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The Euler characteristic transform (ECT) is an integral transform used widely in topological data analysis. Previous efforts by Curry et al. and Ghrist et al. have independently shown that the ECT is injective on all compact definable sets. In this work, we first study the injectivity of the ECT on definable sets that are not necessarily compact and prove a complete classification of constructible functions that the Euler characteristic transform is not injective on. We then introduce the quadric Euler characteristic transform (QECT) as a natural generalization of the ECT by detecting definable shapes with quadric hypersurfaces rather than hyperplanes. We also discuss some criteria for the injectivity of QECT. [ABSTRACT FROM AUTHOR]

Digital watermarking is an effective technique for image copyright protection. Many digital image watermarking algorithms are sensitive to geometric distortions. These distortions make it difficult to detect and extract watermarks. In this study, a robust color watermarking algorithm combining the Radon transform and DCT transform is proposed. First, the color carrier image is converted to the YUV color space from RGB, and the U component of YUV is transformed to the Radon domain using the Radon transform. Then, a two-dimensional 8 × 8 discrete cosine transform (2D-DCT) is carried out on the selected blocks of the Radon domain, and some fixed midfrequency coefficients are selected to embed watermark information. Moreover, the Arnold transform is applied to encrypt the watermarks and the random permutation function to scramble the embedding positions. Finally, the watermark embedding and blind extraction processes are completed by modifying the midfrequency coefficients using the presented rules. A series of simulation experiments show that the watermark algorithm has high imperceptibility and good robustness to various attacks. [ABSTRACT FROM AUTHOR]

We investigate the distributional extension of the k-plane transform in Rd and of related operators. We parameterize the k-plane domain as the Cartesian product of the Stiefel manifold of orthonormal k-frames in Rd with Rd - k. This parameterization imposes an isotropy condition on the range of the k-plane transform which is analogous to the even condition on the range of the Radon transform. We use our distributional formalism to investigate the invertibility of the dual k-plane transform (the “backprojection” operator). We provide a systematic construction (via a completion process) to identify Banach spaces in which the backprojection operator is invertible and present some prototypical examples. These include the space of isotropic finite Radon measures and isotropic Lp-functions for 1 < p < ∞ . Finally, we apply our results to study a new form of regularization for inverse problems. [ABSTRACT FROM AUTHOR]

Nuclear magnetic resonance (NMR) spectroscopy is one of the most powerful tools in analytical chemistry. An important step in the analysis of NMR data is the assignment of resonance frequencies to the corresponding atoms in the molecule being investigated. The traditional approach considers the spectrum's characteristic parameters: chemical shift values, internuclear couplings, and peak intensities. In this paper, we show how to support the process of assigning a series of spectra of similar organic compounds by using temperature coefficients, that is, the rates of change in chemical shift values associated with given changes in temperature. [ABSTRACT FROM AUTHOR]

In this article, we present a new method called point spread function (PSF)‐Radon transform algorithm. This algorithm consists on recovering the instrument PSF from the Radon transform (in the line direction axis) of the line spread function (i.e., the image of a line). We present the method and tested with synthetic images, and real images from macro lens camera and microscopy. A stand‐alone program along with a tutorial is available, for any interested user, in Martinez (PSF‐Radon transform algorithm, standalone program). Research Highlights: Determining the instrument PSF is a key issue.Precise PSF determinations are mandatory if image improvement is performed numerically by deconvolution.Much less exposure time to achieve the same performance than a measurement of the PSF from a very small bead.Does not require having to adjust the PSF by an analytical function to overcome the noise uncertainties. [ABSTRACT FROM AUTHOR]

The article proposes a method for calculating features in an image to form a training data set for solving various problems of video image classification. This method involves the use of well-known integral transformations — the Radon transform and the Steklov function. The proposed method is compared with convolutional neural networks both in terms of the percentage of correct prediction and in terms of its execution time. As a test task, the problem of finding a fragment of a photograph containing an image of a car is considered.

