The 3D reconstruction pipeline uses the Bundle Adjustment algorithm to refine the camera and point parameters. The Bundle Adjustment algorithm is a compute-intensive algorithm, and many researchers have improved its p...The 3D reconstruction pipeline uses the Bundle Adjustment algorithm to refine the camera and point parameters. The Bundle Adjustment algorithm is a compute-intensive algorithm, and many researchers have improved its performance by implementing the algorithm on GPUs. In the previous research work, “Improving Accuracy and Computational Burden of Bundle Adjustment Algorithm using GPUs,” the authors demonstrated first the Bundle Adjustment algorithmic performance improvement by reducing the mean square error using an additional radial distorting parameter and explicitly computed analytical derivatives and reducing the computational burden of the Bundle Adjustment algorithm using GPUs. The naïve implementation of the CUDA code, a speedup of 10× for the largest dataset of 13,678 cameras, 4,455,747 points, and 28,975,571 projections was achieved. In this paper, we present the optimization of the Bundle Adjustment algorithm CUDA code on GPUs to achieve higher speedup. We propose a new data memory layout for the parameters in the Bundle Adjustment algorithm, resulting in contiguous memory access. We demonstrate that it improves the memory throughput on the GPUs, thereby improving the overall performance. We also demonstrate an increase in the computational throughput of the algorithm by optimizing the CUDA kernels to utilize the GPU resources effectively. A comparative performance study of explicitly computing an algorithm parameter versus using the Jacobians instead is presented. In the previous work, the Bundle Adjustment algorithm failed to converge for certain datasets due to several block matrices of the cameras in the augmented normal equation, resulting in rank-deficient matrices. In this work, we identify the cameras that cause rank-deficient matrices and preprocess the datasets to ensure the convergence of the BA algorithm. Our optimized CUDA implementation achieves convergence of the Bundle Adjustment algorithm in around 22 seconds for the largest dataset compared to 654 seconds for the sequential implementation, resulting in a speedup of 30×. Our optimized CUDA implementation presented in this paper has achieved a 3× speedup for the largest dataset compared to the previous naïve CUDA implementation.展开更多
Multiplicative calculus(MUC)measures the rate of change of function in terms of ratios,which makes the exponential functions significantly linear in the framework of MUC.Therefore,a generally non-linear optimization p...Multiplicative calculus(MUC)measures the rate of change of function in terms of ratios,which makes the exponential functions significantly linear in the framework of MUC.Therefore,a generally non-linear optimization problem containing exponential functions becomes a linear problem in MUC.Taking this as motivation,this paper lays mathematical foundation of well-known classical Gauss-Newton minimization(CGNM)algorithm in the framework of MUC.This paper formulates the mathematical derivation of proposed method named as multiplicative Gauss-Newton minimization(MGNM)method along with its convergence properties.The proposed method is generalized for n number of variables,and all its theoretical concepts are authenticated by simulation results.Two case studies have been conducted incorporating multiplicatively-linear and non-linear exponential functions.From simulation results,it has been observed that proposed MGNM method converges for 12972 points,out of 19600 points considered while optimizing multiplicatively-linear exponential function,whereas CGNM and multiplicative Newton minimization methods converge for only 2111 and 9922 points,respectively.Furthermore,for a given set of initial value,the proposed MGNM converges only after 2 iterations as compared to 5 iterations taken by other methods.A similar pattern is observed for multiplicatively-non-linear exponential function.Therefore,it can be said that proposed method converges faster and for large range of initial values as compared to conventional methods.展开更多
The interaction of Cu(Ⅱ) and human serum albumin (HSA) or bovine serum albumin (BSA) at physiological pH is studied by equilibrium dialysis. The successive stability constants are obtained by non-linear least square ...The interaction of Cu(Ⅱ) and human serum albumin (HSA) or bovine serum albumin (BSA) at physiological pH is studied by equilibrium dialysis. The successive stability constants are obtained by non-linear least square methods fitting Bjerrum formula. For both the Cu(Ⅱ)-HSA and Cu(Ⅱ)-BSA systems, the order of magnitude of K 1 and K 2 was found to be ≈10 4 mol -1·dm 3. There are about twenty stoichiometry binding sites found in one HSA or BSA molecule. They can be divided into two or three sets. Results of equilibrium dialysis experiments suggest that there exists one strong metal binding site in both Cu(Ⅱ)-HSA and Cu(Ⅱ)-BSA. It is the imidazol group nitrogen atoms of His 3 that are primarily concerned with copper binding site. After reaching dialysis equilibrium, there is the interaction among the different binding sites, the values of K all deviate from the simple statistical effect except for K-1 and K-2 in both Cu(Ⅱ)-HSA and Cu(Ⅱ)-BSA systems, and the positive cooperative effect is found.展开更多
