Iterative Refinement Scheme Research Articles

Enhancing cubic polynomial solutions: A comprehensive analysis and iterative refinement strategy in response to the versatility of cubic equations of state

The study presents a comprehensive evaluation of ten distinct methods for solving cubic equations, encompassing both analytical, numerical, and linear algebra-based approaches. Among these, an analytical technique involving the transformation of cubic equations into Chebyshev polynomials emerged as the most efficient. To mitigate issues arising from numerical round-off errors, the study proposes an iterative refinement strategy. Furthermore, the research introduces a novel criterion grounded in Vieta's formulas to identify and isolate areas where round-off errors may occur. This criterion aids in the application of the proposed iterative refinement technique. The novel solution method, which involves the conversion of cubic equations into Chebyshev polynomials and subsequent error-checking and iterative refinement, exhibits significant advantages. Firstly, it proves efficient, reducing computational time by 15–20 % in comparison to the well-established Cardano analytical method. It also demonstrates robustness in effortlessly identifying regions of potential error and offers a method for iterative improvement when needed. Additionally, its reliability is underscored by its independence from the specific cubic equation of state under consideration, making it well-suited for the intensive solution of a wide range of cubic equations.

Inferring gene regulatory networks using transcriptional profiles as dynamical attractors.

Genetic regulatory networks (GRNs) regulate the flow of genetic information from the genome to expressed messenger RNAs (mRNAs) and thus are critical to controlling the phenotypic characteristics of cells. Numerous methods exist for profiling mRNA transcript levels and identifying protein-DNA binding interactions at the genome-wide scale. These enable researchers to determine the structure and output of transcriptional regulatory networks, but uncovering the complete structure and regulatory logic of GRNs remains a challenge. The field of GRN inference aims to meet this challenge using computational modeling to derive the structure and logic of GRNs from experimental data and to encode this knowledge in Boolean networks, Bayesian networks, ordinary differential equation (ODE) models, or other modeling frameworks. However, most existing models do not incorporate dynamic transcriptional data since it has historically been less widely available in comparison to "static" transcriptional data. We report the development of an evolutionary algorithm-based ODE modeling approach (named EA) that integrates kinetic transcription data and the theory of attractor matching to infer GRN architecture and regulatory logic. Our method outperformed six leading GRN inference methods, none of which incorporate kinetic transcriptional data, in predicting regulatory connections among TFs when applied to a small-scale engineered synthetic GRN in Saccharomyces cerevisiae. Moreover, we demonstrate the potential of our method to predict unknown transcriptional profiles that would be produced upon genetic perturbation of the GRN governing a two-state cellular phenotypic switch in Candida albicans. We established an iterative refinement strategy to facilitate candidate selection for experimentation; the experimental results in turn provide validation or improvement for the model. In this way, our GRN inference approach can expedite the development of a sophisticated mathematical model that can accurately describe the structure and dynamics of the in vivo GRN.

Mixed Precision Iterative Refinement with Sparse Approximate Inverse Preconditioning

With the commercial availability of mixed precision hardware, mixed precision GMRES-based iterative refinement schemes have emerged as popular approaches for solving sparse linear systems. Existing analyses of these approaches, however, are based on using full LU factorizations to construct preconditioners for use within GMRES in each refinement step. In practical applications, inexact preconditioning techniques, such as incomplete LU or sparse approximate inverses, are often used for performance reasons. In this work, we investigate the use of sparse approximate inverse preconditioners based on Frobenius norm minimization within GMRES-based iterative refinement. We analyze the computation of sparse approximate inverses in finite precision and derive constraints under which user-specified stopping criteria will be satisfied. We then analyze the behavior of and convergence constraints for a five-precision GMRES-based iterative refinement scheme that uses sparse approximate inverse preconditioning, which we call SPAI-GMRES-IR. Our numerical experiments confirm the theoretical analysis and illustrate the resulting tradeoffs between preconditioner sparsity and GMRES-IR convergence rate.

MDSPACE: Extracting Continuous Conformational Landscapes from Cryo-EM Single Particle Datasets Using 3D-to-2D Flexible Fitting based on Molecular Dynamics Simulation

This article presents an original approach for extracting atomic-resolution landscapes of continuous conformational variability of biomolecular complexes from cryo electron microscopy (cryo-EM) single particle images. This approach is based on a new 3D-to-2D flexible fitting method, which uses molecular dynamics (MD) simulation and is embedded in an iterative conformational-landscape refinement scheme. This new approach is referred to as MDSPACE, which stands for Molecular Dynamics simulation for Single Particle Analysis of Continuous Conformational hEterogeneity. The article describes the MDSPACE approach and shows its performance using synthetic and experimental datasets.

