Iterative Nonlinear Optimization Research Articles

Performance Evaluation of a Simple Strategy to Optimize Formula Constants for Zero Mean or Minimal Standard Deviation or Root-Mean-Squared Prediction Error in Intraocular Lens Power Calculation

PurposeTo investigate the performance of a simple prediction scheme for the formula constants optimized for a mean (MPE), standard deviation (SDPE) or root-mean-squared refractive prediction error (RMSPE). DesignRetrospective cross-sectional study. MethodsUsing IOLMaster 700 biometric data from 888 eyes treated with the Hoya Vivinex lens and 821 eyes treated with the Alcon SA60AT lens, plus the power of the implanted lens and postoperative spherical equivalent refraction, optimized constants for SRKT, Hoffer Q, Holladay 1, Haigis, and K6 formulae were calculated using an iterative nonlinear optimization for zero MPE and minimal SDPE and RMSPE. Start values were detuned by ±1.5 from the MPE optimized constants and formula constants generated using the simple prediction scheme were compared to the corresponding directly optimized constants. ResultsFor all 5 formulae under test and with both datasets, constants optimized using the simple scheme showed excellent agreement with those from the iterative method with either MPE or RMSPE used as the optimization metric, and good agreement with SDPE as the metric. Constants optimized for zero MPE or minimal RMSPE agreed within 0.05, whereas constants for minimal SDPE could be systematically off by up to 0.6 from the MPE values, making SDPE unsuitable as an optimization metric. ConclusionsThis simple formula constant optimization scheme performs excellently for 4 disclosed formulae and one nondisclosed formula in our 2 monocentric datasets with zero MPE or minimal RMSPE as metrics. Multicentric studies with other study populations and biometers are required to further investigate the clinical applicability.

Online Calibration Based on Laser-Encoder Odometry

This paper proposes a new online calibration method for the differential-drive mobile robot equipped with a laser scanner. Our algorithm can jointly estimate the 3-DoF extrinsic parameters of the laser scanner and the intrinsic parameters (radii and wheel spacing) of the differential-drive kinematic model. Applying the pre-integration theory initially developed the for IMU sensor to the differential-drive kinematic model, we adopt iterative nonlinear optimization to minimize the cost derived from laser and encoder measurements. Experiments results confirm that the proposed method can do online calibration precisely.

Improved subspace modal identification of industrial robots

AbstractIndustrial robots have become key components for manufacturing automations due to their larger workspaces and flexibility. However, low stiffness and high compliance of industrial robots may inevitably lead to vibration by self‐excitation or periodic force dependent on workspace configuration. Therefore, the knowledge of the robot's modal properties should be accurately required to enhance the operation accuracy of industrial robots. To improve the identification accuracy of experimental modal parameters of field industrial robots, an improved subspace identification method is proposed to perform nonlinear iterative optimization for updating the state parameters of industrial robots. Experimental response measurement of a six‐degrees‐of‐freedom industrial robot is carried out to obtain modal parameters under various poses. The identification results of the improved subspace modal method are preferable to that of the traditional method. Moreover, the reconstructed three‐dimension working frequency space is presented to exactly characterize experimental modal frequencies throughout its workspace. The proposed method effectively improves the identification accuracy of modal parameters when compared with the traditional algorithms and the influence of robots' pose change on modal parameters is also investigated by experimental modal measurements.

Indexing Inefficacy of Efforts to Stop Escalation of COVID Mortality

Background: COVID-19 efforts were often ineffective in controlling the spread of the pandemic. Thus, identifying ineffective controls during a pandemic is vital. Method: Utilizing publicly available data on COVID deaths in the counties of US states, we created an index to capture and interpret ineffectiveness in the efforts to reduce the spread of the pandemic in US counties. This index is based on the Intervened Poisson Distribution (IPD) introduced originally by Shanmugam. Motivation for the research idea occurred when we noticed the data dispersion of the COVID deaths was smaller than the average only in some counties. Under-dispersed data is common in statistical modeling. A novel approach we adapted in this article includes the estimation of an intervention parameter estimated through iterative non-linear optimization. Results: Twenty-five counties in California, Idaho, Minnesota, Mississippi, Montana, Nebraska, North Carolina, North Dakota, Texas, and Utah were found to be ineffective in controlling for fatalities based on the expected probability distribution. A review of the policies enacted in these areas would provide insight into ineffective prevention efforts, and some of these issues are documented in the current literature. Conclusions: The IPD index an innovate way to document efficacy of interventions during pandemics.