In order to implement 3D scanning of those complicated parts such as blades in the aviation field,a non-contact optical measuring system is established in the paper,which integrates a laser displacement sensor,a probe...In order to implement 3D scanning of those complicated parts such as blades in the aviation field,a non-contact optical measuring system is established in the paper,which integrates a laser displacement sensor,a probe head,the frame of a coordinate measuring machine（CMM）,etc.As the output of the laser sensor directly obtained possesses the 1D length of the laser beam,it needs to determine the unit direction vector of the laser beam denoted as（l,m,n）by calibration so as to convert the 1D values into 3D coordinates of target points.Therefore,an extrinsic calibration method based on a standard sphere is proposed to accomplish this task in the paper.During the calibration procedure,the laser sensor moves along with the motion of the CMM and gathers the required data on the spherical surface.Then,both the output of the laser sensor and the grating readings of the CMM are substituted into the constraint equation of the spherical surface,in which an over-determined nonlinear equation group containing unknown parameters is established.For the purpose of solving the equation group,a method based on non-linear least squares optimization is put forward.Finally,the system after calibration is utilized to measure the diameter of a metallic sphere 10 times from different orientations to verify the calibration accuracy.In the experiment,the errors between the measured results and the true values are all smaller than 0.03 mm,which manifests the validity and practicality of the extrinsic calibration method presented in the paper.展开更多
In this thesis,we establish non-linear wavelet density estimators and studying the asymptotic properties of the estimators with data missing at random when covariates are present.The outstanding advantage of non-linea...In this thesis,we establish non-linear wavelet density estimators and studying the asymptotic properties of the estimators with data missing at random when covariates are present.The outstanding advantage of non-linear wavelet method is estimating the unsoothed functions,however,the classical kernel estimation cannot do this work.At the same time,we study the larger sample properties of the ISE for hazard rate estimator.展开更多
文摘The 3D reconstruction pipeline uses the Bundle Adjustment algorithm to refine the camera and point parameters. The Bundle Adjustment algorithm is a compute-intensive algorithm, and many researchers have improved its performance by implementing the algorithm on GPUs. In the previous research work, “Improving Accuracy and Computational Burden of Bundle Adjustment Algorithm using GPUs,” the authors demonstrated first the Bundle Adjustment algorithmic performance improvement by reducing the mean square error using an additional radial distorting parameter and explicitly computed analytical derivatives and reducing the computational burden of the Bundle Adjustment algorithm using GPUs. The naïve implementation of the CUDA code, a speedup of 10× for the largest dataset of 13,678 cameras, 4,455,747 points, and 28,975,571 projections was achieved. In this paper, we present the optimization of the Bundle Adjustment algorithm CUDA code on GPUs to achieve higher speedup. We propose a new data memory layout for the parameters in the Bundle Adjustment algorithm, resulting in contiguous memory access. We demonstrate that it improves the memory throughput on the GPUs, thereby improving the overall performance. We also demonstrate an increase in the computational throughput of the algorithm by optimizing the CUDA kernels to utilize the GPU resources effectively. A comparative performance study of explicitly computing an algorithm parameter versus using the Jacobians instead is presented. In the previous work, the Bundle Adjustment algorithm failed to converge for certain datasets due to several block matrices of the cameras in the augmented normal equation, resulting in rank-deficient matrices. In this work, we identify the cameras that cause rank-deficient matrices and preprocess the datasets to ensure the convergence of the BA algorithm. Our optimized CUDA implementation achieves convergence of the Bundle Adjustment algorithm in around 22 seconds for the largest dataset compared to 654 seconds for the sequential implementation, resulting in a speedup of 30×. Our optimized CUDA implementation presented in this paper has achieved a 3× speedup for the largest dataset compared to the previous naïve CUDA implementation.