Fast Compressed Segmentation Volumes for Scientific Visualization.

Voxel-based segmentation volumes often store a large number of labels and voxels, and the resulting amount of data can make storage, transfer, and interactive visualization difficult. We present a lossless compression technique which addresses these challenges. It processes individual small bricks of a segmentation volume and compactly encodes the labelled regions and their boundaries by an iterative refinement scheme. The result for each brick is a list of labels, and a sequence of operations to reconstruct the brick which is further compressed using rANS-entropy coding. As the relative frequencies of operations are very similar across bricks, the entropy coding can use global frequency tables for an entire data set which enables efficient and effective parallel (de)compression. Our technique achieves high throughput (up to gigabytes per second both for compression and decompression) and strong compression ratios of about 1% to 3% of the original data set size while being applicable to GPU-based rendering. We evaluate our method for various data sets from different fields and demonstrate GPU-based volume visualization with on-the-fly decompression, level-of-detail rendering (with optional on-demand streaming of detail coefficients to the GPU), and a caching strategy for decompressed bricks for further performance improvement.

DecoupledPoseNet: Cascade Decoupled Pose Learning for Unsupervised Camera Ego-Motion Estimation

Although many impressive works on learning-based camera ego-motion estimation methods have been proposed recently, most of them promote the accuracy of camera pose estimation by various sequential learning with loop closure optimization, while neglecting the improvement of PoseNet itself. In this paper, we focus on the coupling of rotation and translation in ego-motion estimation, and design a cascade decoupling structure to separately learn the rotation and translation of camera relative motion between adjacent frames. Meanwhile, a rigid-aware unsupervised learning framework with iterative pose refinement scheme is proposed for camera ego-motion estimation. It can disambiguate rigid motion and deformations in dynamic scenarios by jointly learning of optical flow, stereo disparity and camera pose. Validated with evaluation experiments on the public available datasets, our method is superior to the state-of-the-art unsupervised methods, and can achieve comparable results with the supervised ones.

6D Object Pose Tracking with Optical Flow Network for Robotic Manipulation

In this paper, we design a novel 6-DOF object pose tracking framework for robotic manipulation tasks. The framework takes a RGB-D video stream as input observations and outputs a 6D pose estimate corresponding to each frame for the interested object to be tracked. The novelty lies in the pose change estimation where we leverage a segmentation network and an optical flow network to estimate the pose change between previous and current frames. The final 6D pose estimate is the multiplication of the 6D pose matrix in previous frame and the pose change. Unlike most tracking networks, our pose tracking model does not require any object 3D model as auxiliary input. We take two consecutive frames as the input and estimate their optical flow map by using a pre-trained optical flow network. Our framework is a keypoint based estimation method. The estimated flow map can extract the temporal motion information that can be used to generate keypoint candidates. Then an iterative keypoint refinement scheme is used to validate the selected keypoints. Our experimental results show that our framework can outperform some existing works or achieve comparable results in three selected datasets.

Multistage mixed precision iterative refinement

AbstractLow precision arithmetic, in particular half precision (16‐bit) floating point arithmetic, is now available in commercial hardware. Using lower precision can offer significant savings in computation and communication costs with proportional savings in energy. Motivated by this, there has been a renewed interest in mixed precision iterative refinement schemes for solving linear systems , and new variants of GMRES‐based iterative refinement have been developed. Each particular variant with a given combination of precisions leads to different condition number‐based constraints for convergence of the backward and forward errors, and each has different performance costs. The constraints for convergence given in the literature are, as an artifact of the analyses, often overly strict in practice, and thus could lead a user to select a more expensive variant when a less expensive one would have sufficed. In this work, we develop a multistage mixed precision iterative refinement solver which aims to combine existing mixed precision approaches to balance performance and accuracy and improve usability. For a user‐specified initial combination of precisions, the algorithm begins with the least expensive approach and convergence is monitored via inexpensive computations with quantities produced during the iteration. If slow convergence or divergence is detected using particular stopping criteria, the algorithm switches to use a more expensive, but more reliable variant. A novel aspect of our approach is that, unlike existing implementations, our algorithm first attempts to use “stronger” GMRES‐based solvers for the solution update before resorting to increasing the precision(s). In some scenarios, this can avoid the need to refactorize the matrix in higher precision. We perform extensive numerical experiments on a variety of random dense problems and problems from real applications which confirm the benefits of the multistage approach.

