Rotation Estimation Research Articles

A Minimal Closed-form Solution for the Perspective Three Orthogonal Angles (P3oA) Problem: Application To Visual Odometry

We provide a simple closed-form solution to the Perspective three orthogonal angles (P3oA) problem: given the projection of three orthogonal lines in a calibrated camera, find their 3D directions. Upon this solution, an algorithm for the estimation of the camera relative rotation between two frames is proposed. The key idea is to detect triplets of orthogonal lines in a hypothesize-and-test framework and use all of them to compute the camera rotation in a robust way. This approach is suitable for human-made environments where numerous groups of orthogonal lines exist. We evaluate the numerical stability of the P3oA solution and the estimation of the relative rotation with synthetic and real data, comparing our results to other state-of-the-art approaches.

Correcting Distortion of Polarimetric SAR Data Induced by Ionospheric Scintillation

A correction methodology for distortions induced by ionospheric scintillation on fully polarimetric synthetic aperture radar (SAR) data is proposed. The correction is based on deriving the phase distortion induced by the ionosphere from Faraday rotation estimates. The estimated phase distortion is then used for correction. In order to compensate the phase and time–Doppler history distortions, the correction has to be performed at the slant range of the ionospheric layer, i.e., on partially focused single-look complex data. Accordingly, the performance of the proposed correction methodology depends, among other factors, on knowledge of the altitude of the effective ionospheric layer (assuming the thin ionospheric layer model). Its estimation from the SAR data itself is therefore also addressed. The methodology was applied and validated on simulated P-band data for various ionospheric conditions and on real L-band data acquired by the Advanced Land Observation Satellite Phased Array L-band SAR (PALSAR).

Accuracy improved image registration based on pre-estimation and compensation

In this paper, we propose to improve the registration accuracy by pre-estimation and compensation. The idea is motivated by the observation of some registration algorithms that, for a given algorithm, the accuracies of the translation-only model are much higher than those of other complex models. Therefore, it seems that, if pre-estimation and compensation are performed and the residual model is close to translation only, the following estimation could achieve improved accuracy. To verify the idea, we implement two algorithms in the rotation-translation (RT) model. We use the Fourier–Mellin transform to isolate and convert the rotation into translation, then apply the classical Lucas–Kanade algorithm to obtain the high accuracy rotation estimation. In the following, the one takes account into the incomplete rotation compensation, and use the Keren algorithm for the residual model; the other assumes the rotation compensation is complete, and uses the second Lucas–Kanade algorithm. Finally, we perform simulations using typical test images, and the results confirm the accuracy improvement.

Incomplete separability of Antarctic plate rotation from glacial isostatic adjustment deformation within geodetic observations

Geodetic measurements of Antarctic solid Earth deformation include signals from plate rotation and glacial isostatic adjustment (GIA). Through simulation, we investigate the degree to which these signals are separable within horizontal GPS site velocities that commonly define plate rotation estimates and that promise new constraints on models of GIA. Using a suite of GIA model predictions that incorporate both 1-D and 3-D Earth rheologies, we show that, given the present location of GPS sites within East Antarctica, unmodelled or mismodelled GIA signal within GPS velocities produces biased estimates of plate rotation. When biased plate rotation is removed from the GPS velocities, errors as large as 0.8 mm yr−1 are introduced; a value commonly larger than the predicted GIA signal magnitude. In the absence of reliable forward models of plate rotation or GIA then Antarctic geodetic velocities cannot totally and unambiguously constrain either process, especially GIA.

Kinematics of jointed pipes and design estimates of joint rotation under differential ground movements

Centrifuge testing of reduced-scale models has been used to examine the kinematics of jointed pipelines crossing normal ground faults. The model pipeline was fabricated at 1/30th scale using segments of a semicircular cross section cut from an aluminum rod. Threaded rods were used to connect those segments and model a variety of joints having longitudinal bending stiffnesses from 3% to 47% of the bending stiffness of the pipe segments. The semicircular segments were placed against a glass sidewall of the test box and buried in sand. During testing under 30g, differential ground movements of up to 70% of the pipe diameter were imposed, and the pipe movements were monitored using particle image velocimetry. It is shown that maximum rotations occur at the joints when the shear zone generated by the ground fault passes across the joint rather than the pipe segment, and that joint stiffness has little impact on the pipe kinematics. A simplified kinematic model is introduced that permits straightforward, safe estimates of maximum joint rotation.

