Fast reconstruction algorithm for fan‐Beam CT system

In order to explore the advantages of swarm intelligence and strong self-assembly deformation adaptability of swarm robots, a small docking positioning and navigation strategy for autonomous robots is presented in this paper. The robot has a polygonal shape. Based on monocular camera image recognition and ultrasonic sensor to achieve navigation docking. Realize group networking through ZigBee. Based on the configuration characteristics of the robot platform, a three-element configuration description method is proposed. Each robot individual is described by a vector, and the configuration of the robot platform is described in polar coordinates. In the process of constructing the configuration, the overall configuration data are updated through polar coordinate transformation. Then, the navigation strategy is planned through polar coordinate data. This method has small data quantity and convenient formation construction and reconstruction. For the formation of the whole array, the target configuration array is constructed by controlling the finite state machine.

The ground-based arc-scanning synthetic aperture radar (ArcSAR) is capable of 360° scanning of the surroundings with the antenna fixed on a rotating arm. ArcSAR has much wider field of view when compared with conventional ground-based synthetic aperture radar (GBSAR) scanning on a linear rail. It has already been used in deformation monitoring applications. This paper mainly focuses on the accurate and fast imaging algorithms for ArcSAR. The curvature track makes the image focusing challenging and, in the classical frequency domain, fast imaging algorithms that are designed for linear rail SAR cannot be readily applied. This paper proposed an efficient frequency domain imaging algorithm for ArcSAR. The proposed algorithm takes advantage of the angular shift-invariant property of the ArcSAR signal, and it deduces the accurate matched filter in the angular-frequency domain, so panoramic images in polar coordinates with wide swath can be obtained at one time without segmenting strategy. When compared with existing ArcSAR frequency domain algorithms, the proposed algorithm is more accurate and efficient, because it has neither far range nor narrow beam antenna restrictions. The proposed method is validated by both simulation and real data. The results show that our algorithm brings the quality of image close to the time domain back-projection (BP) algorithm at a processing efficiency about two orders of magnitude better, and it has better image quality than the existing frequency domain Lee’s algorithm at a comparable processing speed.

Convolutional neural networks (CNNs) have been demonstrated to be powerful tools to automatically learn effective features from large datasets. Though features learned in CNNs are approximately scale-, translation-, and position-invariant, and their capacity in dealing with image rotations remains limited. In this article, a novel cyclic polar coordinate convolutional layer (CPCCL) is proposed for CNNs to handle the problem of rotation invariance for feature learning. First, the proposed CPCCL converts rotation variation into translation variation using polar coordinates transformation, which can easily be handled by CNNs. Moreover, cyclic convolution is designed to completely handle the translation variation converted from rotation variation by conducting convolution in a cyclic shift mode. Note that the proposed CPCCL is capable of generalization and can be used as a preprocessing layer for classification CNNs to learn the rotation-invariant feature. Extensive experiments over three benchmark datasets demonstrate that the proposed CPCCL can clearly handle the rotation-sensitive problem in traditional CNNs and outperforms several state-of-the-art rotation-invariant feature learning algorithms.

This paper describes an implementation of reception and real-time decoding of Asynchronous Sigma-Delta modulator (ASDM) encoded and wirelessly (On-off keying) transmitted signals. By using Fast reconstruction algorithm it is possible to reconstruct the original signal ≈ 25 times faster than by Classical reconstruction algorithm, if the signal lenght is 1 second, and ≈ 61, ≈ 130 and ≈ 228 times faster, if the length of the signal is 2, 4 and 8 seconds, respectively. Developed overall system consists of 3 parts - superheterodyne receiver, digitizer, PC with adaptive data reconstruction algorithm. Real-time decoding algorithm, which consist of data acquistion, filtering, processing, reconstruction and vizualization is implemented in LabView as a virtual instrument with graphical user interface (GUI).

