this technique phase component present in Two dimensional (2D) Discrete Fourier Transform (DFT) of given images are used to determine similarity between two images. This technique can be used for developing applications such as access control system. But here problem is size of iris database. As number of individuals using such application will go on increasing, size of iris database will also go on increasing. This paper discusses the method which is used to address this problem. In this paper 2D Fourier phase code (2D FPC) is used to represent iris information. Instead of storing whole iris image, only 2D FPC is stored in the database which reduces size of required database significantly. This method is evaluated with CASIA iris image database (version 1.0). General Terms Pattern Recognition, Security.

2D discrete Fourier transform on sliding windows.

Discrete Fourier transform (DFT) is the most widely used method for determining the frequency spectra of digital signals. In this paper, a 2D sliding DFT (2D SDFT) algorithm is proposed for fast implementation of the DFT on 2D sliding windows. The proposed 2D SDFT algorithm directly computes the DFT bins of the current window using the precalculated bins of the previous window. Since the proposed algorithm is designed to accelerate the sliding transform process of a 2D input signal, it can be directly applied to computer vision and image processing applications. The theoretical analysis shows that the computational requirement of the proposed 2D SDFT algorithm is the lowest among existing 2D DFT algorithms. Moreover, the output of the 2D SDFT is mathematically equivalent to that of the traditional DFT at all pixel positions.

Multimodal Face Recognition System Using Spectral Transformation of 2D Texture Feature and Statistical Processing of Face Range Images

3D Face recognition has been an area of interest for the past few decades in pattern recognition. This paper focuses on problems of person identification using 3D Face data. Here unregistered Face data, i.e. both texture and depth is fed to classifier in spectral representations of data. 2D Discrete Fourier Transform (DFT) is used for spectral representation. Fusion of scores improves the recognition accuracy significantly since use of depth information alone in spectral representation was not sufficient to increase accuracy. Statistical method seems to degrade performance of system when applied to texture data and was effective for depth data.

A finger-knuckle-print recognition algorithm using phase-based local block matching

This paper proposes a Finger-Knuckle-Print (FKP) recognition algorithm using Band-Limited Phase-Only Correlation (BLPOC)-based local block matching. The phase information obtained from 2D Discrete Fourier Transform (DFT) of images contains important information of image representation. The phase-based image matching, especially BLPOC-based image matching, is successfully applied to image recognition tasks for biometric recognition applications. To calculate the matching score, the proposed algorithm corrects the global and local deformation between FKP images using phase-based correspondence matching and the BLPOC-based local block matching, respectively. Experimental evaluation using the PolyU FKP database demonstrates the efficient recognition performance of the proposed algorithm compared with the state-of-the-art conventional algorithms.

A pixel is an artifact: On the necessity of zero‐filling in fourier imaging

AbstractMR imaging data is sometimes presented in a “patchwork quilt” format with individual pixels visible as squares of uniform intensity. This phenomenon often arises by default from an image space convolution (performed implicitly by the graphics system) used to convert the sparse point sampling of the spatial domain offered by the discrete Fourier transform (DFT) into a sufficiently dense sampling to allow assignment of an intensity value to each addressable point on the display device. Typical examples are fMRI maps, spectroscopic images and zoomed‐in views. These square patches are image structure not present in the object, i.e., artifacts. This form of image display is studied by both an image analysis method and by Fourier analysis. Image formation by display of the 2D DFT of an acquired k‐space matrix as a 2D pixel array is a poor reconstruction because it does not ensure a faithful representation of the spatial frequency content actually present in the data. By analysis of the visual appearance of 2D pixel arrays we show that there are two principal effects: (a) attenuation of higher spatial frequencies (i.e., low‐pass filtering); (b) introduction of artifactual high frequency image structure. These effects can lead to very poor performance with an artifact/signal ratio of over 200% in the corners of 2D k‐space. Generated k‐space maps demonstrate that both detrimental effects increase radially in k‐space. The simple remedy is to zero‐fill (resulting in image interpolation) until individual pixels become invisible in the displayed image. Alternatively, data modeling may be used. © 2013 Wiley Periodicals, Inc. Concepts Magn Reson Part 42A: 32–44, 2013.

FPGA Architecture for 2D Discrete Fourier Transform Based on 2D Decomposition for Large-sized Data

Applications based on Discrete Fourier Transforms (DFT) are extensively used in various areas of signal and digital image processing. Of particular interest is the two-dimensional (2D) DFT which is more computation- and bandwidth-intensive than the one-dimensional (1D) DFT. Traditionally, a 2D DFT is computed using Row-Column (RC) decomposition, where 1D DFTs are computed along the rows followed by 1D DFTs along the columns. Both application specific and reconfigurable hardware have been used for high-performance implementations of 2D DFT. However, architectures based on RC decomposition are not efficient for large input size data due to memory bandwidth constraints. In this paper, we propose an efficient architecture to implement the 2D DFT for large-sized input data based on a novel 2D decomposition algorithm. This architecture achieves very high throughput by exploiting the inherent parallelism due to the algorithm decomposition and by utilizing the row-wise burst access pattern of the external memory. A high throughput memory interface has been designed to enable maximum utilization of the memory bandwidth. In addition, an automatic system generator is provided for mapping this architecture onto a reconfigurable platform of Xilinx Virtex5 devices. For a 2K×2K input size, the proposed architecture is 1.96x times faster than RC decomposition based implementation under the same memory constraints, and also outperforms other existing implementations.

Assessment of acoustic pressure holograms from membrane velocity measurements

The aim of this paper is to demonstrate experimentally the possibility of acquiring acoustic pressure holograms using a light membrane and a scanning laser vibrometer. The velocity of a light membrane placed in an acoustic field can be measured without contact by means of a laser vibrometer. The ideal membrane must be optically reflective, acoustically transparent (having as little mass as possible), impermeable, and mounted without tension. The measured velocity is equal for continuity reasons to the normal acoustic velocity, but differs from the acoustic velocity without the membrane because the membrane is never completely transparent to acoustic waves. The effect of the mass of the membrane can be taken into account to correct this difference. Then, acoustic pressure holograms can be deduced from velocity holograms using the 2D Discrete Fourier Transform. An experimental validation is carried out; acoustic pressures derived from laser measurements are compared with microphone measurements, with a very satisfying match over a wide frequency range.