Powell Algorithm Research Articles

Markerless human body motion capture using Markov random field and dynamic graph cuts

Current vision-based human body motion capture methods always use passive markers that are attached to key locations on the human body. However, such systems may confront subjects with cumbersome markers, making it difficult to convert the marker data into kinematic motion. In this paper, we propose a new algorithm for markerless computer vision-based human body motion capture. We compute volume data (voxels) representation from the images using the method of SFS (shape from silhouettes), and consider the volume data as a MRF (Markov random field). Then we match a predefined human body model with pose parameters to the volume data, and the calculation of this matching is transformed into energy function minimization. We convert the problem of energy function construction into a 3D graph construction, and get the minimal energy by the max-flow theory. Finally, we recover the human pose by Powell algorithm.

NUMERICAL APPROACH TO DETERMINING INSTANTANEOUS CONTACT REGION FOR CONJUGATE SURFACES

According to the defect of traditional method of determining instantaneous contact regions for conjugate surfaces, a numerical approach to the determination is proposed. A local coordinate system is built by using the surface unit tangent and unit normal at the contact point. Considering that the gap forming the boundary of instantaneous contact region in the direction of the common normal vectors is given, a system of nonlinear equations is built to fred the instantaneous contact boundary in local coordinate system, a modified Powell's hybrid algorithm of finite-difference approximation to the Jacobian used to solve the system. The new method simplifies the task of determining instantaneous contact regions without calculating curvature and relative curvature. The validity of the proposed approach is verified by an example of hypoid gears.

New Tabu Search based global optimization methods outline of algorithms and study of efficiency

The study presents two new nonlinear global optimization routines; the Gradient Only Tabu Search (GOTS) and the Tabu Search with Powell's Algorithm (TSPA). They are based on the Tabu-Search strategy, which tries to determine the global minimum of a function by the steepest descent-mildest ascent strategy. The new algorithms are explained and their efficiency is compared with other approaches by determining the global minima of various well-known test functions with varying dimensionality. These tests show that for most tests the GOTS possesses a much faster convergence than global optimizer taken from the literature. The efficiency of the TSPA compares to the efficiency of genetic algorithms.

A Non-derivative MFCC Optimization Study of Cyclohexapeptide Monohydrate

The MFCC-downhill simplex method is presented to study the binding structure of small ligands in large molecular complex systems. This method employs the Molecular Fractionation with Conjugated Caps (MFCC) approach to compute the interaction energy-structure relation of the system and implements the downhill simplex algorithm for structural optimization. The method is tested on a molecular system of cyclo-AAGAGGH2O to optimize the binding position of water molecule to the fixed cyclohexapeptide. The MFCC-downhill simplex optimization results are in good agreement with the crystal structure. An MFCC-Powell optimization method which uses the Powell's minimization algorithm is also described and tested on the same system. The MFCC-downhill simplex optimization is more efficient than the MFCC-Powell method.

Accuracy of Two-Dipole Source Localization Using a Method Combining BP Neural Network with NLS Method from 32-Channel EEGs

The electroencephalogram (EEG) has become a widely used tool for investigating brain function. Brain signal source localization is a process of inverse calculation from sensor information (electric potentials for EEG) to the identification of multiple brain sources to obtain the locations and orientation parameters. In this paper, we describe a combination of the backpropagation neural network (BPNN) with the nonlinear least-square (NLS) method to localize two dipoles with reasonable accuracy and speed from EEG data computerized by two dipoles randomly positioned in the brain. The trained BPNN, obtains the initial values for the two dipoles through fast calculation and also avoids the influence of noise. Then the NLS method (Powell algorithm) is used to accurately estimate the two dipole parameters. In this study, we also obtain the minimum distance between the assumed dipole pair, 0.8 cm, in order to localize two sources from a smaller limited distance between the dipole pair. The present simulation results demonstrate that the combined method can allow us to localize two dipoles with high speed and accuracy, that is, in 20 seconds and with the position error of around 6.5%, and to reduce the influence of noise.

