Search

Robust estimation of location for data on the unit sphere S p − 1 is an important problem in directional statistics even though the influence functions of the sample mean direction and other location estimators are bounded. A significant limitation of previous literature on this topic is that robust estimators and procedures have been developed under the assumption that the underlying population is rotationally symmetric. This assumption often does not hold with real data and in these cases there is a needless loss of efficiency in the estimator. In this article, we propose two estimators for spherical data, both of which are analogous to the affine-equivariant spatial median in Euclidean space. The influence functions of the new location estimators are obtained under a new semiparametric elliptical symmetry model on the sphere and are shown to be standardized bias robust in the highly concentrated case; the influence function of the companion scatter matrix is also obtained. An iterative algorithm that computes both estimators is described. Asymptotic results, including consistency and asymptotic normality, are also derived for the location estimators that result from applying a fixed number of steps in this algorithm. Numerical studies demonstrate that both location estimators may be expected to perform well in practice in terms of efficiency and robustness. A brief example application from the geophysics literature is also provided. for this article are available online. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Measurement Science & Instrumentation is the property of Journal of Measurement Science & Instrumentation 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 analysis of spectral reflectance data is an important tool for obtaining relevant information about the mineral composition of objects and has been used for research in chemistry, geology, biology, archaeology, pharmacy, medicine, anthropology, and other disciplines. In archaeology, the use of spectroscopic data allows us to characterize and classify artifacts and ecofacts, to analyze patterns, and to study the exchange of materials, etc., as well as to explain some properties, such as color or post-depositional processes. The spectroscopic data are of the so-called “big data” type and must be analyzed using multivariate statistical techniques, usually principal component analysis and cluster analysis. Although there are different transformations of the raw data, in this paper, we propose preprocessing by means of an affine transformation. From a mathematical point of view, this process modifies the values of reflectance for each spectral signature scaling them into a [0, 1] interval using minimum and maximum values of reflectance, thus highlighting the features of spectral curves. This method optimizes the characteristics of amplitude and shape, reduces the influence of noise, and improves results by highlighting relevant features as peaks and valleys that may remain hidden using the raw data. This methodology has been applied to a case study of prehistoric chert (flint) artifacts retrieved in archaeological excavations in the Andévalo area located in the Archaeological Museum of Huelva (Huelva, Andalusia). The use of transformed data considerably improves the results obtained with raw data, highlighting the peaks, valleys, and the shape of spectral signatures.

In order to further research the relationship between fractals and complicated networks in terms of self-similarity, the uniform convergence property of the sequence of fractal interpolation functions which can generate self-similar graphics through iterated function system defined by affine transformation is studied in this paper. The result illustrates that it is can be proved that the sequence of fractal interpolation functions uniformly converges to its limit function and its limit function is continuous and integrable over a closed interval under the uniformly convergent condition of the sequence of fractal interpolation functions. The following two conclusions can be indicated. First, both the number sequence limit operation of the sequence of fractal interpolation functions and the function limit operation of its limit function are exchangeable over a closed interval. Second, the two operations of limit and integral between the sequence of fractal interpolation functions and its limit function are exchangeable over a closed interval.

Since Chinese characters are composed of components, deforming the components in a small number of existing calligraphy characters to generate new characters is an effective method to produce a Chinese character library in the same style. Usually, the component deformation is achieved by affine transformation. However, when calculating the parameters in affine transformation, existing methods usually have the problems of a large amount of manual participation or complicated calculation. In this paper, we proposed an Analytic Hierarchy Process (AHP)-based Chinese character component deformation method, which is simple in calculation and can effectively realize the deformation of Chinese character components on the basis of reducing manual intervention. We first determined the factors that affect the selection of control points in affine transformation, then used AHP to calculate the weights of feature points and select the control points according to the weights. As a prerequisite for affine transformation, a matching method of Chinese character feature points based on the Chinese character skeleton map and neighborhood information is also proposed, which helps to achieve more efficient deformation. Experimental results on different fonts demonstrate the effectiveness and generality of our method.