Skin Lesion Segmentation Using Recurrent Attentional Convolutional Networks

Accurate segmentation of lesion region from skin lesion images can provide guidance for medical experts to make an early diagnosis of skin cancer. In this study, we construct Recurrent Attentional Convolutional Networks (O-Net), which exploits the skin lesion’s attention class feature with a recurrent O-shape structure, in an iterative refinement strategy for skin lesion image segmentation. Inspired by the recently proposed attention class feature network, we integrate the attention class feature module into the proposed networks. The O-Net, with recurrent unit to iteratively refine the segmentation result, is designed to extract attention feature information and enable coarse-to-fine feature representation by iteratively integrating attention feature maps into network. Furthermore, O-Net calculates the attentional class feature by extracting attention information from the coarse segmentation result. Two currently popular datasets ISIC-2017 and PH2 are employed to explore the validity of our proposed model. The study provides detailed comparisons of our proposed network, the attention class feature network and Recurrent U-Net. O-Net achieved Dice coefficient by 87.04% on the ISIC-2017 dataset, 92.12% on the PH2 dataset with corresponding Jaccard indices of 80.36% and 86.15%, respectively, on the same dataset, which exhibits competitive performance for skin lesion image segmentation in results. The visual results also shown that more detailed tissues are extracted by O-Net than other methods.

NBR-Net: A Nonrigid Bidirectional Registration Network for Multitemporal Remote Sensing Images

Remote sensing image registration is the basis of change detection, environmental monitoring, and image fusion. Under severe appearance differences, feature-based methods have difficulty in finding sufficient feature matches to solve the global transformation and tackling the local deformation caused by height undulations and building shadows. By contrast, nonrigid registration methods are more flexible than feature-based matching methods, while often ignoring the reversibility between images, resulting in misalignment and inconsistency. To this end, this article proposes a nonrigid bidirectional registration network (NBR-Net) to estimate the flow-based dense correspondence for remote sensing images. We first propose an external cyclic registration network to strengthen the registration reversibility and geometric consistency by registering Image A to Image B and then reversely registering back to Image A. Second, we design an internal iterative refinement strategy to optimize the rough predicted flow caused by large distortion and viewpoint difference. Extensive experiments demonstrate that our method shows a performance superior to the state-of-the-art models on the multitemporal satellite image dataset. Furthermore, we attempt to extend our method to heterogeneous remote sensing image registration, which is more common in the real world. Therefore, we test our pretrained model in a satellite and unmanned aerial vehicle (UAV) image registration task. Due to the cyclic registration mechanism and coarse-to-fine refinement strategy, the proposed approach obtains the best performance on two GPS-denied UAV image datasets. Our code will be released at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/xuyingxiao/</uri> NBR-Net.

Automated prediction of lattice parameters from X-ray powder diffraction patterns.

A key step in the analysis of powder X-ray diffraction (PXRD) data is the accurate determination of unit-cell lattice parameters. This step often requires significant human intervention and is a bottleneck that hinders efforts towards automated analysis. This work develops a series of one-dimensional convolutional neural networks (1D-CNNs) trained to provide lattice parameter estimates for each crystal system. A mean absolute percentage error of approximately 10% is achieved for each crystal system, which corresponds to a 100- to 1000-fold reduction in lattice parameter search space volume. The models learn from nearly one million crystal structures contained within the Inorganic Crystal Structure Database and the Cambridge Structural Database and, due to the nature of these two complimentary databases, the models generalize well across chemistries. A key component of this work is a systematic analysis of the effect of different realistic experimental non-idealities on model performance. It is found that the addition of impurity phases, baseline noise and peak broadening present the greatest challenges to learning, while zero-offset error and random intensity modulations have little effect. However, appropriate data modification schemes can be used to bolster model performance and yield reasonable predictions, even for data which simulate realistic experimental non-idealities. In order to obtain accurate results, a new approach is introduced which uses the initial machine learning estimates with existing iterative whole-pattern refinement schemes to tackle automated unit-cell solution.

3-D Human Pose Estimation Using Iterative Conditional Squeeze and Excitation Networks.