A boundary element method for calculating the shape and velocity of two-dimensional long bubble in stagnant and flowing liquid

A numerical method based on a boundary element method (BEM) has been developed for computing the velocity and the shape of long bubbles moving steadily in stagnant and flowing liquid in 2D case: plane and axisymmetrical. The flow is assumed to be inviscid and incompressible. The method consists in solving simultaneously a Poisson equation characterizing the flow and an equation for bubble shape in the form of a functional-differential equation resulting from both Bernoulli equation and the jump conditions at the interface. The Poisson equation is solved by a BEM with an iterative loop for nonlinear source term while the system of nonlinear algebraic equations obtained by discretizing the equation on the interface is solved by the Powell's hybrid algorithm. The bubble shape and velocity are obtained as a part of the solution. The problem of multiple solutions is investigated numerically and the maximum velocity criterion is used for selecting the physical solution. The results obtained by the simulation are in good agreement with the experimental and numerical results of previous studies.

Rapid determination of dry layer mass transfer resistance for various pharmaceutical formulations during primary drying using product temperature profiles

Mass transfer resistance of the dry layer during the primary drying phase of a lyophilizaton cycle is probably the most important factor affecting maximum product temperature and drying time. Product resistance parameters should be determined for each formulation because of their dependence of formulation composition and concentration. The purpose of this study was to determine the dry layer mass transfer resistance, using a simple and rapid method, for various pharmaceutical formulations during primary drying in a laboratory dryer, using monitored product temperature profiles. The mathematical tools used for the determination were a primary drying simulation program in conjunction with Powell's optimization algorithm. For each formulation studied, primary drying was performed using a shelf temperature of −15 or −20 °C and the chamber pressure controlled at 100 mTorr (0.1 Torr). The product temperature profiles ( T b) during primary drying were recorded and became the input data for the parameter estimation. The normalized product resistance, R pN, as a function of the dry layer thickness, ℓ , can be described by: R pN = R 0 + A 1 ℓ / ( 1 + A 2 ℓ ) , where the constants R 0, A 1 and A 2 are product resistance parameters of water vapor through the dry layer. Even when the parameter A 1 was negative, indicating that product temperature atypically decreased over time, the dry layer product resistance parameters of the various pharmaceutical formulations could be rapidly and successfully determined using the proposed approach. The product resistance equation obtained in this work for 5% marmitol, expressed as R pN = 0.0002025 + 20.23 ℓ , is similar to that obtained by Pikal [Pikal, M.J., 1985. Use of laboratory data in freeze drying process design: heat and product resistance parameters and the compute simulation of freeze drying. J. Parent. Sci. Technol. 39, 115–138.] using the microbalance method, expressed as R pN = 1.40 + 16.0 ℓ . The product resistance values obtained for the 3% lactose–LDH formulation are also very close to those obtained by (Milton, N., Pikal, M.J., Roy, M.L., Nail, S.L., 1997. Evaluation of manometric temperature measurement as a method of monitoring product temperature during lyophilization. PDA J. Pharm. Sci. Technol. 51, 7–16.) for 5% lactose using the MTM (manometric temperature measurement) method. With the obtained values of the parameters R 0, A 1, and A 2, simulations can be performed to determine the maximum product temperature and the drying time during primary drying. As such, optimum cycle parameters can be determined to avoid collapse of the product. The proposed approach requires only accurately measured product temperature profiles, easily obtained in a laboratory dryer.

Simultaneous surface registration of ictal and interictal SPECT and magnetic resonance images for epilepsy studies

Subtraction of ictal and interictal single photon emission computed tomography (SPECT) images is known to be successful in localizing the seizure focus in the pre-surgical evaluation of patients with partial epilepsy. A computer-aided methods for producing subtraction ictal SPECT co-registered to the magnetic resonance image (MRI) (the SISCOM method) is commonly used. The two registrations involved in SISCOM are (1) between the ictal-interictal SPECT images, which was shown to be the more critical, and (2) between the ictal image and MRI. To improve the accuracy of ictal-interictal registration in SISCOM by registering all three images (ictal, interictal SPECT, MRI) simultaneously. The registration problem is formulated as the minimization of a cost function between three surfaces. Then, to achieve a global minimum of this cost function, the Powell algorithm with randomly distributed initial configurations is used. This technique is tested by a realistic simulation study, a phantom study and a patient study. The results of the simulation study demonstrate that, in surface-based registration, the triple-registration method results in a smaller ictal-interictal SPECT registration error than the pair-wise registration method (P<0.05) for a range of values of the cost-function parameter. However, the improved registration error is still larger than that obtained by the normalized mutual information method (P<0.001), which is a voxel-based registration algorithm. The phantom and patient studies reveal no observable difference between registration results. Although the improved accuracy of triple registration is slightly worse than voxel-based registration, it will soon be possible to apply the results of this study in research utilizing the triple-registration principle to improving voxel-based results of ictal-interictal registration.