We propose a neural network model to estimate the current frame from two reference frames, using affine transformation and adaptive spatially-varying filters. The estimated affine transformation allows for using shorter filters compared to existing approaches for deep frame prediction. The predicted frame is used as a reference for coding the current frame. Since the proposed model is available at both encoder and decoder, there is no need to code or transmit motion information for the predicted frame. By making use of dilated convolutions and reduced filter length, our model is significantly smaller, yet more accurate, than any of the neural networks in prior works on this topic. Two versions of the proposed model – one for uni-directional, and one for bi-directional prediction – are trained using a combination of Discrete Cosine Transform (DCT)-based $\ell _{1}$ -loss with various transform sizes, multi-scale Mean Squared Error (MSE) loss, and an object context reconstruction loss. The trained models are integrated with the HEVC video coding pipeline. The experiments show that the proposed models achieve about 7.3%, 5.4%, and 4.2% bit savings for the luminance component on average in the Low delay P, Low delay, and Random access configurations, respectively. [ABSTRACT FROM AUTHOR]

Vector addition systems with states (VASS) are widely used for the formal verification of concurrent systems. Given their tremendous computational complexity, practical approaches have relied on techniques such as reachability relaxations, e.g., allowing for negative intermediate counter values. It is natural to question their feasibility for VASS enriched with primitives that typically translate into undecidability. Spurred by this concern, we pinpoint the complexity of integer relaxations with respect to arbitrary classes of affine operations. More specifically, we provide a trichotomy on the complexity of integer reachability in VASS extended with affine operations (affine VASS). Namely, we show that it is NP-complete for VASS with resets, PSPACE-complete for VASS with (pseudo-)transfers and VASS with (pseudo-)copies, and undecidable for any other class. We further present a dichotomy for standard reachability in affine VASS: it is decidable for VASS with permutations, and undecidable for any other class. This yields a complete and unified complexity landscape of reachability in affine VASS. We also consider the reachability problem parameterized by a fixed affine VASS, rather than a class, and we show that the complexity landscape is arbitrary in this setting. [ABSTRACT FROM AUTHOR]

In this paper, we consider affine self-similar solutions for the affine curve shortening flow in the Euclidean plane. We obtain the equations of all affine self-similar solutions up to affine transformations and solve the equations or give descriptions of the solutions for the degenerate case. Some new special solutions for the affine curve shortening flow are found. [ABSTRACT FROM AUTHOR]

The imperative protection of digital information and its secure transmission has evolved into a complex challenge. Within this context, non-linear dynamical systems assume a pivotal role in fortifying content security by their unpredictable behavior and susceptibility to initial conditions. This study introduces an innovative 3D-chaotic system. The proposed map is then examined through bifurcation diagrams and randomness tests, revealing an intricate chaotic behavior of the system. Moreover, an advanced method of securing information is introduced, incorporating a non-associative LA-field sequences-oriented affine transformation. The initial procurement of a non-associative LA field through computational approaches is succeeded by utilizing sequences of its components to establish an affine transformation. This transformative process serves as the central aspect of the suggested color image encryption method. In this strategy, the NTK-3D map and the innovative affine transformation collaborate to introduce both confusion and diffusion, thereby fortifying the overall security stance. The non-associative behavior of the involved algebraic structure, combined with a dynamical system, results in highly resilient encryption. The proposed scheme is not only time-efficient but also has an expanded key space. The results of some performance assessments demonstrate that the suggested encryption technique for the digital medium is capable of resisting well-known attacks. [ABSTRACT FROM AUTHOR]

Wide-angle video frames typically contain more information, but they also exhibit distortion that degrades the visual quality, especially at the edges. To eliminate this distortion from videos, we propose a self-supervised iterative optimization method in this paper. Specifically, we construct a motion parameter estimation model utilizing two consecutive distorted frames, where motion parameters comprise affine transform and distortion parameters. We apply the Gauss–Newton algorithm to minimize the sum-of-squares error between frames and update parameters. Treating inter-frame motion as undistort-affine-distort transformations, frame alignment is achieved by continuously adjusting transform parameters. Ultimately, frames are corrected using the converged parameters. We generated a synthetic dataset with various distortion parameters for evaluation. Experiments demonstrate superior performance versus state-of-the-art methods on synthetic and real wide-angle videos. Our algorithm also achieves higher parameter estimation accuracy without sacrificing efficiency. • proposes a algorithm for video distortion correction based on iterative optimization. • the distort transform and undistort transform are derived separately and the range of parameters and the experimental error are given. • Based on this, we transform the distortion correction into a parameter estimation problem in image alignment. • optimize the parameter estimation problem using Gauss-Newton algorithm. • Experimental results show that the proposed algorithms outperform some state-of-art algorithms in accuracy, without reducing robustness and efficiency. [ABSTRACT FROM AUTHOR]