Investigating the evolution of disk galaxies and the dynamics of proto-stellar disks can involve the use of both a hydrodynamical and a Poisson solver. These systems are usually approximated as infinitesimally thin disks using two- dimensional Cartesian or polar coordinates. In Cartesian coordinates, the calcu- lations of the hydrodynamics and self-gravitational forces are relatively straight- forward for attaining second order accuracy. However, in polar coordinates, a second order calculation of self-gravitational forces is required for matching the second order accuracy of hydrodynamical schemes. We present a direct algorithm for calculating self-gravitational forces with second order accuracy without artifi- cial boundary conditions. The Poisson integral in polar coordinates is expressed in a convolution form and the corresponding numerical complexity is nearly lin- ear using a fast Fourier transform. Examples with analytic solutions are used to verify that the truncated error of this algorithm is of second order. The kernel integral around the singularity is applied to modify the particle method. The use of a softening length is avoided and the accuracy of the particle method is significantly improved.

Through the reconstruction of the fluorescent probe distributions, fluorescence molecular tomography (FMT) can three-dimensionally resolve the molecular processes in small animals in vivo. In this paper, we propose an FMT reconstruction algorithm based on the iterated shrinkage method. By incorporating a surrogate function, the original optimization problem can be decoupled, which enables us to use the general sparsity regularization. Due to the sparsity characteristic of the fluorescent sources, the performance of this method can be greatly enhanced, which leads to a fast reconstruction algorithm. Numerical simulations and physical experiments were conducted. Compared to Newton method with Tikhonov regularization, the iterated shrinkage based algorithm can obtain more accurate results, even with very limited measurement data.

(NOTE: Every chapter ends with Questions to Guide Your Review, Practice Exercises, and Additional Exercises.) P. Preliminaries. Real Numbers and the Real Line. Coordinates, Lines, and Increments. Functions. Shifting Graphs. Trigonometric Functions. 1. Limits and Continuity. Rates of Change and Limits. Rules for Finding Limits. Target Values and Formal Definitions of Limits. Extensions of the Limit Concept. Continuity. Tangent Lines. 2. Derivatives. The Derivative of a Function. Differentiation Rules. Rates of Change. Derivatives of Trigonometric Functions. The Chain Rule. Implicit Differentiation and Rational Exponents. Related Rates of Change. 3. Applications of Derivatives. Extreme Values of Functions. The Mean Value Theorem. The First Derivative Test for Local Extreme Values. Graphing with y e and y . Limits as x a a, Asymptotes, and Dominant Terms. Optimization. Linearization and Differentials. Newton's Method. 4. Integration. Indefinite Integrals. Differential Equations, Initial Value Problems, and Mathematical Modeling. Integration by Substitution--Running the Chain Rule Backward. Estimating with Finite Sums. Riemann Sums and Definite Integrals. Properties, Area, and the Mean Value Theorem. Substitution in Definite Integrals. Numerical Integration. 5. Applications of Integrals. Areas Between Curves. Finding Volumes by Slicing. Volumes of Solids of Revolution--Disks and Washers. Cylindrical Shells. Lengths of Plan Curves. Areas of Surfaces of Revolution. Moments and Centers of Mass. Work. Fluid Pressures and Forces. The Basic Pattern and Other Modeling Applications. 6. Transcendental Functions. Inverse Functions and Their Derivatives. Natural Logarithms. The Exponential Function. ax and logax. Growth and Decay. L'Hopital's Rule. Relative Rates of Growth. Inverse Trigonomic Functions. Derivatives of Inverse Trigonometric Functions Integrals. Hyperbolic Functions. First Order Differential Equations. Euler's Numerical Method Slope Fields. 7. Techniques of Integration. Basic Integration Formulas. Integration by Parts. Partial Fractions. Trigonometric Substitutions. Integral Tables and CAS. Improper Integrals. 8. Infinite Series. Limits of Sequences of Numbers. Theorems for Calculating Limits of Sequences. Infinite Series. The Integral Test for Series of Nonnegative Terms. Comparison Tests for Series of Nonnegative Terms. The Ratio and Root Tests for Series of Nonnegative Terms. Alternating Series, Absolute and Conditional Convergence. Power Series. Taylor and Maclaurin Series. Convergence of Taylor Series Error Estimates. Applications of Power Series. 9. Conic Sections, Parametrized Curves, and Polar Coordinates. Conic Sections and Quadratic Equations. Classifying Conic Sections by Eccentricity. Quadratic Equations and Rotations. Parametrizations of Plan Curves. Calculus with Parametrized Curves. Polar Coordinates. Graphing in Polar Coordinates. Polar Equations for Conic Sections. Integration in Polar Coordinates. 10. Vectors and Analytic Geometry in Space. Vectors in the Plane. Cartesian (Rectangular) Coordinates and Vectors in Space. Dot Products. Cross Products. Lines and Planes in Space. Cylinders and Quadric Surfaces. Cylindrical and Spherical Coordinates. 11. Vector-Valued Functions and Motion in Space. Vector-Valued Functions and Space Curves. Modeling Projectile Motion. Arc Length and the Unit Tangent Vector T. Curvature, Torison, and the TNB Frame. Planetary Motion and Satellites. 12. Multivariable Functions and Partial Derivatives. Functions of Several Variables. Limits and Continuity. Partial Derivatives. Differentiability, Linearization, and Differentials. The Chain Rule. Partial Derivatives with Constrained Variables. Directional Derivatives, Gradient Vectors, and Tangent Planes. Extreme Values and Saddle Points. Lagrange Multipliers. Taylor's Formula. 13. Multiple Integrals. Double Integrals. Areas, Moments, and Centers of Mass. Double Integrals in Polar Form. Triple Integrals in Rectangular Coordinates. Masses and Moments in Three Dimensions. Triple Integrals in Cylindrical and Spherical Coordinates. Substitutions in Multiple Integrals. 14. Integration in Vector Fields. Line Integrals. Vector Fields, Work, Circulation, and Flux. Path Independence, Potential Functions, and Conservative Fields. Green's Theorem in the Plane. Surface Area and Surface Integrals. Parametrized Surfaces. Stokes's Theorem. The Divergence Theorem and a Unified Theory. Appendices. Mathematical Induction. Proofs of Limit Theorems in Section 1.2. Complex Numbers. Simpson's One-Third Rule. Cauchy's Mean Value Theorem and the Stronger Form of L'Hopital's Rule. Limits that Arise Frequently. The Distributive Law for Vector Cross Products. Determinants and Cramer's Rule. Euler's Theorem and the Increment Theorem.