Spacecraft optimal rendezvous controller design using simulated annealing

A new global approach for rendezvous Linear Quadratic controller design is presented in this paper. Instead of solving the algebraic Riccati equation, a continuous simulated annealing (SA) algorithm is used to design rendezvous LQ controller. Optimization of one automatic rendezvous controller with 18 design parameters is illustrated. The results show that the SA algorithm can locate the global solution effectively and robust, besides a great number of global solutions have been obtained by the SA. The SA has demonstrated better performance than other optimization algorithms such as floating-coded Genetic Algorithm, Simplex method and Powell algorithm.

On the estimation of the number of dipole sources in EEG source localization

Objective The purpose of the present study was to determine the number of the equivalent dipole sources corresponding to the scalp EEG using the information criterion method based on the instantaneous-state modeling. Methods A three-concentric-spheres head model was used to represent the head volume conductor. The Powell algorithm was used to solve the inverse problem of estimating the equivalent dipoles from the scalp EEG. The information criterion with different penalty functions was used to determine the dipole number. Computer simulations were conducted to evaluate effects of various parameters on the estimation of dipole number. Results The present results suggest that the present method is able to estimate the number of equivalent current dipoles (ECDs) from instantaneous scalp EEG measurements, and that increase in the electrode number can improve the accuracy of estimation of the ECD number. For two ECDs, the best performance of estimation with 20% white noise were 85%, 92% and 94%, when 64, 128 and 256 electrodes are used, respectively. When there are 3 ECDs, the present results suggest that using 256 electrodes gave up to 82% estimation accuracy. The present simulation results also indicate that the accuracies of identification are similar when the minimum distance between dipoles is either 1 or 2 cm, which was used in the simulation. It was also found that the different penalty functions used in the information criterion method could have substantial influence on the estimation accuracy. Conclusions The present method can estimate the number of ECDs from instantaneous scalp EEG distribution for up to three dipoles. Significance The successful estimation of the number of ECDs will play an important role in expanding the applicability of dipole source localization to multiple sources.

Application of the Powell method to the optimization of flow injection systems

This paper describes the application of the Powell algorithm to the optimization of a flow injection system configuration. The performance of this algorithm has been compared with the modified simplex method. The system studied is the determination of ammonia, based on the indophenol blue reaction. A linear combination of sensitivity and sample throughput is used as the objective function because of its simultaneous optimization capability. Results obtained show that the proposed method may reach the optimal conditions with a lower number of experimental evaluations.

CONDOR, a new parallel, constrained extension of Powell's UOBYQA algorithm: Experimental results and comparison with the DFO algorithm

This paper presents an algorithmic extension of Powell's UOBYQA algorithm ( Unconstrained Optimization BY Quadratical Approximation). We start by summarizing the original algorithm of Powell and by presenting it in a more comprehensible form. Thereafter, we report comparative numerical results between UOBYQA, DFO and a parallel, constrained extension of UOBYQA that will be called in the paper CONDOR ( COnstrained, Non-linear, Direct, parallel Optimization using trust Region method for high-computing load function). The experimental results are very encouraging and validate the approach. They open wide possibilities in the field of noisy and high-computing-load objective functions optimization (from 2 min to several days) like, for instance, industrial shape optimization based on computation fluid dynamic codes or partial differential equations solvers. Finally, we present a new, easily comprehensible and fully stand-alone implementation in C++ of the parallel algorithm.