We present a method of approximation of a deformation field based on the local affine transformations constructed based on n nearest neighbors with respect to points of adopted grid. The local affine transformations are weighted by means of inverse distance squared between each grid point and observed points (nearest neighbors). This work uses a deformation gradient, although it is possible to use a displacement gradient instead – the two approaches are equivalent. To decompose the deformation gradient into components related to rigid motions (rotations, translations are excluded from the deformation gradient through differentiation process) and deformations, we used a polar decomposition and decomposition into a sum of symmetric and an anti-symmetric matrices (tensors). We discuss the results from both decompositions. Calibration of a local affine transformations model (i.e., number of nearest neighbors) is performed on observed points and is carried out in a cross-validation procedure. Verification of the method was conducted on simulated data-grids subjected to known (functionally generated) deformations, hence, known in every point of a study area.

The paper proposes a conversion of plane shooting targets using twodimensional affine transformations. It is assumed that affine transformations will be useful for target generation in firearms training simulators (FATS). The structure and the matrix formation algorithm of target vertex matrices are described as well as transformation matrices and output matrices. Vertex matrices were formed for twelve plane shooting targets. Transformation matrices 3×3 in size were used for conversions. Mathematical modelling and computer simulation of software-configurable plane shooting targets for FATS were performed in the Mathcad v.15 software. / Для трансформации плоскостных стрелковых мишеней предложено использовать аффинные преобразования. Предполагается, что этот тип трансформации полезен при программной генерации мишеней в специализированном программном обеспечении тренажера, обучающего стрельбе из огнестрельного оружия. В статье приведено подробное описание матриц, сопровождающих этапы трансформации: от матрицы формирования контура стрелковой мишени, матрицы аффинного преобразования, до результирующей матрицы. Математическое и компьютерное моделирование программно-конфигурируемой мишени для стрелкового тренажёра выполнено в программном обеспечении Mathcad v.15. / Za gađanje pomoću dvodimenzionalnih afine transformacija u radu je predložena konverzija dvodimenzionalnih meta. Pošlo se od pretpostavke da će afine transformacije biti korisne za generisanje meta u simulatorima za obuku u rukovanju vatrenim oružjem (FATS). Za matrice vrhova meta opisani su struktura i algoritam formiranja matrica, transformacione matrice. kao i matrice izlaza. Matrice vrhova formirane su za dvanaest dvodimenzionalnih meta za gađanje. Za konverziju su korišćene transformacione matrice formata 3x3. Za matematičko modeliranje i kompjutersku simulaciju softverskigenerisanih dvodimenzionalnih meta za gađanje za FATS korišćen je softver Mathcad v.15.

An improved SURF (Speeded-Up Robust Feature） algorithm is proposed to deal with the time-consuming and low precision of positioning of industrial robot. Hessian matrix determinant is used to extract feature points from the target image and a multi-scale spatial pyramid is constructed. The location and scale value of feature points are determined by neighbourhood non-maximum suppression method. The direction of feature points is defined as directional feature descriptors by the binary robust independent elementary feature (BRIEF). The progressive sample consensus (PROSAC) is used to carry out second precise matching and remove mismatching points based on the Hamming distance. Then, an affine transformation model is established to describe the relationship between the template and target images. Centroid coordinates of the target can be obtained based on the affine transformation. Comparative tests were carried out to demonstrate that the proposed method can effectively improve the recognition rate and positioning accuracy of the industrial robots. The average time consuming is less than 0.2 s, the matching accuracy is 96 %, and the positioning error of the robot is less than 1.5 mm. Therefore, the proposed method has practical application importance.