A first, we used our knowledge of Fourier series to solve several interesting boundary value problems by the method of separation of variables. The success of our method depended to a large extent on the fact that the domains under consideration were easily described in Cartesian coordinates. In this paper/research we address problems where the domains are easly described in polar and cylindrical coordinates. Spesifically we consider boundary value problems for the wave, heat, Laplace and Poisson equation over disks or cylinders. Upon restating these problems in suitable coordinat systems and separating variables, we will encounter new ordinary differential equations, Bessel’s equation, whose solutions are called Bessel function in ways analogous to Fourier series expansions. The vibrations of the membrane are governed by the two-dimensional wave equation, which will be expressed in polar coordinantes, because these are the coordinates best suited to this problem. Finally, we will solve the two dimensional wave equation in polar coordinates (general case).

Objective To compare the reproducibility and reliability of facial soft tissue landmarks using a direct and an indirect placement methods in facial three-dimensional (3D) soft tissue assessment.Methods 3D coordinates of 37 soft tissue landmarks were obtained respectively in 35 normal healthy volunteers from 3D optical capture system and Materialise's interactive medical image control system (Mimics).Landmarks were affixed on the cutaneous surface (direct method) and marked on the 3D reconstructed craniofacial model (indirect method).Intra-class correlation coefficients (ICCs) and paired t-tests were used to compare the reliability and reproducibility of facial landmarks between two placement methods.Results For the direct placement method,86.5 ％ landmarks had an ICC higher than 0.75.For the indirect placement method,75.7％ landmarks had an ICC higher than 0.75.The inter-observer variability using the direct placement method was (1.259±0.566) mm,which was significantly smaller (P＜0.05) than (1.420±0.638) mm obtained by the indirect placement method.Conclusions Compared with indirect method,direct method has higher reliability and reproducibility in evaluating facial soft tissue. Key words: Computed tomography; Cephalometrics; Optical capture technology

A fast and flexible algorithm for microstructure reconstruction combining simulated annealing and deep learning

