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Distributed Point Source Method for CNDE
Published in Sourav Banerjee, Cara A.C. Leckey, Computational Nondestructive Evaluation Handbook, 2020
Sourav Banerjee, Cara A.C. Leckey
Radon transform is frequently used in the field of computed tomography (CT) and 3D image reconstruction from a cluster of 2D projection images taken on different planes. The transformation of 3D function into multiple functions projected on 2D planes is made possible by Radon transform by parameterizing the orientation of the planes (μ^). Contrary to that, the transformation of images on the 2D planes to a 3D image is made possible by inverse Radon transform. For example, in X-Ray scan and MRI scans [33], source and detectors are kept opposite side of the patient's body part and by rotating the source-target setup, i.e., changing the θ, sinogram is achieved. Then through inverse Radon transform, the patient's body part is visualized. However, in this case for anisotropic elastodynamic Green's function, first a forward Radon transform is applied. Radon transform gives a set of coupled ordinary differential equations. Here, the 2D planes in 3D are parameterized by μ^ as shown in Fig. 7.24. Eq. (7.189) was originally solved by Wang and Achenbach using Radon Transform [24, 25, 28, 32].
Content-Based Image Retrieval Techniques
Published in Wahiba Ben Abdessalem Karaa, Nilanjan Dey, Mining Multimedia Documents, 2017
Sayan Chakraborty, Prasenjit Kumar Patra, Nilanjan Dey, Amira S. Ashour
Visual features were used to design a CBIR technique proposed by Chang et al. in 2013 that was later optimized [12] employing particle swarm optimization. In 2014, color edge detection and discrete wavelet transformation (DWT) were both used for CBIR [3] by Agarwal et al. A novel technique that combined CBIR, DWT, and color edge detection was proposed in this work, which claimed to be different from the existing methods based on histogram analysis. Recently, Ghuge and Patil proposed an approach [4] based on radeon projection to retrieve images in CBIR. In this work, the authors proposed a CBIR technique that used radon transform and histogram. Radon transform is based on the image intensity’s projection along a radial line at a precise angle. Yasmin et al. [11] introduced EI classification in the CBIR technique, which was based on color feature extraction. In this work, images were converted into a minimum of 16 squares up to 24 squares of equal size. Edge detection was later applied to the converted parts followed by pixel classification. Pixel classification in this approach relied on pixels found inside and at the edge of the image.
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Published in Borko Furht, Darko Kirovski, Multimedia Security Handbook, 2004
The frequency f is uniformly sampled along the radial direction, and bilinear interpolation is used for simplicity. This is equivalent to the 1-D Fourier transform of the Radon transform. The p (θ) is computed along the columns of Ip (f, θ) by Equation 11.17 to construct the feature vector p of length N. The similarity s is defined with the RMSE between the extracted vector p and the given watermark w as follows: () s(p,w)=1N∑i=1N[p(θi)−wi]2
New iterative reconstruction methods for fan-beam tomography
Published in Inverse Problems in Science and Engineering, 2018
Daniil Kazantsev, Valery Pickalov
Direct reconstruction methods in X-ray computed tomography (CT) are proven to be fast and simple to implement [1,2]. They are based on a one-step approximation of a solution to inverse problem by backprojecting all measured tomographic projections. In order to overcome the blurring effect of the back-summation procedure, projections are convolved with a high-pass filter (e.g. a ramp filter). In practice, commonly used direct methods include Filtered Back Projection (FBP) algorithm for parallel and fan-beam geometries and Feldkamp–Davis–Kress (FDK) algorithm for the cone-beam geometry [3]. The filtered backprojection procedure can be considered as a discrete approximation to inverse Radon transform formula which maps the space of measurements to the space of objects.
A Multi-Level Set Approach for Bone Segmentation in Lumbar Ultrasound Images
Published in IETE Journal of Research, 2022
V. Umamaheswari, P.M. Venkatasai, S. Poonguzhali
For the projections of Radon transform, the Ridge let coefficients of t are given by the 1-D wavelet transform in which the direction θ is constant and p is varying. The 1-D inverse Fourier transform can be applied to the 2-D Fourier transform for obtaining the Radon transform which is restricted to the radial lines that are going through the origin. where is the 2-D Fourier transform of t.
New Weighted Mean-Based Patterns for Texture Analysis and Classification
Published in Applied Artificial Intelligence, 2021
Hadis Heidari, Abdolah Chalechale
The transform-based feature extraction methods involve analyzing the changes in the intensity of pixels and the characteristics of the frequency distribution of the image. The transforms commonly used in these methods include wavelet transform (Srivastava and Khare 2017), Fourier transform (Yang and Yu 2018), Gabor wavelet transform (Li, Huang, and Zhu 2016), Radon transform (Khatami et al. 2018), and Contourlet transform (Meng et al. 2016). Wavelet transform is a method of analysis based on small waveforms. This transform can display an image in several resolutions based on a specific frequency. For example, in a study by Srivastava and Khare (2017), they provided a multi-resolution analysis for image retrieval based on wavelet transform. In this work, LBP was combined with Legendre moments in several resolutions, where these moments are orthogonal moments that are based on orthogonal polynomials. Fourier transform is a method for converting the spatial data of image and analyzing their frequency domain information. This transform is widely used for analyzing image processing methods. For example Yang and Yu (2018) introduced a multi-dimensional Fourier descriptor for identifying different shapes. This descriptor captures the local and global characteristics of shapes. Li, Huang, and Zhu (2016) presented an approach for texture and color retrieval by the use of a Gabor wavelet-based copula model. In this method, three types of dependency including color, scale, and orientation were used. Radon transform can also be used to analyze the pattern of an image in a set of angles so that a pattern can be extracted from the sum of pixel intensities in each orientation. In a study by Khatami et al. (2018), they used a combination of Radon transform and local binary patterns in a hierarchical search space for image retrieval. Contourlet transform provides directional data on multiple scales. Meng et al. (2016) used a method based on this transform for the retrieval of visible and infrared images.