We prove that a maximally modulated singular oscillatory integral operator along a hypersurface defined by (y , Q (y)) ⊆ R n + 1 , for an arbitrary non-degenerate quadratic form Q, admits an a priori bound on L p for all 1 < p < ∞ , for each n ≥ 2 . This operator takes the form of a polynomial Carleson operator of Radon-type, in which the maximally modulated phases lie in the real span of { p 2 , … , p d } for any set of fixed real-valued polynomials p j such that p j is homogeneous of degree j, and p 2 is not a multiple of Q(y). The general method developed in this work applies to quadratic forms of arbitrary signature, while previous work considered only the special positive definite case Q (y) = | y | 2 . [ABSTRACT FROM AUTHOR]

The existing mine image denoising algorithms have limited effectiveness in removing complex noise, and their processing speed cannot meet the requirements of real-time monitoring. In order to solve the above problems, a mine image denoising algorithm based on improved trimmed mean is proposed. Firstly, a trimmed mean filter is used to preliminarily filter out image noise, and a secondary inspection mechanism is introduced to handle residual noise points. By introducing discrete coefficients, the algorithm's capability to distinguish different pixels is improved, enhancing the denoising performance. Secondly, a classification processing and retesting mechanism based on the number of extreme values is adopted to effectively reduce the problem of residual noise. Thirdly, new control variables are introduced into the wavelet function to optimize the soft threshold function and hard threshold function, and a dual threshold function is constructed. The method combines with Radon transform to enhance the processing of linear features and enhance the detection capability of mine images. Finally, mean square error (MSE) and peak signal-to-noise ratio (PSNR) are used for image quality evaluation. The experimental results show that compared to the trimmed mean algorithm, hard threshold algorithm, and soft threshold algorithm, the MSE growth of the mine image denoising algorithm based on the improved trimmed mean is relatively slow, with the smallest MSE and the best image denoising effect. After introducing the discrete coefficient, the MSE of the model is about 300 dB lower than before, and the PSNR is about 20 dB higher than before. Introducing the discrete coefficient can effectively reduce the impact of noise points on the algorithm. Compared with Kalman genetic optimization algorithm, transform domain image denoising algorithm, and cross branch convolutional denoising network, the MSE of the proposed algorithm is reduced by 27, 21, and 13 dB respectively. The PSNR is improved by 8, 6, and 3 dB respectively. The time consumption is shortened by 0.20, 0.16, and 0.14 seconds, respectively.

Multiple reflections are among the most challenging noises to suppress in seismic data, as they differ from effective waves only in terms of apparent velocity. Also, radon transform, an essential technique for attenuating multiple reflections, has been widely incorporated into various commercial software packages. Thus, this study introduces a 3D radon transform method based on the |${L_{p - 1}}$| norm to enhance sparsity-constraining capability in the transform domain, leveraging high-resolution radon transform techniques. Specifically, an iteratively reweighted least-squares algorithm is employed to obtain the transformed data in the radon domain. Given that the |${L_{p - 1}}$| norm was first applied to the Radon transform in seismic data processing methods, this paper theoretically demonstrates its powerful sparsity-constraining capability. Indeed, the proposed strategy enhances energy concentration in the radon transform domain, better separating primaries from multiples, and ultimately suppressing the multiples. Both model tests and real data indicate that the 3D radon transform constrained by the |${L_{p - 1}}$| norm outperforms existing high-resolution radon transform methods with sparsity constraints regarding energy concentration and effectiveness in multiple reflection attenuation. [ABSTRACT FROM AUTHOR]