We propose a new method for single-camera real-world 3-D human pose estimation. Our method uses multitask training together with iterative pose refinement using a novel conditional attention mechanism. For iterative pose refinement, the output of each convolutional layer is conditioned on the latest pose estimate, using a conditioned squeeze-and-excitation network architecture that incorporates novel feedback connections. Multitask training on both an in-the-wild 2-D pose dataset and a controlled 3-D pose dataset allows for real-world 3-D pose estimation without the need for a large-scale in-the-wild 3-D pose dataset, which is unavailable. Experiments are performed on several real-world datasets, as well as the Human 3.6 Million and HumanEva-I datasets, to show that the combined attention mechanism, iterative refinement scheme, and multitask training allow us to achieve robust and competitive performance with only a simple network architecture. In addition, we show that our method is efficient enough to run on commodity hardware, producing pose estimates in real time.

Sentence embeddings in NLI with iterative refinement encoders

AbstractSentence-level representations are necessary for various natural language processing tasks. Recurrent neural networks have proven to be very effective in learning distributed representations and can be trained efficiently on natural language inference tasks. We build on top of one such model and propose a hierarchy of bidirectional LSTM and max pooling layers that implements an iterative refinement strategy and yields state of the art results on the SciTail dataset as well as strong results for Stanford Natural Language Inference and Multi-Genre Natural Language Inference. We can show that the sentence embeddings learned in this way can be utilized in a wide variety of transfer learning tasks, outperforming InferSent on 7 out of 10 and SkipThought on 8 out of 9 SentEval sentence embedding evaluation tasks. Furthermore, our model beats the InferSent model in 8 out of 10 recently published SentEval probing tasks designed to evaluate sentence embeddings’ ability to capture some of the important linguistic properties of sentences.

3D Dix inversion using bound-constrained total variation regularization

Given the ill-conditioned nature of Dix inversion, the resultant Dix interval-velocity field is often unrealistic, noisy, and highly dependent on the quality of the provided root-mean-square velocities. While the classic least-squares regularization techniques, e.g., various forms of Tikhonov regularization, lead to somewhat suboptimal stability, we formulated the Dix inversion as a new constrained optimization problem. This enables one to incorporate prior knowledge as soft and/or hard bounds for the optimization, effectively treating it as a denoising problem. The solution to the problem is achieved by a bound-constrained total variation (TV) regularization. TV regularization has the advantage of being able to recover the discontinuities in the model, but it often comes with a large memory and compute requirements. Therefore, we have developed a simple and memory-efficient algorithm using iterative refinement strategy. The quality of the new algorithm is also cross-examined against different strategies, which are currently used in practice. Overall, we observe that the proposed method outperforms classic Dix inversion methods on the synthetic and real data examples.

Single-shot 3D hand pose estimation using radial basis function networks trained on synthetic data

In this work, we present a novel framework to perform single-shot hand pose estimation using depth data as input. The method follows a coarse to fine strategy and employs several radial basis function networks (RBFNs) that are trained on a dataset containing only synthetically generated depth maps. Thus, compared to most contemporary deep learning approaches, it does not require the laborious annotation of large, real-world datasets. At run time, an initialization RBFN is used to provide a rough estimation of the hand’s 3D pose. Subsequently, several specialized RBFNs are employed to improve that initial estimation in an iterative refinement scheme. To train the RBFNs, we select a set of hand poses from a real-world sequence that are as diverse as possible. We use this representative set, along with a dense sampling of all possible rotations, as a seed to generate a large synthetic training set. The method is parallelizable, taking advantage of the inherent data parallelism of RBFNs. Furthermore, the method requires few real-world data and virtually no manual annotation. We perform a quantitative evaluation of our method on a testing sequence of our own. We also present quantitative and qualitative results on a public dataset that is commonly used to evaluate hand pose estimation and tracking methods. We show that in all cases, our approach achieves promising results. Moreover, it can achieve comparable or even faster computational performance than current deep learning approaches but on a single CPU core, i.e., without requiring GPU processing.

Learning-based CBCT correction using alternating random forest based on auto-context model.