Broadband Multi-Way Microstrip Power Dividers

This paper treats multi-way microstrip power dividers composed of multi-step, multi-furcation, and comers. Since the design procedure is founded on the planar circuit approach in combination with the segmentation method, optimization of the circuit configuration can be performed in a reasonable short computation time when applying the Powell's optimization algorithm. Actually, broadband 3- and 4-way power dividers with mitered bends are designed, and fractional bandwidths of about 90% and 100% are realized for the power-split imbalance less than 0.2 dB and the return loss better than -20 dB, respectively. The validity of the design results is confirmed by an EM-simulator (HFSS) and experiments.

유출성분을 고려한 Tank 모형의 매개변수 자동추정

Tank 모형의 매개변수를 추정하는데 있어 유출성분을 고려하여 모의할 수 있는 방법을 제안하였다. 제안된 방법은 관측수문곡선을 Digital filter 방법을 사용하여 유출성분별로 분리하고 각 유출성분을 고려하여 Powell 방법으로 매개변수를 추정하는 것이다. 본 연구에서는 한강유역의 4개 댐지점을 선정하여 유출성분을 고려한 경우와 그렇지 않은 경우를 구분하여 모의유량을 관측유량과 비교 검토하였다. 그 결과 자동추적법으로만 매개변수를 추정할 때에는 전체적인 유출량은 모의하지만 성분별 유출량은 모의하지 못하는 것으로 나타났다. 따라서 본 연구에서 제시한 유출성분을 고려하는 방법이 더 객관적이고 정확한 매개변수를 추정하는 방법으로 판단되었으며, 자동추적법을 사용하여 매개변수를 추정할 때는 유출성분을 고려하여 매개변수를 추정하는 것이 보다 타당할 것이다. The objective of this study is to propose an automatic parameter estimation scheme considering runoff components of Tank model. It estimates model parameters by Powell's automatic algorithm based on the runoff component separation of the observed hydrograph by using digital filter method. The selected study areas are the 4 main dam sites on the Han River. The simulated flows are compared with the observed flows depending on whether runoff component consideration or not. As a result, the estimated model parameters from classical Powell's method only can relatively well simulate the time variation of total runoff, but gives poor runoff component simulations. Therefore, it can be concluded that the proposed automatic parameter estimation scheme in this study Is more reliable and objective.

Characterization of pinhole SPECT acquisition geometry.

A method is presented to estimate the acquisition geometry of a pinhole single photon emission computed tomography (SPECT) camera with a circular detector orbit. This information is needed for the reconstruction of tomographic images. The calibration uses the point source projection locations of a tomographic acquisition of three point sources located at known distances from each other. It is shown that this simple phantom provides the necessary and sufficient information for the proposed calibration method. The knowledge of two of the distances between the point sources proves to be essential. The geometry is estimated by fitting analytically calculated projections to the measured ones, using a simple least squares Powell algorithm. Some mild a priori knowledge is used to constrain the solutions of the fit. Several of the geometrical parameters are however highly correlated. The effect of these correlations on the reconstructed images is evaluated in simulation studies and related to the estimation accuracy. The highly correlated detector tilt and electrical shift are shown to be the critical parameters for accurate image reconstruction. The performance of the algorithm is finally demonstrated by phantom measurements. The method is based on a single SPECT scan of a simple calibration phantom, executed immediately after the actual SPECT acquisition. The method is also applicable to cone-beam SPECT and X-ray CT.

Machining with tool–chip contact on the tool secondary rake face—Part I: a new slip-line model

Given the growing number of applications of groove-type chip breaker tools in modern machining, it is becoming increasingly important to study the tool–chip contact on the tool secondary rake face. This type of tool–chip contact significantly changes not only the state of stresses in the plastic deformation region, but also changes the distribution of forces and temperatures over the tool rake face. A new slip-line model accounting for the tool–chip contact on the tool secondary rake face is proposed in this paper. The model also takes into account chip curl and incorporates seven slip-line models developed for machining during the last six decades as special cases. Dewhurst and Collins's matrix technique for numerically solving slip-line problems and Powell's algorithm of nonlinear optimization are employed in the mathematical formulation of the model. The inputs of the model include (a) the tool primary rake angle γ 1, (b) the tool secondary rake angle γ 2, (c) the tool land length h, (d) the undeformed chip thickness t 1, (e) the ratio of hydrostatic pressure P A to the material shear flow stress k, (f) the ratio of frictional shear stress τ 1 on the tool primary rake face to the material shear flow stress k, and (g) the ratio of frictional shear stress τ 2 on the tool secondary rake face to the material shear flow stress k. The outputs of the model include (a) the cutting force F c/ kt 1 w and the thrust force F t/ kt 1 w, (b) the chip up-curl radius R u, (c) the chip thickness t 2, and (d) the natural tool–chip contact length l n.