We prove new results of Mattila–Sjölin type, giving lower bounds on Hausdorff dimensions of thin sets E ⊂ R d ensuring that various k-point configuration sets, generated by elements of E, have nonempty interior. The dimensional thresholds in our previous work (Greenleaf et al., Mathematika 68(1):163–190, 2022) were dictated by associating to a configuration function a family of generalized Radon transforms, and then optimizing L 2 -Sobolev estimates for them over all nontrivial bipartite partitions of the k points. In the current work, we extend this by allowing the optimization to be done locally over the configuration’s incidence relation, or even microlocally over the conormal bundle of the incidence relation. We use this approach to prove Mattila–Sjölin type results for (i) areas of subtriangles determined by quadrilaterals and pentagons in a set E ⊂ R 2 ; (ii) pairs of ratios of distances of 4-tuples in R d ; and (iii) similarity classes of triangles in R d , as well as to (iv) give a short proof of Palsson and Romero Acosta’s result on congruence classes of triangles in R d . [ABSTRACT FROM AUTHOR]

Copyright of Journal of Mine Automation is the property of Industry & Mine Automation Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The proposed research study investigates the relationship between Bone Mineral Density (BMD) values extracted from computed tomography (CT) scans, with a primary focus on their significance in vertebral segmentation. The study includes 25 subjects spanning five age groups; the study reveals a continuous reduction in mean Hounsfield Unit (HU) values with aging, validated by statistical analysis that emphasizes the importance of these findings across different vertebral levels. The data exposes a steady decline in mean BMD values with age, ranging from 175.05 HU in the 40s to 51.8 HU in the over-80s age group, exhibiting statistically significant differences ( $\text{p} < 0.05$ ). Subgroup analysis provides granular insights into age-related variations at specific lumbar vertebrae levels by contributing valuable information to the complexities of bone health assessment. The research connects mathematics and medical imaging to improve our understanding of vertebral characteristics by introducing the Radon Transform as a fundamental tool in CT image reconstruction. These findings include both p and mean values which have the potential to revolutionize the field of bone health assessment by affecting public health policy and opening the way for more personalized and successful treatment options. This includes the earlier detection of conditions like osteoporosis and improvements in patient care.

The Radon transform is the mathematical tool behind nowadays widely used medical imaging techniques for diagnostic purposes such as Computer Tomography (CT). In this paper we discuss two of our web-based approaches which allow one to interactively create sample images and examine their Radon transform in order to study simple examples and basic properties of the transform. We present that the transform (more precisely its support) can be calculated in an analytic way such that it allows (near) real-time visualization, orders of magnitude faster than in earlier accessible solutions. We claim that currently this may be the best approach for introductory educational and science communication purposes about the Radon transform. [ABSTRACT FROM AUTHOR]

The applications of spherical Radon transforms include synthetic aperture radar, sonar tomography, and medical imaging modalities. A spherical Radon transform maps a function to its integrals over a family of spheres. Recently, several types of incomplete spherical Radon transforms have received attention in research. This study examines two types of quarter-spherical Radon transforms that assign a function to its integral over a quarter of a sphere: 1) center of a quarter sphere of integration on a plane, and 2) center on a line and the rotation of the quarter sphere. Furthermore, we present inversion formulas for these two quarter-spherical Radon transforms.

The Euler characteristic transform (ECT) is an integral transform used widely in topological data analysis. Previous efforts by Curry et al. and Ghrist et al. have independently shown that the ECT is injective on all compact definable sets. In this work, we first study the injectivity of the ECT on definable sets that are not necessarily compact and prove a complete classification of constructible functions that the Euler characteristic transform is not injective on. We then introduce the quadric Euler characteristic transform (QECT) as a natural generalization of the ECT by detecting definable shapes with quadric hypersurfaces rather than hyperplanes. We also discuss some criteria for the injectivity of QECT.