Non-contrast free-breathing whole-heart 3D cine cardiovascular magnetic resonance with a novel 3D radial leaf trajectory

PurposeTo develop and validate a non-contrast free-breathing whole-heart 3D cine steady-state free precession (SSFP) sequence with a novel 3D radial leaf trajectory. MethodsWe used a respiratory navigator to trigger acquisition of 3D cine data at end-expiration to minimize respiratory motion in our 3D cine SSFP sequence. We developed a novel 3D radial leaf trajectory to reduce gradient jumps and associated eddy-current artifacts. We then reconstructed the 3D cine images with a resolution of 2.0mm3 using an iterative nonlinear optimization algorithm. Prospective validation was performed by comparing ventricular volumetric measurements from a conventional breath-hold 2D cine ventricular short-axis stack against the non-contrast free-breathing whole-heart 3D cine dataset in each patient (n = 13). ResultsAll 3D cine SSFP acquisitions were successful and mean scan time was 07:09 ± 01:31 min. End-diastolic ventricular volumes for left ventricle (LV) and right ventricle (RV) measured from the 3D datasets were smaller than those from 2D (LV: 159.99 ± 42.99 vs. 173.16 ± 47.42; RV: 180.35 ± 46.08 vs. 193.13 ± 49.38; p-value≤0.044; bias<8%), whereas ventricular end-systolic volumes were more comparable (LV: 79.12 ± 26.78 vs. 78.46 ± 25.35; RV: 97.18 ± 32.35 vs. 102.42 ± 32.53; p-value≥0.190, bias<6%). The 3D cine data had a lower subjective image quality score. ConclusionOur non-contrast free-breathing whole-heart 3D cine sequence with novel leaf trajectory was robust and yielded smaller ventricular end-diastolic volumes compared to 2D cine imaging. It has the potential to make examinations easier and more comfortable for patients.

Automated Force-Coupled Ultrasound Method for Calibration-Free Carotid Artery Blood Pressure Estimation.

We develop, automate and evaluate a calibration-free technique to estimate human carotid artery blood pressure from force-coupled ultrasound images. After acquiring images and force, we use peak detection to align the raw force signal with an optical flow signal derived from the images. A trained convolutional neural network selects a seed point within the carotid in a single image. We then employ a region-growing algorithm to segment and track the carotid in subsequent images. A finite-element deformation model is fit to the observed segmentation and force via a two-stage iterative non-linear optimization. The first-stage optimization estimates carotid artery wall stiffness parameters along with systolic and diastolic carotid pressures. The second-stage optimization takes the output parameters from the first optimization and estimates the carotid blood pressure waveform. Diastolic and systolic measurements are compared with those of an oscillometric brachial blood pressure cuff. In 20 participants, average absolute diastolic and systolic errors are 6.2 and 5.6 mm Hg, respectively, and correlation coefficients are r = 0.7 and r = 0.8, respectively. Force-coupled ultrasound imaging represents an automated, standalone ultrasound-based technique for carotid blood pressure estimation, which motivates its further development and expansion of its applications.

Non-metric correction method for complete lens distortion using dual-characteristics joint measurement

In practical vision systems, due to the limitation of manufacturing technology, charge-coupled device pixel cells are difficult to satisfy the standard square, and the lens inevitably has imaging nonlinearity, which leads to geometric distortion of the image. To ensure the accuracy of subsequent visual processing, it is necessary to correct the image distortion. A non-metric correction method for complete lens distortion using dual-characteristics joint measurement is proposed. We not only considered the influence of the distortion center in the correction process but also constructed a mapping matrix to standardize the pixel cells, thus establishing a complete lens distortion model. Simultaneously, the linear residual function of the dual-characteristics joint measurement was defined according to the geometric constraint between the vanishing point and the straightness. In addition, the distortion model coefficients were determined by nonlinear iterative optimization. Extensive experiment results demonstrated that the proposed method enables effective and accurate lens distortion correction, which is significantly superior to the existing single characteristic measurement distortion correction approach.