GLOBAL ROTATION ESTIMATION USING WEIGHTED ITERATIVE LIE ALGEBRAIC AVERAGING

Abstract. In this paper we present an approach for a weighted rotation averaging to estimate absolute rotations from relative rotations between two images for a set of multiple overlapping images. The solution does not depend on initial values for the unknown parameters and is robust against outliers. Our approach is one part of a solution for a global image orientation. Often relative rotations are not free from outliers, thus we use the redundancy in available pairwise relative rotations and present a novel graph-based algorithm to detect and eliminate inconsistent rotations. The remaining relative rotations are input to a weighted least squares adjustment performed in the Lie algebra of the rotation manifold SO(3) to obtain absolute orientation parameters for each image. Weights are determined using the prior information we derived from the estimation of the relative rotations. Because we use the Lie algebra of SO(3) for averaging no subsequent adaptation of the results has to be performed but the lossless projection to the manifold. We evaluate our approach on synthetic and real data. Our approach often is able to detect and eliminate all outliers from the relative rotations even if very high outlier rates are present. We show that we improve the quality of the estimated absolute rotations by introducing individual weights for the relative rotations based on various indicators. In comparison with the state-of-the-art in recent publications to global image orientation we achieve best results in the examined datasets.

The Impact of System Effects on Estimates of Faraday Rotation From Synthetic Aperture Radar Measurements

Radio waves traversing the Earth's ionosphere suffer from Faraday rotation with noticeable effects on measurements from lower frequency space-based radars, but these effects can be easily corrected given estimates of the Faraday rotation angle, i.e., $\Omega$ . Several methods to derive $\Omega$ from polarimetric measurements are known, but they are affected by system distortions (crosstalk and channel imbalance) and noise. A first-order analysis for the most robust Faraday rotation estimator leads to a differentiable expression for the bias in the estimate of $\Omega$ in terms of the amplitudes and phases of the distortion terms and the covariance properties of the target. The analysis applies equally to L-band and P-band. We derive conditions on the amplitudes and phases of the distortion terms that yield the maximum bias and a compact expression for its value for the important case where $\Omega=0$ . Exact simulations confirm the accuracy of the first-order analysis and verify its predictions. Conditions on the distortion amplitudes that yield a given maximum bias are derived numerically, and the maximum bias is shown to be insensitive to the amplitude of the channel imbalance terms. These results are important not just for correcting polarimetric data but also for assessing the accuracy of the estimates of the total electron content derived from Faraday rotation.

Rotation and translation covariant match kernels for image retrieval

Most image encodings achieve orientation invariance by aligning the patches to their dominant orientations and translation invariance by completely ignoring patch position or by max-pooling. Albeit successful, such choices introduce too much invariance because they do not guarantee that the patches are rotated or translated consistently. In this paper, we propose a geometric-aware aggregation strategy, which jointly encodes the local descriptors together with their patch dominant angle or location. The geometric attributes are encoded in a continuous manner by leveraging explicit feature maps. Our technique is compatible with generic match kernel formulation and can be employed along with several popular encoding methods, in particular Bag-of-Words, VLAD and the Fisher vector. The method is further combined with an efficient monomial embedding to provide a codebook-free method aggregating local descriptors into a single vector representation. Invariance is achieved by efficient similarity estimation of multiple rotations or translations, offered by a simple trigonometric polynomial. This strategy is effective for image search, as shown by experiments performed on standard benchmarks for image and particular object retrieval, namely Holidays and Oxford buildings.