We present in this work alternative analytic formulations for the fan-beam tomographic backprojection operation and its associated adjoint transform in standard (equiangular) and linear (equidistant) detector geometries. The proposed formulations are obtained from a recent backprojection theorem in parallel tomography. Such formulations are written as a Bessel–Neumann series in the frequency domain that can be implemented as an O ⁢ (N 2.3729) matrix multiplication. Proofs are provided together with numerical simulations compared with conventional fan-beam O ⁢ (N 3) backprojection representations showing more robustness when dealing with highly noisy data. [ABSTRACT FROM AUTHOR]

The equivalence of the norms of deviations of the desired density of a body from operators such as finite density transformation with specially constructed elements and the Radon transformation from it is stated. It is shown how computer science, previously established in the theory of computational (numerical) diameter, immediately leads to nontrivial results in computed tomography. [ABSTRACT FROM AUTHOR]

In ultrasonic structural health monitoring (SHM) and nondestructive evaluation (NDE), the scattered waves caused by damage sites and defects are the key to damage diagnosis. However, structural components and boundaries also interact with traveling waves, creating events that can bury damage scattered waves. The baseline subtraction method, which directly subtracts the waveform of a damage signal from that of a pristine baseline signal, is a common processing technique to separate these damage scattered waves. However, baseline subtraction is less effective when a component is measured in different environmental/loading conditions from when its baseline was recorded. For instance, baseline subtraction can be ineffective in aerospace structural parts because such parts expect significant and routine changes in ambient temperature, pressure, and humidity. To overcome the limitations of baseline subtraction, this paper proposes to develop an spex-shifted Radon transform (ASRT)-based damage scattered event extraction technique without baseline subtraction. Our proposed ASRT method converts the original time-space (t − x) domain signals to a time delay–curvature–apex offset (τ − q − y) domain, which targets specific geometries of scattered/reflected waves in the t − x domain and compresses them into a single point-like region in the new domain. In this domain, identifying and isolating targeted events becomes significantly easier. To benchmark the performance of this baseline-subtraction-free (BSF) method, ASRT is applied for signals acquired from (1) spectral finite element-based simulations to scan a water-immersed steel specimen (2) 3-D wave simulations in a bent aluminum plate, and (3) a full matrix capture for experimentally scanning a high-density polyethylene (HDPE) with multiple holes. The goal in each case is to target and separate events of interest from the original signals using the proposed algorithm. The results suggest the ASRT method is effective as a damage scattered wave extraction tool for ultrasonic SHM and NDE. [ABSTRACT FROM AUTHOR]

The quality of the underwater image is impairing with the atmospheric conditions. In this, one of the most significant issues in recent days is due to the motion blur induced by the imaging device or by the movement of the object in underwater image quality degradation. The various parameters of the blurred image must be identified to fix the effect of blurring in post-imaging. Therefore, spectrum-based parameter estimation method is proposed. Initially, to estimate the point spread function (PSF), the angle and the length is measured from image spectrum using radon transform. Then, for the accurate estimation of PSF, Optimized Polynomial Lagrange Interpolation (OPLI) is proposed. The data were collected and analyzed in various natural and structured water bodies in Chennai without affecting the real environment. It is observed that for the underwater images collected, the proposed OPLI approach outperforms compared to few existing traditional estimation methods like cepstral, hough, and radon. Then this veracious interpolated measure of angle and length (VIMAL) is restored using modified Lucy algorithm and is evaluated which results in high performance than the existing classical state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of the study is to propose an algorithm to implement and visualize radiation attenuation-integrated Radon transform based on Beer-Lambert law during emission computed tomography simulation using a deterministic model and also to perform image analysis on resulting images. Methods: Two types of phantoms are designed: plain-disk phantom and patterned-disk phantom. The large disk is filled with an activity of 5 units and the smaller disks have 10 units of activity of 99mTc isotope as an emission map. Three transmission maps for patterned-disk phantom are created with uniform linear attenuation coefficient. Phantoms are scanned with 360° and 180° acquisition arcs. Then, using the algorithm designed, the exponential Radon transform is implemented. After that, the projections are back-projected and filtered to generate tomographic slices. Finally, all slices are analyzed using profile plotting and curve fitting. Moreover, an attenuation Hadamard matrix is provided to facilitate attenuation modeling. Results: The uniform intensity of activity in the phantoms is converted to a disk with progressively decreasing intensity from the periphery to the center in the tomographic slices. Similarly, the circles positioned more centrally appear less intense than those positioned in the periphery, despite all circles having equal activity. When the phantom is scanned in 180° arc, the circles closest to the camera are visualized more intensely. The profile curves of the slices generated by exponential Radon transformation are depicted as U-shaped in profile plotting and are fitted to a bi-exponential function with a near-perfect precision. Conclusions: The incorporation of radiation attenuation results in the development of more realistic models for quantification purposes. [ABSTRACT FROM AUTHOR]