An algorithm of dynamic segmentation of sequential frame pairs was proposed. A comparative analysis of segmentation quality when finding shifts and affine inter-frame transformations for the segments was conducted. In addition, we compared the performance of the proposed method with some static segmentation approaches.

In this paper, we propose a novel robust algorithm for image recovery via affine transformations and the L2,1 norm. To be robust against miscellaneous adverse effects such as occlusions, outliers, and heavy sparse noise, the new algorithm integrates affine transformations with low-rank plus sparse decomposition, where the low-rank component lies in a union of disjoint subspaces, so the distorted or misaligned images can be rectified to render more faithful image representation. In addition, the L2,1 norm is employed to remove the correlated samples across the images, enabling the new approach to be more resilient to outliers and large variations in the images. The determination of the variables involved and the affine transformations is cast as a convex optimization problem. To alleviate the computational complexity, the Alternating Direction Method of Multipliers (ADMM) method is utilized to derive a new set of recursive equations to update the optimization variables and the affine transformations iteratively in a round-robin manner. The convergence of the developed updating equations is addressed and experimentally validated as well. The conducted simulations demonstrate that the new algorithm is superior to the state-of-the-art works in terms of accuracy on some public databases.

The transfer of graphics to a product’s surface is a widely known technology. Printing, engraving, and etching are used every day in production processes with countless types of materials. This paper deals with quality control for laser engraving on surfaces with variable dimensions via optical sensors. The engraving process, apart from colour changes, can induce volume and moisture changes, which lead to dimension changes in some materials. Natural materials and biomaterials are among the ones most affected. Combined with the porous and inhomogeneous structure of such a material, it can be difficult to measure the quality of graphic transfer, especially for shaded products. The quality control of laser-engraved photographs on thin layers of wood veneer was selected as a suitable problem to solve. A complex method for the quality measurement of the specified production was designed and tested. We used an affine transformation to determine the system behaviour and to determine the transfer function of material changes during the production process. Moreover, there is a possibility to compensate the image deformation of the engraved product.

We present a fast 3D analytical affine transformation (F3DAAT) method to obtain polygon-based computer-generated holograms (CGHs). CGHs consisting of tens of thousands of triangles from 3D objects are obtained by this method. We have attempted a revised method based on previous 3D affine transformation methods. In order to improve computational efficiency, we have derived and analyzed our proposed affine transformation matrix. We show that we have further increased the computational efficiency compared with previous affine methods. We also have added flat shading to improve the reconstructed image quality. A 3D object from a 3D camera is reconstructed holographically by numerical and optical experiments.

For the problem that the positioning error of inertial navigation system accumulated with time, a geo magnetic matching positioning algorithm based on affine transformation is proposed. The correlation constraint be tween the matched trajectory and the measured geomagnetic field eigenvalue established by the square difference algorithm. The constraint function is expanded and discretized by Taylor, and the affine transformation model is introduced. The constraint function is transformed into a multivariate index function of the displacement, angle and con traction error of the curve. According to the relativity principle, the geomagnetic matching problem is transformed into solving nonlinear equations. The iterative and numerical method in Mathematica is used to solve the nonlinear equations. The obtained solutions are input into MATLAB for matching and positioning. Experiments show that the final registration point of the matched track differs from the end point of the real track by 293.3 m, and the longitude and latitude errors between the matched track and the real track are 0. 003 and 0.000 4° respectively, which verifies the feasibility of the proposed algorithm. [ABSTRACT FROM AUTHOR]

A sedentary routine at work can cause various muscular, skeletal or visual diseases, however these can be prevented with what is known as active pauses. This article is intended to illustrate how software can help reduce the risk of occupational disease due to the sedentary lifestyle of an office job, for this purpose a web application was developed under the SCRUM methodology, which makes use of the TensorFlow, Flask PoseNet model and python, for an active pause control application which is a proven practice of reducing the type of diseases already mentioned. With these tools it was possible to develop an algorithm capable of comparing two human figures; which serves to compare whether the user of the program is performing or not correctly performing the active pause exercise, with an average error squared on the order of 10−32. Finally, The application can keep track of the figure and exercises performed by the user just by using the user personal webcam and the comparison algorithm developed, leaving behind the use of tools such as Kinect. [ABSTRACT FROM AUTHOR]

The Householder transformation, allowing a rewrite of probabilities into expectations of dichotomic observables, is generalized in terms of its spectral decomposition. The dichotomy is modulated by allowing more than one negative eigenvalue or by abandoning binaries altogether, yielding generalized operator-valued arguments for contextuality. We also discuss a form of contextuality by the variation of the functional relations of the operators, in particular by additivity.