Opportunities for measuring wheelchair kinematics in match settings; reliability of a three inertial sensor configuration

Knowledge of wheelchair kinematics during a match is prerequisite for performance improvement in wheelchair basketball. Unfortunately, no measurement system providing key kinematic outcomes proved to be reliable in competition. In this study, the reliability of estimated wheelchair kinematics based on a three inertial measurement unit (IMU) configuration was assessed in wheelchair basketball match-like conditions. Twenty participants performed a series of tests reflecting different motion aspects of wheelchair basketball. During the tests wheelchair kinematics were simultaneously measured using IMUs on wheels and frame, and a 24-camera optical motion analysis system serving as gold standard. Results showed only small deviations of the IMU method compared to the gold standard, once a newly developed skid correction algorithm was applied. Calculated Root Mean Square Errors (RMSE) showed good estimates for frame displacement (RMSE≤0.05m) and speed (RMSE≤0.1m/s), except for three truly vigorous tests. Estimates of frame rotation in the horizontal plane (RMSE<3°) and rotational speed (RMSE<7°/s) were very accurate. Differences in calculated Instantaneous Rotation Centres (IRC) were small, but somewhat larger in tests performed at high speed (RMSE up to 0.19m). Average test outcomes for linear speed (ICCs>0.90), rotational speed (ICC>0.99) and IRC (ICC> 0.90) showed high correlations between IMU data and gold standard. IMU based estimation of wheelchair kinematics provided reliable results, except for brief moments of wheel skidding in truly vigorous tests. The IMU method is believed to enable prospective research in wheelchair basketball match conditions and contribute to individual support of athletes in everyday sports practice.

A micromechanical study on the stress rotation in granular materials due to fabric evolution

In the present study, the non-coaxiality between the axes of principal stress and strain rate tensors is investigated from micromechanical point of view. Based on the so called stress–force–fabric (SFF) relationship, which describes the macro–micro relation, an expression is derived for the principal direction of stress tensor in terms of micromechanical parameters of the fabric. In general, the rotation of principal stress axis and accordingly, the non-coaxiality angle, are influenced by both the anisotropy coefficients and directions of anisotropy of the fabric characteristics. The derived macro–micro relationship was evaluated by performing DEM simulations of 2D specimens of aggregates. It was shown that the principal directions of anisotropy parameters are almost coincident for the assemblies containing circular particles or elongated angular particles with random distribution. In such case, the principal direction of stress tensor can be regarded as the average principal direction of anisotropy. However, when the aggregate with elongated particles has inherently-anisotropic fabric, a correct estimation of the stress angle rotation requires considering all the anisotropy parameters including both anisotropy coefficients and directions.

Retrospective head motion correction approaches for diffusion tensor imaging: Effects of preprocessing choices on biases and reproducibility of scalar diffusion metrics.

To evaluate how retrospective head motion correction strategies affect the estimation of scalar metrics commonly used in clinical diffusion tensor imaging (DTI) studies along with their across-session reproducibility errors. Fractional anisotropy (FA), mean diffusivity (MD), radial diffusivity (RD), axial diffusivity (AD) and their respective across-session reproducibility errors were measured on a 4T test-retest dataset of healthy participants using five processing pipelines. These differed in: 1) the number of b0 volumes used for motion correction reference (one or five); 2) the estimations of the gradient matrix rotation (based on 6 or 12 degrees of freedom derived from coregistration); and 3) the software packages used (FSL or DTIPrep). Biases and reproducibility were evaluated in three regions of interest (ROIs) (bilateral arcuate fasciculi, cingula, and the corpus callosum) and also at the full brain level with tract based skeleton images. Preprocessing choices affected DTI measures and their reproducibility. The DTIPrep pipeline exhibited higher DTI metrics: FA/MD and AD (P < 0.05) relative to FSL pipelines both at the ROI and full brain level, and lower RD estimates (P < 0.05) at the ROI level. Within FSL pipelines no such effects were found (P-values ranging between 0.25 and 0.97). The DTIPrep pipeline showed the highest number of white matter skeleton voxels, with significantly higher reproducibility (P < 0.001) relative to the other pipelines (tested on P < 0.01 uncorrected maps). The use of an iteratively averaged b0 image as motion correction reference (as performed by DTIPrep) affects both scalar values and improves test-retest reliability relative to the other tested pipelines. These considerations are potentially relevant for data analysis in longitudinal DTI studies.