A fuzzy logic based approach for parametric optimization of MOS operational amplifiers

In this work, we have used the concept of fuzzy logic to build a CAD tool for the parametric optimization of MOS operational amplifiers (op-amps). In order to capture human intentions to express the requirements for a particular application, e.g. minimize power, maximize gain, etc., each of the performance specifications of a given topology is assigned a membership function to measure the degree of fulfillment of the objectives and the constraints. A number of objectives are optimized simultaneously by assigning weights to each of them representing their relative importance, and then by clustering them to form the objective function, which is solved by Powell's direct search algorithm. After optimization, the program creates a SPICE netlist of the circuit topology for the verification of the design. Initially, this approach was used for parametric optimization of simple bipolar and MOS circuits, e.g. current mirrors, gain stages, differential amplifiers, etc. Encouraged by these results, it was applied to much more complex blocks, such as op-amps. The design results obtained from our optimization program showed an excellent agreement with those obtained from SPICE simulation for the op-amp topologies considered in this work.

Energetic neutral atom imaging at low altitudes from the Swedish microsatellite Astrid: Extraction of the equatorial ion distribution

Energetic neutral atom (ENA) images obtained by the imager on board the Astrid satellite in the polar cap at 1000 km during a moderate magnetic storm (Dst ≥ −80 nT) on February 8, 1995, are simulated using a parameterized model of the equatorial ion distribution and a six‐component Chamberlain exosphere with parameters from the Mass Spectrometer Incoherent Scatter Extended (MSISE‐90) model. By changing the ion parameters until a matching ENA image is obtained, one can extract the equatorial ion distribution. Four consecutive images from different view points several minutes apart are simulated assuming H+ and O+, respectively, as parent ions. The optimal set of parameters is extracted by minimizing the χ2 difference between simulated and observed ENA images using Powell's minimization algorithm. The optimal equatorial model ion distribution consists of O+ peaked around dusk. The lower intensity of fluxes obtained from vantage points closer to the pole is an effect of the loss cone of the parent ion distribution being empty.

An inverse dynamics approach to face animation.

Muscle-based models of the human face produce high quality animation but rely on recorded muscle activity signals or synthetic muscle signals that are often derived by trial and error. This paper presents a dynamic inversion of a muscle-based model (Lucero and Munhall, 1999) that permits the animation to be created from kinematic recordings of facial movements. Using a nonlinear optimizer (Powell's algorithm), the inversion produces a muscle activity set for seven muscles in the lower face that minimize the root mean square error between kinematic data recorded with OPTOTRAK and the corresponding nodes of the modeled facial mesh. This inverted muscle activity is then used to animate the facial model. In three tests of the inversion, strong correlations were observed for kinematics produced from synthetic muscle activity, for OPTOTRAK kinematics recorded from a talker for whom the facial model is morphologically adapted and finally for another talker with the model morphology adapted to a different individual. The correspondence between the animation kinematics and the three-dimensional OPTOTRAK data are very good and the animation is of high quality. Because the kinematic to electromyography (EMG) inversion is ill posed, there is no relation between the actual EMG and the inverted EMG. The overall redundancy of the motor system means that many different EMG patterns can produce the same kinematic output.

A comparative study of Powell's and Downhill Simplex algorithms for a fast multimodal surface matching in brain imaging

Multimodal images registration can be very helpful for diagnostic applications. However, even if a lot of registration algorithms exist, only a few really work in clinical routines. We developed a method based on surface matching and compared two minimization algorithms: Powell's and Downhill Simplex. We studied the influence of some factors (chamfer map computation, number and order of parameters to determine, minimization criteria) on the final accuracy of the algorithm. Using this comparison, we improved some processing steps to allow a clinical use, and selected the simplex algorithm which presented the best results.