A global variable-permutation based approach for estimating tree transformation parameters used in phylogenetically controlled multivariate regression v1

This protocol provides a method to realize phylogenetic control in multivariate regression modeling while estimating tree transformation parameters en route. The protocol requires compiling a list of all possible variable combinations (at multiple model lengths) and iterating through these while estimating the transformation parameters along side the regression. A combination of AIC and the coefficient of determination can be used, for example, to select the "best" model from numerous possible model lengths. The average of the tree transformation parameters can then be used on these "best" models to perform the final phylogenetically controlled multivariate regression.

A Closed-Form Solution to Linear Feature-Based Registration of LiDAR Point Clouds

Due to the high complexity of geo-spatial entities and the limited field of view of LiDAR equipment, pairwise registration is a necessary step for integrating point clouds from neighbouring LiDAR stations. Considering that accurate extraction of point features is often difficult without the use of man-made reflectors, and the initial approximate values for the unknown transformation parameters must be estimated in advance to ensure the correct operation of those iterative methods, a closed-form solution to linear feature-based registration of point clouds is proposed in this study. Plücker coordinates are used to represent the linear features in three-dimensional space, whereas dual quaternions are employed to represent the spatial transformation. Based on the theory of least squares, an error norm (objective function) is first constructed by assuming that each pair of corresponding linear features is equivalent after registration. Then, by applying the extreme value analysis to the objective function, detailed derivations of the closed-form solution to the proposed linear feature-based registration method are given step by step. Finally, experimental tests are conducted on a real dataset. The derived experimental result demonstrates the feasibility of the proposed solution: By using eigenvalue decomposition to replace the linearization of the objective function, the proposed solution does not require any initial estimates of the unknown transformation parameters, which assures the stability of the registration method.

A Two-Stage Deep Learning Registration Method for Remote Sensing Images Based on Sub-Image Matching

The registration of multi-temporal remote sensing images with abundant information and complex changes is an important preprocessing step for subsequent applications. This paper presents a novel two-stage deep learning registration method based on sub-image matching. Unlike the conventional registration framework, the proposed network learns the mapping between matched sub-images and the geometric transformation parameters directly. In the first stage, the matching of sub-images (MSI), sub-images cropped from the images are matched through the corresponding heatmaps, which are made of the predicted similarity of each sub-image pairs. The second stage, the estimation of transformation parameters (ETP), a network with weight structure and position embedding estimates the global transformation parameters from the matched pairs. The network can deal with an uncertain number of matched sub-image inputs and reduce the impact of outliers. Furthermore, the sample sharing training strategy and the augmentation based on the bounding rectangle are introduced. We evaluated our method by comparing the conventional and deep learning methods qualitatively and quantitatively on Google Earth, ISPRS, and WHU Building Datasets. The experiments showed that our method obtained the probability of correct keypoints (PCK) of over 99% at α = 0.05 (α: the normalized distance threshold) and achieved a maximum increase of 16.8% at α = 0.01, compared with the latest method. The results demonstrated that our method has good robustness and improved the precision in the registration of optical remote sensing images with great variation.

Total Least-Squares Determination of Body Segment Attitude

To examine segment and joint attitudes when using image based motion capture it is necessary to determine the rigid body transformation parameters from an inertial reference frame to a reference frame fixed in a body segment. Determine the rigid body transformation parameters must account for errors in the coordinates measured in both reference frames, a total least-squares problem. This study presents a new derivation that shows that a singular value decomposition based method provides a total least-squares estimate of rigid body transformation parameters. The total least-squares method was compared with an algebraic method for determining rigid body attitude (TRIAD method). Two cases were examined: Case 1 where the positions of a marker cluster contained noise after the transformation, and Case 2 where the positions of a marker cluster contained noise both before and after the transformation. The white noise added to position data had a standard deviation from zero to 0.002 m, with 101 noise levels examined. For each noise level 10000 criterion attitude matrices were generated. Errors in estimating rigid body attitude were quantified by computing the angle, error angle, required to align the estimated rigid body attitude with the actual rigid body attitude. For both methods and cases as the noise level increased the error angle increased, with errors larger for Case 2 compared with Case 1. The SVD based method was superior to the TRIAD algorithm for all noise levels and both cases, and provided a total least-squares estimate of body attitude.