Cyclic response of I-shaped bridge columns with substandard transverse reinforcement

The cyclic response of a typical bridge column with I-shaped cross-section and substandard transverse reinforcement was investigated by means of experimental and analytical research. The amount of transverse reinforcement was sufficient to ensure adequate shear strength, but other requirements of the Eurocode 8/2 standard related to the confinement and buckling of the longitudinal bars were not fulfilled. Failure was brittle due to the buckling and rupture of the longitudinal bars, which caused a progressive reduction of strength. The results of the experiment showed that the requirements of Eurocode 8/2 (which are quite stringent) related to the minimum volumetric ratio and the maximum centre-to-centre distance of the stirrups along the column, as well as the maximum distance between the engaged longitudinal bars, are justified in the investigated case. It was demonstrated that improperly designed stirrup hooks can cause a significant reduction in the ductility capacity of the column.An attempt was made to strengthen the column using CFRP sheets. The strengthening was not straightforward. Two types of anchoring were investigated. The most efficient method of anchoring was based on the use of bolted steel plates. Due to the unfavorable dimension ratio of the column cross-section, the efficiency of the strengthening was limited.The results of the experiment were used in order to identify the most suitable numerical models. Two engineering numerical macro models were analysed: a fibre based beam with hinges model, and a Giberson’s model. In both cases agreement with the results of the experiment was fairly good, as long as the buckling of the flexural reinforcement was not pronounced, and substantial in-cycle strength degradation was consequently obtained. Some of the parameters (e.g. the ultimate deformation of the concrete in non-strengthened column) were calibrated according to the experiment, since the available models, reported in the literature, did not suit the investigated case. These parameters require further investigation.The methods included in Eurocode 8/3, which are used to estimate the properties of the strengthened column, were compared. The procedures for estimation of the ultimate deformation capacity were also compared with some methods proposed in the literature. In the investigated case the best simulation of the experiment was obtained when the Lam and Teng’s model of confined concrete was taken into account, together with a standard theoretical procedure for the estimation of the maximum chord rotation.

Unidirectional rotating coordinate rotation digital computer algorithm based on rotational phase estimation.

The improved coordinate rotation digital computer (CORDIC) algorithm gives high precision and resolution phase rotation, but it has some shortages such as high iterations and big system delay. This paper puts forward unidirectional rotating CORDIC algorithm to solve these problems. First, using under-damping theory, a part of unidirectional phase rotations is carried out. Then, the threshold value of angle is determined based on phase rotation estimation method. Finally, rotation phase estimation completes the rest angle iterations. Furthermore, the paper simulates and implements the numerical control oscillator by Quartus II software and Modelsim software. According to the experimental results, the algorithm reduces iterations and judgment of sign bit, so that it decreases system delay and resource utilization and improves the throughput. We always analyze the error brought by this algorithm. It turned out that the algorithm has a good application prospect in global navigation satellite system and channelized receiver.

Rotational components in structural loading

In this paper, the rotational loading pattern of multi-storey buildings supported on the spread and continuous interconnected single foundations is discussed. To achieve this, simplified relations for the estimation of (1) point rotations; (2) spatial variation of strong ground motions, and (3) foundation input motions are derived. The height-wise variation of the earthquake rotational loading of multi-storey buildings is parametrically evaluated by considering the location of the first rigid floor diaphragm and foundation type. In addition, the effect of the kinematic soil–structure interaction on the response spectrum of the rotational and translational components is studied. The numerical results provide a deeper insight into the rotational loading of structures in the middle-field zone, and show how the rotational components may detrimentally affect the structural response of multi-storey buildings depending on their kinematic characteristics.

Toward a generalized plate motion reference frame

AbstractAn absolute plate motion (APM) model is required to address issues such as the thermochemical evolution of Earth's mantle. All APM models have to rely on indirect inferences, including those based on hot spots and seismic anisotropy, each with their own set of uncertainties. Here, we explore a seafloor spreading‐aligned reference frame. We show that this reference frame fits azimuthal seismic anisotropy in the uppermost mantle very well. The corresponding Euler pole is close to those of hot spot reference frames, ridge motion minimizing models, and geodynamic estimates of net rotation and predicts clear trench motion patterns. We conclude that a net rotation pole guided by the spreading‐aligned model (at 64°E, 61°S, with moderate rotation of ∼ 0.2 … 0.3°/Myr) could indeed represent a standard, comprehensive reference frame for present‐day plate motions with respect to the deep mantle.