Let Δ be the set of all triple points {A,B,C} in ℝn such that the largest angle of the triangle ABC is less than 2π/3. In this paper, we proved that if a mapping f:ℝn → ℝn preserves the Fermat-Torricelli points of the triangles in Δ, then f is an affine transformation. [ABSTRACT FROM AUTHOR]

An unbounded elliptically orthotropic elastic solid containing a single anisotropic ellipsoidal inhomogeneity is considered. The problem statement assumes arbitrary orientation of ellipsoid with respect to the orthotropy axes and non-uniform far loading. By applying the appropriate affine transformations, the boundary value problem is reduced to that one with the isotropic constituents. The complete displacement solution to the transformed problem is obtained using the Papkovich-Neuber representation with the scalar potentials written in terms of ellipsoidal solid harmonics. By accurate fulfilling the interface conditions, the boundary value problem is reduced to the system of the linear algebraic equations for the constants entering the potentials. For the Eshelby problem (uniform remotely applied loading and perfect interface), an explicit analytical solution is written in terms of ellipsoidal harmonics. This result yields solution for the elliptical crack problem in the remarkably simple way. The numerical examples illustrate an effect of the matrix anisotropy on the stress concentration and stress intensity factors. An application of the obtained solution to the micromechanics is discussed. The effective elastic stiffness tensor of a particulate composite with elliptically orthotropic matrix is evaluated using Maxwell homogenization scheme. [ABSTRACT FROM AUTHOR]

The correspondence problem is conventionally performed at the pairwise level, i.e., finding the correspondence model, e.g., affine transformation between two input images. While, this paper tackles the scenario when more than two images, e.g., a sequence of images are considered either for model learning or inference. Our proposed approach is based on the recent work on convolutional neural network for geometric matching model. Specifically, we extend this baseline by introducing sequential cycle consistency check that can involve multiple images. The learning is performed in a supervised setting provided with ground truth parametric transformation information, while it meanwhile leverages the consistency information as a regularizer during learning. Extensive experiments are performed on the public benchmark dataset, whereby qualitative and quantitative results are both presented. Our method improves the two-image geometric matching network learning baseline by fusing more than two images' information during learning, while it can still be applied for two-image matching for testing.

In order to solve the problem of low efficiency and large influence of human factors on the airtightness testing of the valve body, a method based on improved SIFT lo detect the airtightness of the valve body is proposed. First of all* the algorithm of difference shadow is used to preprocess the collected images; Then based on the SIFT algorithm, combined with improved SUSAN operator, affine transformation, the image mosaic is matched; Finally, the traversal of the shape elements is repealed to obtain the real parameters of the air bubble, so as lo judge whether the valve is qualified. The experiments show that the method improves the bubble detection efficiency, and the detection accuracy reaches 98%, which is suitable for testing the airtightness of the same of valves. [ABSTRACT FROM AUTHOR]

• State of the art removal of jittery artifacts. • Image alignment from different modalities. • High quality image using Transformation with Optimization. • Diminutive information retrieval with Multimodal images fusion. • Superior FSR methodology than conventional techniques. Medical imaging is a boon to mankind. Processing of medical images is extensively blooming with the aid of technological advancements. Medical images taken from different modalities are stabilized to remove the jittery artifacts and further processed for fusing the images to enable the physicians to visualize the combined features of CT and MRI. Alignment of both the images is performed to ensure parametric registration so as to effectively blend and overlay for proper diagnosis. To assure the quality of the images, basic optimization is implemented and the subjective visualization and objective evaluation are performed. The proposed approach, image fusion with stabilization and registration outperforms the existing techniques in terms of subjective and objective evaluation. [ABSTRACT FROM AUTHOR]