A new linear optimized time–space domain spatial implicit and temporal high-order finite-difference scheme for scalar wave modeling

Suppressing the numerical dispersion is one of the key items for the finite-difference (FD) method. Usually, approximating the spatial derivatives by the implicit FD stencil is an effective approach to suppress the spatial dispersion for acoustic wave modeling. However, the temporal accuracy is still limited. To tackle this issue, we propose a new time–space domain (TS-D) implicit FD scheme, which could reach the arbitrary even-order temporal and spatial accuracy by adding a few additional grid points to the original implicit FD stencil. Compared with the existing spatial implicit and temporal high-order methods in the TS-D, our new scheme reduces 4N + 1 grid points, while reaches equivalent temporal and spatial high-order accuracy. To further enhance the simulation accuracy, a linear optimization strategy is developed by combining the Taylor series expansion (TE) and the least-squares methods. Our linear optimization strategy avoids the non-linear iterative optimization of the current spatial implicit and temporal high-order methods. Comparisons of the conventional TE- and optimization-based implicit methods demonstrate the accuracy and efficiency superiorities of our new linear optimized FD scheme.

An Indoor Wi-Fi Localization Algorithm Using Ranging Model Constructed With Transformed RSSI and BP Neural Network

This paper focuses on improving indoor Wi-Fi localization by mitigating the effect of fluctuation of received signal strength indication (RSSI). The RSSI data collected at each reference point is first transformed through translation and scaling. The BP (Back Propagation) neural network is then used to construct the ranging model using the transformed RSSI to determine the distances between the target point and each reference point. A genetic algorithm (GA) is developed to optimize the initial values of weights and biases of the BP neural network. For convenience, our proposed ranging model is denoted as GTBPD. A new localization algorithm is then proposed, which uses the GTBPD model and the sequential quadratic programming (SQP, an iterative nonlinear optimization algorithm), and the algorithm is denoted as GTBPD-LSQP for simplicity. Experiments were conducted in three areas of two different teaching buildings with complex environments. The performance of the proposed GTBPD-LSQP algorithm is evaluated and compared with four existing algorithms. The experimental results show that our proposed GTBPD-LSQP algorithm achieves significantly higher location accuracy than the four existing algorithms.

Prediction of entire tablet formulations from pure powder components’ spectra via a two-step non-linear optimization methodology

Process analytical technology in the pharmaceutical industry requires the monitoring of critical quality attributes (CQA) through calibrated models. However, the development, implementation, and maintenance of these quantitative models are both resource and time-intensive. This study proposes the implementation of a non-linear iterative optimization technology (IOT) to study the magnitude of analytical errors when the calibration tablet used to extract the λ vector deviates physically and chemically from the test samples. IOT is based on mathematical optimization of excess spectral absorbance. It requires minimum calibration effort and allows simultaneous prediction of the entire formulation instead of only the active pharmaceutical ingredient (API), with just one standard and pure component spectral data. Unlike Partial Least Squares (PLS), which requires the development of standards to incorporate variations in the process, this non-destructive methodology minimizes significant calibration effort by developing a mathematical model that uses only one standard and spectral information of pure powders present in the tablet. The method described in this study allows a fast re-calculation to include factors such as change of spectroscopic instruments, variations in raw materials, environmental conditions, and methods of tablet preparation. The robustness of the proposed approach for variation in compaction (physical changes) and variation in composition (chemical changes) was evaluated for correlated and uncorrelated formulations. For uncorrelated formulation a PLS model was also constructed to compare the robustness of the proposed methodology. The RMSEP of API in target formulation predicted using non-linear IOT method was varied from 0.17 to 1.50 depends on compaction of tablet chosen to compute λ vector. On the other hand, the RMSEP of API in target formulation predicted using PLS-based model was varied from 0.13 to 0.57 depending on compaction of tablet. The additional accuracy achieved in PLS based model required significant calibration effort of preparing 84 tablets compared to just one in proposed non-linear IOT method.

High-resolution pediatric age\u2013specific 18F-FDG PET template: a pilot study in epileptogenic focus localization