文摘Multiplicative calculus(MUC)measures the rate of change of function in terms of ratios,which makes the exponential functions significantly linear in the framework of MUC.Therefore,a generally non-linear optimization problem containing exponential functions becomes a linear problem in MUC.Taking this as motivation,this paper lays mathematical foundation of well-known classical Gauss-Newton minimization(CGNM)algorithm in the framework of MUC.This paper formulates the mathematical derivation of proposed method named as multiplicative Gauss-Newton minimization(MGNM)method along with its convergence properties.The proposed method is generalized for n number of variables,and all its theoretical concepts are authenticated by simulation results.Two case studies have been conducted incorporating multiplicatively-linear and non-linear exponential functions.From simulation results,it has been observed that proposed MGNM method converges for 12972 points,out of 19600 points considered while optimizing multiplicatively-linear exponential function,whereas CGNM and multiplicative Newton minimization methods converge for only 2111 and 9922 points,respectively.Furthermore,for a given set of initial value,the proposed MGNM converges only after 2 iterations as compared to 5 iterations taken by other methods.A similar pattern is observed for multiplicatively-non-linear exponential function.Therefore,it can be said that proposed method converges faster and for large range of initial values as compared to conventional methods.
文摘The interaction of Cu(Ⅱ) and human serum albumin (HSA) or bovine serum albumin (BSA) at physiological pH is studied by equilibrium dialysis. The successive stability constants are obtained by non-linear least square methods fitting Bjerrum formula. For both the Cu(Ⅱ)-HSA and Cu(Ⅱ)-BSA systems, the order of magnitude of K 1 and K 2 was found to be ≈10 4 mol -1·dm 3. There are about twenty stoichiometry binding sites found in one HSA or BSA molecule. They can be divided into two or three sets. Results of equilibrium dialysis experiments suggest that there exists one strong metal binding site in both Cu(Ⅱ)-HSA and Cu(Ⅱ)-BSA. It is the imidazol group nitrogen atoms of His 3 that are primarily concerned with copper binding site. After reaching dialysis equilibrium, there is the interaction among the different binding sites, the values of K all deviate from the simple statistical effect except for K-1 and K-2 in both Cu(Ⅱ)-HSA and Cu(Ⅱ)-BSA systems, and the positive cooperative effect is found.
基金supported by the National Science and Technology Major Project for ‘‘High-grade Numerical Control Machine Tools and Basic Manufacturing Equipment” of China (No. 2013ZX04001071)
文摘In order to implement 3D scanning of those complicated parts such as blades in the aviation field,a non-contact optical measuring system is established in the paper,which integrates a laser displacement sensor,a probe head,the frame of a coordinate measuring machine（CMM）,etc.As the output of the laser sensor directly obtained possesses the 1D length of the laser beam,it needs to determine the unit direction vector of the laser beam denoted as（l,m,n）by calibration so as to convert the 1D values into 3D coordinates of target points.Therefore,an extrinsic calibration method based on a standard sphere is proposed to accomplish this task in the paper.During the calibration procedure,the laser sensor moves along with the motion of the CMM and gathers the required data on the spherical surface.Then,both the output of the laser sensor and the grating readings of the CMM are substituted into the constraint equation of the spherical surface,in which an over-determined nonlinear equation group containing unknown parameters is established.For the purpose of solving the equation group,a method based on non-linear least squares optimization is put forward.Finally,the system after calibration is utilized to measure the diameter of a metallic sphere 10 times from different orientations to verify the calibration accuracy.In the experiment,the errors between the measured results and the true values are all smaller than 0.03 mm,which manifests the validity and practicality of the extrinsic calibration method presented in the paper.
文摘In this thesis,we establish non-linear wavelet density estimators and studying the asymptotic properties of the estimators with data missing at random when covariates are present.The outstanding advantage of non-linear wavelet method is estimating the unsoothed functions,however,the classical kernel estimation cannot do this work.At the same time,we study the larger sample properties of the ISE for hazard rate estimator.