Quantitative Cone Beam CT (CBCT) imaging is increasing in demand for precise image-guided radiotherapy because it provides a foundation for advanced image-guided techniques, including accurate treatment setup, online tumor delineation, and patient dose calculation. However, CBCT is currently limited only to patient setup in the clinic because of the severe issues in its image quality. In this study, we develop a learning-based approach to improve CBCT's image quality for extended clinical applications. An auto-context model is integrated into a machine learning framework to iteratively generate corrected CBCT (CCBCT) with high-image quality. The first step is data preprocessing for the built training dataset, in which uninformative image regions are removed, noise is reduced, and CT and CBCT images are aligned. After a CBCT image is divided into a set of patches, the most informative and salient anatomical features are extracted to train random forests. Within each patch, alternating RF is applied to create a CCBCT patch as the output. Moreover, an iterative refinement strategy is exercised to enhance the image quality of CCBCT. Then, all the CCBCT patches are integrated to reconstruct final CCBCT images. The learning-based CBCT correction algorithm was evaluated using the leave-one-out cross-validation method applied on a cohort of 12 patients' brain data and 14 patients' pelvis data. The mean absolute error (MAE), peak signal-to-noise ratio (PSNR), normalized cross-correlation (NCC) indexes, and spatial nonuniformity (SNU) in the selected regions of interest (ROIs) were used to quantify the proposed algorithm's correction accuracy and generat the following results: mean MAE=12.81±2.04 and 19.94±5.44HU, mean PSNR=40.22±3.70 and 31.31±2.85dB, mean NCC=0.98±0.02 and 0.95±0.01, and SNU=2.07±3.36% and 2.07±3.36% for brain and pelvis data. Preliminary results demonstrated that the novel learning-based correction method can significantly improve CBCT image quality. Hence, the proposed algorithm is of great potential in improving CBCT's image quality to support its clinical utility in CBCT-guided adaptive radiotherapy.

Efficient Interpolation Strategies in Multiscale Multigrid Computation

We introduce two new interpolation strategies, SOR strategy and rotated grid strategy, to compute the fine grid high order accurate solution in multiscale multigrid computation based on the Richardson extrapolation technique for solving partial differential equations. These new interpolation strategies effectively accelerate or eliminate the iterative refinement process previously employed in multiscale multigrid computation to obtain high order accurate solution on the fine grid. Experimental results show that the proposed new interpolation strategies are much more efficient and faster than the previously used iterative refinement strategy to compute high order accurate solution on the fine grid.

Relative motion estimation using visual–inertial optical flow

This paper proposes a method to measure the motion of a moving rigid body using a hybrid visual---inertial sensor. The rotational velocity of the moving object is computed from visual optical flow by solving a depth-independent bilinear constraint, and the translational velocity of the moving object is estimated by solving a dynamics constraint that reveals the relation between scene depth and translational motion. By fusing an inertial sensor, the scale of translational velocities can be estimated, which is otherwise unrecoverable from monocular visual optical flow. An iterative refinement scheme is introduced to deal with observation noise and outliers, and the extended Kalman filter is applied for motion tracking. The performance of the proposed method is evaluated by simulation studies and practical experiments, and the results show the effectiveness of the proposed method in terms of accuracy and robustness.

4D imaging through spray-on optics

Light fields are a powerful concept in computational imaging and a mainstay in image-based rendering; however, so far their acquisition required either carefully designed and calibrated optical systems (micro-lens arrays), or multi-camera/multi-shot settings. Here, we show that fully calibrated light field data can be obtained from a single ordinary photograph taken through a partially wetted window. Each drop of water produces a distorted view on the scene, and the challenge of recovering the unknown mapping from pixel coordinates to refracted rays in space is a severely underconstrained problem. The key idea behind our solution is to combine ray tracing and low-level image analysis techniques (extraction of 2D drop contours and locations of scene features seen through drops) with state-of-the-art drop shape simulation and an iterative refinement scheme to enforce photo-consistency across features that are seen in multiple views. This novel approach not only recovers a dense pixel-to-ray mapping, but also the refractive geometry through which the scene is observed, to high accuracy. We therefore anticipate that our inherently self-calibrating scheme might also find applications in other fields, for instance in materials science where the wetting properties of liquids on surfaces are investigated.

Search for optimal sailing policy

A dynamic programming model has been formulated to derive the minimal time sailing route for a vessel to sail from an origin to a destination, while passing n different segments in which deterministic wind conditions prevail. Turning times and crossing wind-lines were considered. A discrete computer solution procedure was programmed that had to cope with ranges of inadmissibility of the continuous decision variables caused by inability to sail at certain angles around a facing wind. Binary search method and iterative refinement schemes were applied to reduce calculation times to the order of magnitude of one minute, while obtaining sufficient accuracy. Numerical examples are provided. Sensitivity analysis has indicated robust behavior of the best derived solutions with respect to changes in the values of the different parameters. Despite of numerical validation the best derived solution is not termed optimal, as optimality was not been proven mathematically.