BackgroundPET imaging has been widely used in diagnosis of neurological disorders; however, its application to pediatric population is limited due to lacking pediatric age–specific PET template. This study aims to develop a pediatric age–specific PET template (PAPT) and conduct a pilot study of epileptogenic focus localization in pediatric epilepsy.MethodsWe recruited 130 pediatric patients with epilepsy and 102 age-matched controls who underwent 18F-FDG PET examination. High-resolution PAPT was developed by an iterative nonlinear registration-averaging optimization approach for two age ranges: 6–10 years (n = 17) and 11–18 years (n = 50), respectively. Spatial normalization to the PAPT was evaluated by registration similarities of 35 validation controls, followed by estimation of potential registration biases. In a pilot study, epileptogenic focus was localized by PAPT-based voxel-wise statistical analysis, compared with multi-disciplinary team (MDT) diagnosis, and validated by follow-up of patients who underwent epilepsy surgery. Furthermore, epileptogenic focus localization results were compared among three templates (PAPT, conventional adult template, and a previously reported pediatric linear template).ResultsSpatial normalization to the PAPT significantly improved registration similarities (P < 0.001), and nearly eliminated regions of potential biases (< 2% of whole brain volume). The PAPT-based epileptogenic focus localization achieved a substantial agreement with MDT diagnosis (Kappa = 0.757), significantly outperforming localization based on the adult template (Kappa = 0.496) and linear template (Kappa = 0.569) (P < 0.05). The PAPT-based localization achieved the highest detection rate (89.2%) and accuracy (80.0%). In postsurgical seizure-free patients (n = 40), the PAPT-based localization also achieved a substantial agreement with resection areas (Kappa = 0.743), and the highest detection rate (95%) and accuracy (80.0%).ConclusionThe PAPT can significantly improve spatial normalization and epileptogenic focus localization in pediatric epilepsy. Future pediatric neuroimaging studies can also benefit from the unbiased spatial normalization by PAPT.Trial registration.NCT04725162: https://clinicaltrials.gov/ct2/show/NCT04725162

Parallel Dislocation Model Implementation for Earthquake Source Parameter Estimation on Multi-Threaded GPU

Graphics processing units (GPUs) have been in the spotlight in various fields because they can process a massive amount of computation at a relatively low price. This research proposes a performance acceleration framework applied to Monte Carlo method-based earthquake source parameter estimation using multi-threaded compute unified device architecture (CUDA) GPU. The Monte Carlo method takes an exhaustive computational burden because iterative nonlinear optimization is performed more than 1000 times. To alleviate this problem, we parallelize the rectangular dislocation model, i.e., the Okada model, since the model consists of independent point-wise computations and takes up most of the time in the nonlinear optimization. Adjusting the degree of common subexpression elimination, thread block size, and constant caching, we obtained the best CUDA optimization configuration that achieves 134.94×, 14.00×, and 2.99× speedups over sequential CPU, 16-threads CPU, and baseline CUDA GPU implementation from the 1000×1000 mesh size, respectively. Then, we evaluated the performance and correctness of four different line search algorithms for the limited memory Broyden–Fletcher–Goldfarb–Shanno with boundaries (L-BFGS-B) optimization in the real earthquake dataset. The results demonstrated Armijo line search to be the most efficient one among the algorithms. The visualization results with the best-fit parameters finally derived by the proposed framework confirm that our framework also approximates the earthquake source parameters with an excellent agreement with the geodetic data, i.e., at most 0.5 cm root-mean-square-error (RMSE) of residual displacement.

Rayleigh Wave Dispersion Curve Inversion with the Artificial Bee Colony Algorithm

Rayleigh wave dispersion curve inversion is a non-linear iterative optimization process with multi-parameter and multi-extrema. It is difficult to carry out inversion and reconstruction of stratigraphic parameters quickly and accurately with a single linear or non-linear inversion for the data processing of Rayleigh waves with complex seismic geological conditions. We proposed a new method that combines artificial bee colony algorithm (ABC) and damped least squares algorithm (DLS) to invert Rayleigh wave dispersion curve. First, food sources are initialized in a large scale of the model based on the prior geological information. Then, after three kinds of bee operators (employed bees, onlooker bees and scout bees) transform each other and perform search optimization with several iterations, the targets are converged near the optimal solution to obtain an initial S-wave velocity model. Finally, the final S-wave velocity model is obtained by local optimization of DLS inversion with fast convergence and strong stability. The correctness of the method has been verified by one high-velocity interlayer model, and it was further applied to a real Rayleigh wave dataset. The results show that our method not only absorbs the advantages of ABC global search optimization and strong adaptability, but also makes full use of the advantages of DLS inversion, such as high accuracy and fast convergence speed. The inversion strategy can effectively suppress the inversion falling into local extrema, get rid of the dependence on an initial model, enhance the inversion stability, further improve the convergence speed and inversion accuracy, while has good anti-noise ability.