Algebraic structures and their hardware–software implementation gain considerable attention in the field of information security and coding theory. Research progress in the applications of arithmetic properties of algebraic structures is being frequently made. These structures are mostly useful in improvement of the cryptographic algorithms. A novel technique is given to design a cryptosystem responsible for lossless for image encryption. The proposed scheme is for the RGB image whose pixels are considered as 24 binary bits, accordingly a unique arrangement for the construction of S-boxes over a Galois field G F 2 9 is employed. Consequently, it generates multiple different S-boxes with excellent cryptographic characteristic and hence confusing process of the cryptosystem has been working. Whereas the diffusion process in this cryptosystem is based on Affine transformation over a unit elements of an integers modulo ring Z n . The scrambling of the image data through the Affine transformation escalate the security asset, avoid computational effort and abbreviated the time complexity. In addition, the simulation test and comparative scrutinize illustrate that the proposed scheme is highly sensitive, large keyspace, excellent statistical properties and secure against differential attacks. Therefore, the proposed algorithm is valuable for confidential communication. Furthermore, due to the arithmetic properties of algebraic structures, the proposed scheme would be easily implemented, secure and fast enough to be utilized in real-world applications. [ABSTRACT FROM AUTHOR]

The purpose of this research is to show how the complicated and irregular fractal interpolation function is represented by Fourier series. First, on the closed interval [0,1], even prolongation is operated to the fractal interpolation function generated by iterated function system constituted by affine transform and Fourier cosine series representation of fractal interpolation function is proved. Second, for fractal interpolation function, odd prolongation is done and Fourier sine series formula of fractal interpolation function is proved. Final, Fourier series expansion of fractal interpolation function on the closed interval [ − 1 , 1 ] is proved. The result shows that complex fractal interpolation function can be represented by Fourier sine series and Fourier cosine series, so relatively simple Fourier series can be used to represent relatively complicated fractal interpolation function. [ABSTRACT FROM AUTHOR]

In this article, we consider the distributed planar formation control problem, in which only three agents have access to the desired geometry information specified by different sensing control variables, including the distance and bearing (angle). With the aim to achieve flexible transformation motions, the stress matrix is invoked to activate the affine formation control technique, rendering the system more freedom in the sense that the whole formation shape can be altered via controlling a small number of agents. By integrating the distance and bearing (angle) measurements, a new control algorithm is proposed such that the formation can be smoothly changed according to the prescribed control variables imposed on the informed agents. Moreover, the orientation of the whole formation is also controllable while forming the desired geometry shape. Finally, simulation results are presented to validate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This paper is a review of results of studies of affine transformations in generalized spaces over real linear algebras over the past 15-20 years. [ABSTRACT FROM AUTHOR]

The widespread application of the Internet makes the protection of image copyright face serious challenges. For resolving this problem, this paper designs a blind color digital image watermarking algorithm which meets the requirements of invisibility, security and robustness. The advantages of the proposed method include the following two points: 1) the proposed method uses Affine transformation with large key space to encrypt the watermark information; 2) Schur decomposition with low complexity is selected and performed on the matrix blocks in different color channels of the host image. In this proposed method, the watermark embedding and blind extraction are completed by quantizing the eigenvalues on the diagonal of the decomposed matrix with different quantization steps. Experimental results show that the proposed method not only has good invisibility, but also has high security and strong robustness. [ABSTRACT FROM AUTHOR]

Similarity transformation model does not provide a satisfactory solution for non-uniformly deformed systems because it allows only for a uniform scale and right angles. Instead, an affine model can be used, since it characterizes non-uniform dilatations and obliquity of the three axes. The general affine transformation contains 12 parameters. Nonetheless, it is not always necessary to use them all. The question of how many parameters should take part in the transformation and in what combinations is examined in the paper. In order to choose the proper transformation, a refined AIC is proposed. The paper also presents how to conduct the conversion of parameters between different coordinate systems with reference to the invariance property of coordinate transformation. To demonstrate the impact of using variable number of parameters and to observe the influence of coordinate systems on the transformation outcome, we use a network of 18 permanent GNSS stations in Israel as a case study. [ABSTRACT FROM AUTHOR]