This paper focuses on the analysis of the unearthed bronze solar wheel and gold mask. For the bronze solar wheel: Firstly, a plane coordinate system is established to transform the three dimensional plane diagram into a two dimensional plane map. Then, polar coordinates are introduced, and linear interpolation is constructed to obtain the curve equation of cultural relics. Mathematical model of the bronze solar wheel needs to be established, and the general equation of the internal arc should be derived. With the center of the bronze solar wheel as the origin of XOY, according to the general equation of the circle and by substituting the disk data, the bronze sun wheel curve equation can be obtained. On the XOY plane rectangular coordinate frame, through introducing polar coordinates, the POINT command in CAD can determine the intersection coordinates of the five rays in the disk and the angle with the horizontal axis. Substituting these into the polar coordinate equation, the five - ray equation can be obtained. To obtain the general equations of the circular arc, polar coordinates need to be established. For the drawing of bronze solar wheel four, six, eight, and 12 ray patterns, it can be obtained by adjusting the angle θ between the ray and the horizontal axis X through CAD. **************** ACKNOWLEDGEMENTS**************** This work is supported by ministry of education industry-university cooperative education project (Grant No.: 231106441092432), the research and practice of integrating "curriculum thought and politics" into the whole process of graduation design of Mechanical engineering major: (Grant. No.: 30120300100-23-yb-jgkt03), research on the integration mechanism of "course-training-competition-creation-production" for innovation and entrepreneurship of mechanical engineering majors in applied local universities (Grant. No.: CXKT202405), Mechanical manufacturing equipment design school-level "gold class" construction project (Grant. No.: 30120324001).

Multiframe track-before-detect method based on velocity filtering in mixed coordinates

We consider constructing a surface from a given set of point cloud data. We explore two fast algorithms to minimize the weighted minimum surface energy in [Zhao, Osher, Merriman and Kang, Comp Vision and Image Under, 80(3):295–319, 2000]. An approach using Semi-Implicit Method (SIM) improves the computational efficiency through relaxation on the time-step constraint. An approach based on Augmented Lagrangian Method (ALM) reduces the run-time via an Alternating Direction Method of Multipliers-type algorithm, where each sub-problem is solved efficiently. We analyze the effects of the parameters on the level-set evolution and explore the connection between these two approaches. We present numerical examples to validate our algorithms in terms of their accuracy and efficiency.

Hidden Markov models have become the preferred technique for visual recognition of human gestures. However, the recognition rate depends on the set of visual features used, and also on the number of states of the hidden variable. It is difficult to determine a priori the optimal set of features and number of states. We analyse experimentally the use of different features for gesture recognition in an office environment. We considered a set of seven gestures that include interaction with other objects, such as writing, using the mouse, opening a drawer, etc. We use a single camera to detect and track the hand of the user based on adaptive colour histograms. From tracking the hand in a video sequence we obtain several features. The features considered include position and velocity in polar and Cartesian coordinates, and the trajectory represented as a chain code. Given that these features are continuous, we discretized them into a set of symbols using vector quantization. We then tested the recognition rate using HMMs with different: (i) number of discrete symbols; (ii) number of hidden states, (Hi) combination of features. The results show a high variation on the recognition rate depending on these parameters, from below 50% to more than 95%. The best performance (97%) was obtained by using the magnitude and orientation in polar coordinates, 64 discrete symbols and 10 states.

A novel calibration method based on polar coordinate is proposed. The world coordinates are expressed in the form of polar coordinates, which are converted to world coordinates in the calibration process. In the beginning, the calibration points are obtained in polar coordinates. By transformation between polar coordinates and rectangular coordinates, the points turn into form of rectangular coordinates. Then, the points are matched with the corresponding image coordinates. At last, the parameters are obtained by objective function optimization. By the proposed method, the relationships between objects and cameras are expressed in polar coordinates easily. It is suitable for multi-camera calibration. Cameras can be calibrated with fewer points. The calibration images can be positioned according to the location of cameras. The experiment results demonstrate that the proposed method is an efficient calibration method. By the method, cameras are calibrated conveniently with high accuracy.