Weight and bias initialization routines for Sigmoidal Feedforward Network

The success of the Sigmoidal Feedforward Networks in the solution of complex learning task can be attributed to their Universal Approximation Property. These networks are trained using non-linear iterative optimization method (of first-order or second-order) to solve a learning task. The convergence rate in Sigmoidal Feedforward Network training is affected by the initial choice of weights, therefore, in this paper, we propose two new weight initialization routines (Routine-1 and Routine-2) using characteristics of input and output data and property of activation function. Routine-1 uses the linear dependency of weight update step size on derivative of activation function and thus, initialize weights and bias to activate the activation function region near zero (input), where the derivative is maximum, therefore, increasing the weight update step size, and hence, the convergence speed. The same principle is used to derive Routine-2, that initialize weights and bias to activate distinct point in the significant range of activation function (where significant range defines the non-saturated region in activation function), such that, each node evolves independently of each other, and act as distinct feature identifier. Initializing weights in significant range reduces chances of (hidden) nodes getting stuck in saturated state. The networks initialized using proposed routines has higher convergence and higher probability to achieve deeper minima. The efficiency of proposed routines is evaluated by comparing them to conventional random weight initialization routine and 11 weight initialization routines proposed in literature (4 well established routines and 7 recently proposed routines) for several benchmark problems. The proposed routine is also tested for larger networks sizes and larger datasets such as MNIST. The results show that the performance of proposed routines is better than conventional random weight initialization routine and 11 established weight initialization routines.

Application of Forward-Scan Sonar Stereo for 3-D Scene Reconstruction

New generation of underwater 2-D forward-look sonar video cameras operating at near and over 1-MHz frequency offer images with enhanced target details. Within their limited range of only tens of meters, they are the most suitable imaging systems for conducting visually guided missions in turbid waters. These include, but are not limited to inspecting underwater structures for routine maintenance, search, and surveillance, the detection, localization, and identification of small sought after objects, as well as target-based positioning and navigation. To this end, the automatic 3-D reconstruction of 3-D target shape and establishing the 3-D spatial location of interest points are highly desired capabilities in many such operations. As achieved with 2-D optical images, multiple images from nearby positions may be utilized. This paper investigates the estimation of 3-D point locations from two overlapping images collected with two forward-scan (FS) sonar systems in stereo configuration, or with one FS sonar at known relative poses, established from visual motion cues. The first contribution includes the analysis of a sonar stereo epipolar geometry. Beyond reducing the correspondence problem to a 1-D search along epipolar curves, this reveals unique properties associated with sonar measurements of range and azimuth angle. Next, certain linear closed-form reconstruction solutions are presented, their degeneracies are established, and adjustments under degenerate conditions are proposed. Two preferred method for the degenerate and nondegenerate stereo configurations are identified: a regularization-based method and one employing a range constraint approximation, respectively. These primarily provide the initial estimate for an iterative nonlinear optimization scheme based on gradient descent. Finally, the results of experiments with synthetic data are presented to assess various estimation methods, and with real data sets to demonstrate performance under two subsea operational scenarios.

Extended Lagrangian Born-Oppenheimer molecular dynamics using a Krylov subspace approximation.

It is shown how the electronic equations of motion in extended Lagrangian Born-Oppenheimer molecular dynamics simulations [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008); J. Chem. Phys. 147, 054103 (2017)] can be integrated using low-rank approximations of the inverse Jacobian kernel. This kernel determines the metric tensor in the harmonic oscillator extension of the Lagrangian that drives the evolution of the electronic degrees of freedom. The proposed kernel approximation is derived from a pseudoinverse of a low-rank estimate of the Jacobian, which is expressed in terms of a generalized set of directional derivatives with directions that are given from a Krylov subspace approximation. The approach allows a tunable and adaptive approximation that can take advantage of efficient preconditioning techniques. The proposed kernel approximation for the integration of the electronic equations of motion makes it possible to apply extended Lagrangian first-principles molecular dynamics simulations to a broader range of problems, including reactive chemical systems with numerically sensitive and unsteady charge solutions. This can be achieved without requiring exact full calculations of the inverse Jacobian kernel in each time step or relying on iterative non-linear self-consistent field optimization of the electronic ground state prior to the force evaluations as in regular direct Born-Oppenheimer molecular dynamics. The low-rank approximation of the Jacobian is directly related to Broyden's class of quasi-Newton algorithms and Jacobian-free Newton-Krylov methods and provides a complementary formulation for the solution of nonlinear systems of equations.

Head Motion Correction Based on Filtered Backprojection in Helical CT Scanning.