In the digital world, a wide range of handwritten and printed documents should be converted to digital format using a variety of tools, including mobile phones and scanners. Unfortunately, this is not an optimal procedure, and the entire document image might be degraded. Imperfect conversion effects due to noise, motion blur, and skew distortion can lead to significant impact on the accuracy and effectiveness of document image segmentation and analysis in Optical Character Recognition (OCR) systems. In Document Image Analysis Systems (DIAS), skew estimation of images is a crucial step. In this paper, a novel, fast, and reliable skew detection algorithm based on the Radon Transform and Curve Length Fitness Function (CLF), so-called Radon CLF, was proposed. The Radon CLF model aims to take advantage of the properties of Radon spaces. The Radon CLF explores the dominating angle more effectively for a 1D signal than it does for a 2D input image due to an innovative fitness function formulation for a projected signal of the Radon space. Several significant performance indicators, including Mean Square Error (MSE), Mean Absolute Error (MAE), Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Measure (SSIM), Accuracy, and run-time, were taken into consideration when assessing the performance of our model. In addition, a new dataset named DSI5000 was constructed to assess the accuracy of the CLF model. Both two-dimensional image signal and the Radon space have been used in our simulations to compare the noise effect. Obtained results show that the proposed method is more effective than other approaches already in use, with an accuracy of roughly 99.87% and a run-time of 0.048 (s). The introduced model is far more accurate and timeefficient than current approaches in detecting image skew. [ABSTRACT FROM AUTHOR]

The development of cyber-physical systems entails the growth and diversity of malware, which increases the scale of cybersecurity threats. Attackers use malicious software to compromise various components of cyber-physical systems. Existing technologies make it possible to reduce the risk of malware infection using vulnerability and intrusion scanners, network analyzers, and other tools. However, there is no perfect protection against the increasingly sophisticated types of malware. The goal of this research is to solve this problem by combining different visual representations of malware and detection models based on transfer learning. This method considers two pre-trained deep neural network models (AlexNet and MobileNet) that are capable of differentiating various malware families using grayscale images. Radon transform is applied to the resulting grayscale malware images to improve the classification accuracy of the new malware binaries. The proposed model is evaluated using three datasets (Microsoft Malware Classification, IoT_Malware and MalNet-Image datasets). The results show the superiority of the proposed model based on transfer learning over other methods in terms of the efficiency of classifying malware families aimed at infecting cyber-physical systems.

The paper considers ray transforms of the moments of symmetric tensor fields of arbitrary rank given in the unit disk. The basic geometric and differential properties of mixed ray transforms of tensor fields and mixed ray transforms of the moments of tensor fields are established. A simple algorithm for reconstructing a low-rank tensor field from known mixed ray transforms of its moments is proposed and justified. [ABSTRACT FROM AUTHOR]

This study aims to establish equivalences (in norm) of the problems of reconstructing computed tomography and computational (numerical) diameter (C(N)D), which was done in 2019 for functions of two variables. This was based on the equivalence of respective norms in the same two-dimensional Sobolev spaces proved by Frank Natterer. In this study, we prove the equivalence (in norm) of the Radon transform and the function that generated it for the case of functions of any dimension with large-scale prospects for application. [ABSTRACT FROM AUTHOR]