Estimate Hand Poses Efficiently from Single Depth Images

This paper aims to tackle the practically very challenging problem of efficient and accurate hand pose estimation from single depth images. A dedicated two-step regression forest pipeline is proposed: given an input hand depth image, step one involves mainly estimation of 3D location and in-plane rotation of the hand using a pixel-wise regression forest. This is utilized in step two which delivers final hand estimation by a similar regression forest model based on the entire hand image patch. Moreover, our estimation is guided by internally executing a 3D hand kinematic chain model. For an unseen test image, the kinematic model parameters are estimated by a proposed dynamically weighted scheme. As a combined effect of these proposed building blocks, our approach is able to deliver more precise estimation of hand poses. In practice, our approach works at 15.6 frame-per-second (FPS) on an average laptop when implemented in CPU, which is further sped-up to 67.2 FPS when running on GPU. In addition, we introduce and make publicly available a data-glove annotated depth image dataset covering various hand shapes and gestures, which enables us conducting quantitative analyses on real-world hand images. The effectiveness of our approach is verified empirically on both synthetic and the annotated real-world datasets for hand pose estimation, as well as related applications including part-based labeling and gesture classification. In addition to empirical studies, the consistency property of our approach is also theoretically analyzed.

Mathematical model of movement of particles in a rotary separator

The article presents a model of particles movement in the flow of grain mass by means of screw turns of rotary separator with longitudinal arrangement of rotor. The instances of mobile casing and stationary one with screw guide ribs and without them are considered. Theoretical efficiency estimation of rotation of casing and guide ribs is given.

Comparison of hierarchical and six degrees-of-freedom marker sets in analyzing gait kinematics

The objective of this study was to determine how marker spacing, noise, and joint translations affect joint angle calculations using both a hierarchical and a six degrees-of-freedom (6DoF) marker set. A simple two-segment model demonstrates that a hierarchical marker set produces biased joint rotation estimates when sagittal joint translations occur whereas a 6DoF marker set mitigates these bias errors with precision improving with increased marker spacing. These effects were evident in gait simulations where the 6DoF marker set was shown to be more accurate at tracking axial rotation angles at the hip, knee, and ankle.

Faraday Rotation Retrieval Using SMOS Radiometric Data

Faraday rotation is dynamically computed from L-band radiometric data acquired by the Soil Moisture and Ocean Salinity satellite. Improved full polarimetric image reconstruction and smart spatiotemporal filtering are used to obtain good estimations of Faraday rotation, which compare very well with the values theoretically predicted from available ionosphere and geomagnetic field data.

Implicações nutricionais com base em diferentes intensidades de colheita da biomassa de Eucalyptus urophylla x Eucalyptus globulus

A disponibilidade de nutrientes para futuros plantios em um sítio florestal está relacionada principalmente à, intensidade de colheita aplicada. Objetivou-se, com este estudo, avaliar as implicações nutricionais causadas pelas diferentes intensidades de colheita da biomassa de um povoamento de Eucalyptus urophylla x Eucalyptus globulus com dez anos de idade, em Eldorado do Sul - RS. A avaliação das implicações nutricionais conforme a intensidade de colheita florestal foi analisada levando em consideração: o estoque de nutrientes entre o sistema solo - planta; os efeitos da colheita dos diferentes componentes da biomassa acima do solo na remoção dos nutrientes; o número de rotações e a taxa de remoção de nutrientes conforme o sistema de colheita utilizado e o coeficiente de utilização biológica dos nutrientes. Com a colheita da madeira com casca, todos os nutrientes teriam uma remoção superior a 45% de sua quantidade acumulada na biomassa total acima do solo. Entretanto, removendo apenas a madeira comercial, que apresenta o maior coeficiente de utilização de nutrientes, a porcentagem de remoção para os nutrientes, com exceção do Cu e Zn, seria inferior a 50%, chegando até 10% no caso do Ca, em relação ao total contido na biomassa. O fósforo e o cálcio poderão ser os principais nutrientes a tornarem-se limitantes na produtividade nas próximas rotações, pois as estimativas de rotações potenciais estão próximas a um, quando realizada a colheita da madeira com casca