Browsing by Subject "Fourier transform"

Now showing 1 - 8 of 8

Open Access
Contrast enhancement of microscopy images using image phase information
(Institute of Electrical and Electronics Engineers, 2018) Çakır, Serdar; Kahraman, Deniz Cansen; Çetin-Atalay, Rengül; Çetin, A. Enis
Contrast enhancement is an important preprocessing step for the analysis of microscopy images. The main aim of contrast enhancement techniques is to increase the visibility of the cell structures and organelles by modifying the spatial characteristics of the image. In this paper, phase information-based contrast enhancement framework is proposed to overcome the limitations of existing image enhancement techniques. Inspired by the groundbreaking design of the phase contrast microscopy (PCM), the proposed image enhancement framework transforms the changes in image phase into the variations of magnitude to enhance the structural details of the image and to improve visibility. In addition, the concept of selective variation (SV) technique is introduced and enhancement parameters are optimized using SV. The experimental studies that were carried out on microscopy images show that the proposed scheme outperforms the baseline enhancement frameworks. The contrast enhanced images produced by the proposed method have comparable cellular texture structure as PCM images.
Open Access
Contrast enhancement using phase transition information and total variation
(Institute of Electrical and Electronics Engineers, 2018) Çakır, Serdar; Çetin, A.Enis
Contrast enhancement is an important preprocessing step for the analysis of images. The main aim of contrast enhancement techniques is to increase the visibility of the objects by modifying the spatial characteristics of the image. In this paper, phase transition based contrast enhancement framework is proposed to overcome the limitations of existing image enhancement techniques. The proposed image enhancement framework transforms the changes in image phase into the variations of magnitude to enhance the structural details of the image and to improve visibility. In addition, the concept of Selective Variation (SV) technique is introduced and enhancement parameters are optimized using SV. The experimental studies that were carried out on TID2008 dataset, show that the proposed scheme obtains promising results on contrast enhancement.
Open Access
Extensions to common laplace and fourier transforms
(Institute of Electrical and Electronics Engineers, 1997-11) Onural, L.; Erden, M. F.; Özaktaş, Haldun M.
The extended versions of common Laplace and Fourier transforms are given. This is achieved by defining a new function fe(p), p 2 C related to the function to be transformed f(t), t 2 R. Then fe(p) is transformed by an integral whose path is defined on an inclined line on the complex plane. The slope of the path is the parameter of the extended definitions which reduce to common transforms with zero slope. Inverse transforms of the extended versions are also defined. These proposed definitions, when applied to filtering in complex ordered fractional Fourier stages, significantly reduce the required computation.
Open Access
Fractional fourier transform
(Wolfram Research, 2003) Özaktaş, Haldun M.; Weisstein, E. W.
Open Access
Fractional fourier transform meets transformer encoder
(Institute of Electrical and Electronics Engineers, 2022-10-28) Şahinuç, Furkan; Koç, Aykut
Utilizing signal processing tools in deep learning models has been drawing increasing attention. Fourier transform (FT), one of the most popular signal processing tools, is employed in many deep learning models. Transformer-based sequential input processing models have also started to make use of FT. In the existing FNet model, it is shown that replacing the attention layer, which is computationally expensive, with FT accelerates model training without sacrificing task performances significantly. We further improve this idea by introducing the fractional Fourier transform (FrFT) into the transformer architecture. As a parameterized transform with a fraction order, FrFT provides an opportunity to access any intermediate domain between time and frequency and find better-performing transformation domains. According to the needs of downstream tasks, a suitable fractional order can be used in our proposed model FrFNet. Our experiments on downstream tasks show that FrFNet leads to performance improvements over the ordinary FNet.
Open Access
Image super-resolution using deep feedforward neural networks in spectral domain
(2018-03) Aydın, Onur
With recent advances in deep learning area, learning machinery and mainstream approaches in computer vision research have changed dramatically from hardcoded features combined with classi ers to end-to-end trained deep convolutional neural networks (CNN) which give the state-of-the-art results in most of the computer vision research areas. Single-image super-resolution is one of these areas which are considerably in uenced by deep learning advancements. Most of the current state-of-the-art methods on super-resolution problem learn a nonlinear mapping from low-resolution images to high-resolution images in the spatial domain using consecutive convolutional layers in their network architectures. However, these state-of-the-art results are obtained by training a separate neural network architecture for each di erent scale factor. We propose a novel singleimage super-resolution system with the limited number of learning parameters in spectral domain in order to eliminate the necessity to train a separate neural network for each scale factor. As a spectral transform function which converts images from the spatial domain to the frequency domain, discrete cosine transform (DCT) which is a variant of discrete Fourier transform (DFT) is used. In addition, in the post-processing step, an artifact reduction module is added for removing ringing artifacts occurred due to spectral transformations. Even if the peak signal-to-noise ratio (PSNR) measurement of our super-resolution system is lower than current state-of-the-art methods, the spectral domain allows us to develop a single model with a single dataset for any scale factor and relatively obtain better structural similarity index (SSIM) results.
Open Access
On the Lévy-Raikov-Marcinkiewicz theorem
(2004) Ostrovskii I.; Ulanovskii, A.
Let μ be a finite non-negative Borel measure. The classical Lévy-Raikov-Marcinkiewicz theorem states that if its Fourier transform μ̂ can be analytically continued to some complex half-neighborhood of the origin containing an interval (0,iR) then μ̂ admits analytic continuation into the strip {t: 0
Open Access
Visual object tracking using Fourier domain phase information
(Springer U K, 2021-07-02) Çakır, Serdar; Çetin, A. E.
In this article, phase of the Fourier transform (FT), which has observed to be a crucial component in image representation, is utilized for visual target tracking. The main aim of the proposed scheme is to reduce the computational complexity of cross-correlation-based matching frameworks. Normalized cross-correlation (NCC) function-based object tracker is converted to a phase minimization problem under the following assumption: In visual object tracking applications, if the frame rate is high, the moving object can be considered to have translational shifts in image domain in a small time window. Since the proposed tracking framework works in the Fourier domain, the translational shifts in the image space are converted to phase variations in the Fourier domain due to the “translational invariance” property of the FT. The proposed algorithm estimates the spatial target position based on the phase information of the target region. The proposed framework uses the ℓ1-norm and provides a computationally efficient solution for the tracking problem. Experimental studies indicate that the proposed phase-based technique obtain comparable results with baseline tracking algorithms which are computationally more complex.