In the field of complex underground geological structures and irregular topography, prestack seismic data often have a low signal-to-noise ratio (SNR), in which weakly reflected signals are buried beneath strong incoherent, and scattered noise. Stacking, such as beamforming along the moveout surfaces of coherent local events, can significantly improve seismic data quality. Accurate and efficient estimation of the moveout for an irregular acquisition geometry and uneven illumination is important in a complex environment. In this paper, a new optimal stacking approach for enhancing weak prestack reflection signals is presented. The proposed method mainly includes regional division and moveout estimation. Optimal stacking should be implemented within local time and space domains. Based on beam-ray theory, we designed a reasonable regional division of the common-shot (CS), common-receiver (CR) and common-middle-point (CMP) domains. Then, we proposed using the sparse radon transform and dynamic waveform matching method to estimate the moveout surfaces of local reflection events. The sparse radon transform was applied to obtain the linear moveout to ensure the correctness of the reflection wave direction. The residual nonlinear disturbance was estimated using the dynamic waveform matching method. Tests on synthetic and field data demonstrated the effectiveness of the proposed method, which can effectively improve the SNR of prestack seismic data and attenuate incoherent noise. [ABSTRACT FROM AUTHOR]

In this paper we consider the Radon–Kipriyanov transform and its relationship with the special Radon transform. The representation of plane integrals in the Lebesgue–Kipriyanov measure by the corresponding hemisphere integral in is given. The definitions and information necessary for calculating the Radon–Kipriyanov transform from Laplace series for one class of weight spherical functions with one weight variable are given. A generalization of the Funk–Hecke formula is obtained. The formula for the Radon–Kipriyanov transform with one special variable of the Laplace series for weight spherical functions is obtained. [ABSTRACT FROM AUTHOR]

In this work, two methods are proposed for solving the problem of one-dimensional barcode segmentation in images, with an emphasis on augmented reality (AR) applications. These methods take the partial discrete Radon transform as a building block. The first proposed method uses overlapping tiles for obtaining good angle precision while maintaining good spatial precision. The second one uses an encoder–decoder structure inspired by state-of-the-art convolutional neural networks for segmentation while maintaining a classical processing framework, thus not requiring training. It is shown that the second method's processing time is lower than the video acquisition time with a 1024 × 1024 input on a CPU, which had not been previously achieved. The accuracy it obtained on datasets widely used by the scientific community was almost on par with that obtained using the most-recent state-of-the-art methods using deep learning. Beyond the challenges of those datasets, the method proposed is particularly well suited to image sequences taken with short exposure and exhibiting motion blur and lens blur, which are expected in a real-world AR scenario. Two implementations of the proposed methods are made available to the scientific community: one for easy prototyping and one optimised for parallel implementation, which can be run on desktop and mobile phone CPUs. [ABSTRACT FROM AUTHOR]