Head motion may unexpectedly occur during a CT scan. It thereby results in motion artifacts in a reconstructed image and may lead to a false diagnosis or a failure of diagnosis. To alleviate this motion problem, as a hardware approach, increasing the gantry rotation speed or using an immobilization device is usually considered. These approaches, however, cannot completely resolve the motion problem. Hence, motion estimation (ME) and compensation for it have been explored as a software approach instead. In this paper, adopting the latter approach, we propose a head motion correction algorithm in helical CT scanning, based on filtered backprojection (FBP). For the motion correction, we first introduce a new motion-compensated (MC) reconstruction scheme based on FBP, which is applicable to helical scanning. We then estimate the head motion parameters by using an iterative nonlinear optimization algorithm, or the L-BFGS. Note here that an objective function for the optimization is defined on reconstructed images in each iteration, which are obtained by using the proposed MC reconstruction scheme. Using the estimated motion parameters, we then obtain the final MC reconstructed image. Using numerical and physical phantom datasets along with simulated head motions, we demonstrate that the proposed algorithm can provide significantly improved quality to MC reconstructed images by alleviating motion artifacts.

Fast approximate clearance evaluation for rovers with articulated suspension systems

AbstractWe present a light‐weight body‐terrain clearance evaluation algorithm for the automated path planning of NASA's Mars 2020 rover. Extraterrestrial path planning is challenging due to the combination of terrain roughness and severe limitation in computational resources. Path planning on cluttered and/or uneven terrains requires repeated safety checks on all the candidate paths at a small interval. Predicting the future rover state requires simulating the vehicle settling on the terrain, which involves an inverse‐kinematics problem with iterative nonlinear optimization under geometric constraints. However, such expensive computation is intractable for slow spacecraft computers, such as RAD750, which is used by the Curiosity Mars rover and upcoming Mars 2020 rover. We propose the approximate clearance evaluation (ACE) algorithm, which obtains conservative bounds on vehicle clearance, attitude, and suspension angles without iterative computation. It obtains those bounds by estimating the lowest and highest heights that each wheel may reach given the underlying terrain, and calculating the worst‐case vehicle configuration associated with those extreme wheel heights. The bounds are guaranteed to be conservative, hence ensuring vehicle safety during autonomous navigation. ACE is planned to be used as part of the new onboard path planner of the Mars 2020 rover. This paper describes the algorithm in detail and validates our claim of conservatism and fast computation through experiments.

Pose-graph SLAM sparsification using factor descent

Since state of the art simultaneous localization and mapping (SLAM) algorithms are not constant time, it is often necessary to reduce the problem size while keeping as much of the original graph’s information content. In graph SLAM, the problem is reduced by removing nodes and rearranging factors. This is normally faced locally: after selecting a node to be removed, its Markov blanket sub-graph is isolated, the node is marginalized and its dense result is sparsified. The aim of sparsification is to compute an approximation of the dense and non-relinearizable result of node marginalization with a new set of factors. Sparsification consists on two processes: building the topology of new factors, and finding the optimal parameters that best approximate the original dense distribution. This best approximation can be obtained through minimization of the Kullback–Liebler divergence between the two distributions. Using simple topologies such as Chow–Liu trees, there is a closed form for the optimal solution. However, a tree is oftentimes too sparse and produces bad distribution approximations. On the contrary, more populated topologies require nonlinear iterative optimization. In the present paper, the particularities of pose-graph SLAM are exploited for designing new informative topologies and for applying the novel factor descent iterative optimization method for sparsification. Several experiments are provided comparing the proposed topology methods and factor descent optimization with state-of-the-art methods in synthetic and real datasets with regards to approximation accuracy and computational cost.

Robust Task-Oriented Markerless Extrinsic Calibration for Robotic Pick-and-Place Scenarios

Camera extrinsic calibration is an important module for robotic visual tasks. A typical visual task is to use a robot and a color camera to pick an object from a variety of items and place it in a designated area. However, the noise of multi-sensor processing may have a significant impact on the results when running a full-process visual task; in addition, checkerboards are inconvenient or unavailable in pick-and-place scenarios. In this paper, we propose and develop a task-oriented markerless hand-eye calibration method by using nonlinear iterative optimization. The optimization employs a transfer error to construct cost function, which is necessarily observable and estimable for visual tasks. Our method does not require a calibration checkerboard and only uses an available saliency object in the task scene as a marker. It provides an end-to-end method that converts extrinsic parameters into variables that are optimized with the cost function, making it not only robust to sensors with noise but also able to meet the requirements of the tasks' reconstruction accuracy. Different from classic methods detecting a known size calibration pattern, the input of our method is a batch of image points and the corresponding world points. The results show that the accuracy of our extrinsic calibration method is sufficient for the robot's pick-and-place tasks. The experiments of the competition demonstrate that our method is definitely effective in the desired tasks of vision-in-the-loop automatic pick-and-place scenarios.