Aims: Analysis of colonoscopy images is an important diagnostic procedure in the identification of colorectal cancer. It has been observed that owing to advancements in technology, numerous machine-learning models now excel in the analysis of colorectal polyps classification. This work focused on developing a framework that can classify polyps using images during colonoscopy. Materials and Methods: First, the images were corrected by removing their spectral reflection. Second, feature pools were obtained by applying Radon transform (?=45, 90, 135, and 180). From the Radon transform, fractal dimension was calculated as a feature vector combined with Zernike moment obtained from the Zernike features. Finally, Extreme Gradient Boosting (XGBoost) algorithm was applied for the classification and to compare it with state-of-the-art methods. Results: The experimental results obtained with the proposed framework have been reported, cross-validated, and discussed. The proposed method gives a classification accuracy of 93% for light XGBoost and 92% for XGBoost. Conclusion: This study shows that by applying scale invariant features over a small dataset, XGBoost outperforms state-of-the-art methods when it comes to polyp classification. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of the study is to propose an algorithm to implement and visualize radiation attenuation-integrated Radon transform based on Beer–Lambert law during emission computed tomography simulation using a deterministic model and also to perform image analysis on resulting images. Methods: Two types of phantoms are designed: plain-disk phantom and patterned-disk phantom. The large disk is filled with an activity of 5 units and the smaller disks have 10 units of activity of 99mTc isotope as an emission map. Three transmission maps for patterned-disk phantom are created with uniform linear attenuation coefficient. Phantoms are scanned with 360° and 180° acquisition arcs. Then, using the algorithm designed, the exponential Radon transform is implemented. After that, the projections are back-projected and filtered to generate tomographic slices. Finally, all slices are analyzed using profile plotting and curve fitting. Moreover, an attenuation Hadamard matrix is provided to facilitate attenuation modeling. Results: The uniform intensity of activity in the phantoms is converted to a disk with progressively decreasing intensity from the periphery to the center in the tomographic slices. Similarly, the circles positioned more centrally appear less intense than those positioned in the periphery, despite all circles having equal activity. When the phantom is scanned in 180° arc, the circles closest to the camera are visualized more intensely. The profile curves of the slices generated by exponential Radon transformation are depicted as U-shaped in profile plotting and are fitted to a bi-exponential function with a near-perfect precision. Conclusions: The incorporation of radiation attenuation results in the development of more realistic models for quantification purposes.

Aims: Analysis of colonoscopy images is an important diagnostic procedure in the identification of colorectal cancer. It has been observed that owing to advancements in technology, numerous machine-learning models now excel in the analysis of colorectal polyps classification. This work focused on developing a framework that can classify polyps using images during colonoscopy. Materials and Methods: First, the images were corrected by removing their spectral reflection. Second, feature pools were obtained by applying Radon transform (θ=45, 90, 135, and 180). From the Radon transform, fractal dimension was calculated as a feature vector combined with Zernike moment obtained from the Zernike features. Finally, Extreme Gradient Boosting (XGBoost) algorithm was applied for the classification and to compare it with state-of-the-art methods. Results: The experimental results obtained with the proposed framework have been reported, cross-validated, and discussed. The proposed method gives a classification accuracy of 93% for light XGBoost and 92% for XGBoost. Conclusion: This study shows that by applying scale invariant features over a small dataset, XGBoost outperforms state-of-the-art methods when it comes to polyp classification.

Let $F$ represent a digitized version of an image $f\left ({x,y }\right)$ . Assume that the image fits inside a rectangular region and this region is subdivided into $M\,\,\times \,\,N$ squares. We call these squares the shifted box functions. Thus $f\left ({x,y }\right)$ is approximated by $M\,\,\times \,\,N$ matrix $F$ . This paper proofs that $F$ can be recovered exactly and uniquely from the Radon transform of $f$ using only one selected view angle with a well selected family of $MN$ lines. The paper also proposes a precise method for computing the Radon transform of an image. The approach can be categorized as an algebraic reconstruction, but it is merely a theoretical contribution for the field of limited data tomography.

The pitch period as an essential feature is used in various speech-related works. Most actual projects collect speech signals in complex noise environments. Thus, the noise resistance of the algorithm for accurate pitch estimation has become more critical than ever. However, many state-of-the-art algorithms fail to obtain good results when dealing with noisy speech files at a low signal-to-noise ratio (SNR) value. This study presents a new noise-resistant pitch estimation algorithm based on the Radon transform and reduces the influence of formants with the modification of the classical equation. In addition, we use the difference between the pitch candidates of the consecutive frames as part of the criterion for the decoding of the Viterbi algorithm to strengthen the correlation of the pitch estimates and make the pitch contours smoother. We synthesized three noisy speech databases with 18 types of collected environmental noise and compared our algorithm with 7 state-of-the-art algorithms. The proposed algorithm has the best performance on CSTR and self-recorded databases and reduces Gross Pitch Error (GPE) rate by over 12% at 0 dB SNR against Bayesian Pitch Tracker. In particular, the GPE rate of our proposed algorithm can be maintained under 25% at 0 dB SNR, while BaNa only achieves 35%.

In this paper, we present methods for identifying an image from a given set of Radon projections. Given a suitably regular 2-D or 3-D function, we form a new function $g$ from $f$ using a linear transformation. We show how the Radon projections of $f$ and $g$ can be used to determine the transformation. The proposed algorithms introduce three major contributions: 1) Improvements on the 2-D setting using the moments of the Radon projections with only two orthogonal projections. 2) A natural extension of the 2-D setting to work with the 3-D setting. In particular, reducing the 3-D problem to a 2-D problem so that we can recover a translation, a scaling, or a rotation transformation of a 3-D object in the Radon domain. 3) An efficient method of recovering a rotation of a 3-D image around an arbitrary axis and an angle of rotation.

UAVs have been widely used in deformation monitoring because of their high availability and flexibility. However, the quality of UAV images is affected by changing attitude and surveying environments, resulting in a low monitoring accuracy. Cross-shaped markers are used to improve the accuracy of UAV monitoring due to their distinct center contrast and absence of eccentricity. However, existing methods cannot rapidly and precisely detect these markers in UAV images. To address these problems, this paper proposes an adaptive Radon-transform-based marker detection and localization method for UAV displacement measurements, focusing on two critical detection parameters, namely, the radius of marker information acquisition and the edge width of the cross-shaped scoring template. The experimental results show that the marker detection rate is 97.2% under different combinations of flight altitudes, radius ratios of marker information acquisition, and marker sizes. Furthermore, the root mean square error of detection and localization is 0.57 pixels, significantly surpassing the performance and accuracy of other methods. We also derive the critical detection radius and appropriate parameter combinations for different heights to further improve the practicality of the method.

The characterization of suspended dust near the Martian surface is extremely relevant to understand the climate of Mars. In this frame, a Dust Sensor instrument, an infrared device designed to obtain the effective parameters of Martian dust using the scattering properties of the dust particles, was developed. The purpose of this article is to present a novel methodology to calculate, from experimental data, an instrumental function of the Dust Sensor that allows solving the direct problem and providing the signal that this instrument would provide given a distribution of particles. The experimental method is based on recording the signal measured when a Lambertian reflector is gradually introduced into the interaction volume at different distances from the detector and source and applying tomography techniques (inverse Radon transform) to obtain the image of a section of the interaction volume. This method provides a complete mapping of the interaction volume experimentally, which determines the Wf function. The method was applied to solve a specific case study. Among the advantages of this method, it should be noted that it avoids assumptions and idealizations of the dimensions of the volume of interaction and reduces the time required to carry out simulations. [ABSTRACT FROM AUTHOR]

Copyright of Ordnance Industry Automation is the property of Editorial Board for Ordnance Industry Automation and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A multi-image encryption method based on singular value decomposition ghost imaging and RSA public-key cryptography (RSVDGI) is proposed. Radon transform (RT) is first carried out on the target images to obtain Radon spectrums, and then, QR encoding is performed on it. The QR-coded image is used as a plaintext image for singular value decomposition ghost imaging (SVDGI) encryption to obtain the corresponding ciphertext. The public key generated by the RSA algorithm is used to encrypt the keys of the above process. Only the receiver with the private key of the RSA algorithm can successfully extract the keys, decrypt the ciphertext encrypted by SVDGI, and finally reconstruct the required target images. QR code has good error correction performance. Thus, it can restore the target images in high quality within the range of its error correction ability. RSA public-key cryptosystem solves the problem of key management in ghost imaging system and improves the security of encryption system. The feasibility, security, and robustness of this method are verified by computer simulations and optical experiments. [ABSTRACT FROM AUTHOR]