Least-squares adjustment taking into account the errors in variables

In this article, we discuss the procedure for computing the values of the unknowns under the condition of the minimum sum of squares of the observation residuals (least-squares method), taking into account the errors in the unknowns. Many authors have already presented the problem, especially in the field of regression analysis and computations of transformation parameters. We present an overview of the theoretical foundations of the least-squares method and extensions of this method by considering the errors in unknowns in the model matrix. The method, which can be called ‘the total least-squares method’, is presented in the paper for the case of fitting the regression line to a set of points and for the case of calculating transformation parameters for the transition between the old and the new Slovenian national coordinate systems. With the results based on relevant statistics, we confirm the suitability of the considered method for solving such tasks.

Comparison Between IGS and Three ITRS Realizations

Four space geodetic techniques (IGS, SLR, VLBI and DORIS) contribute to the realizations of International Terrestrial Reference System (ITRS). The GNSS-derived terrestrial reference frame generated from the second reprocessing campaign (repro2), named IG2, act as the IGS input to the most recently three realizations (ITRF2014, DTRF2014 and JTRF2014). Its origin and orientation are aligned to the IGb08, and its scale is defined by using the igs08.atx satellite antenna phase center offset (PCO) values. To study the consistencies and discrepancies between IGS solutions and the three ITRS realizations, we corrected the IG2 solutions to be uniform with the IGS14 frame and perform Helmert transformation to compare the IGS frame and the three ITRS realizations. Results indicate that IGS frame is more stable than the two secular frames especially in the periods after 2015. The similarity transformation parameters between the corrected IGS solutions and ITRF2014 show excellent agreement with a notable mean z-offset of around 1 mm. The transformation parameters between the corrected IGS solutions and DTRF2014 show linear discrepancies in the three categories parameters, where the origin offsets are around less than 5.5 mm, rotational alignment is consistent at the level of 4.5 uas/yr (about 0.15 mm/yr) and the scale exhibits a stable offset of 0.16 ppb. Unlike the two secular frames, distinct seasonal signals and interannual variations of translation time series can be observed from the comparison between JTRF2014 and the IGS solutions. The orientation of JTRF2014 is in worst agreement with the IGS solutions, which is related to biased no-net-rotation (NNR) condition due to weekly center of network (CN) variations. Moreover, the scale defined by JTRF2014 suffer from large instability variations over time.

Helmert transformation strategies in analysis of GPS position time-series

SUMMARY Global positioning system (GPS) position time-series generated using inconsistent satellite products should be aligned to a secular Terrestrial Reference Frame by Helmert transformation. However, unmodelled non-linear variations in station positions can alias into transformation parameters. Based on 17 yr of position time-series of 112 stations produced by precise point positioning (PPP), we investigated the impact of network configuration and scale factor on long-term time-series processing. Relative to the uniform network, the uneven network can introduce a discrepancy of 0.7–1.1 mm, 21.3–27.5 μas and 1.3 mm in terms of root mean square (RMS) for the translation, rotation and scale factor (if estimated), respectively, no matter whether the scale factor is estimated. The RMS of vertical annual amplitude differences caused by such network effect reaches 0.5–0.6 mm. Whether estimating the scale factor mostly affects the Z-translation and vertical annual amplitude, leading to a difference of 1.3 mm when the uneven network is used. Meanwhile, the annual amplitude differences caused by the scale factor present different geographic location dependences over the north, east and up components. The seasonal signals derived from the transformation using the uniform network and without estimating scale factor have better consistency with surface mass loadings with more than 41 per cent of the vertical annual variations explained. Simulation studies show that 40–50 per cent of the annual signals in the scale factor can be explained by the aliasing of surface mass loadings. Another finding is that GPS draconitic errors in station positions can also alias into transformation parameters, while different transformation strategies have limited influence on identifying the draconitic errors. We suggest that the uniform network should be used and the scale factor should not be estimated in Helmert transformation. It is also suggested to perform frame alignment on PPP time-series, even though the used satellite products belong to a consistent reference frame, as the origin of PPP positions inherited from satellite orbits and clocks is not so stable during a long period. With Helmert transformation, the seasonal variations would better agree with surface mass loadings, and noise level of time-series is reduced.

RIDF: A ROBUST ROTATION-INVARIANT DESCRIPTOR FOR 3D POINT CLOUD REGISTRATION IN THE FREQUENCY DOMAIN

Registration of point clouds is a fundamental problem in the community of photogrammetry and 3D computer vision. Generally, point cloud registration consists of two steps: the search of correspondences and the estimation of transformation parameters. However, to find correspondences from point clouds, generating robust and discriminative features is of necessity. In this paper, we address the problem of extracting robust rotation-invariant features for fast coarse registration of point clouds under the assumption that the pairwise point clouds are transformed with rigid transformation. With a Fourier-based descriptor, point clouds represented by volumetric images can be mapped from the image to feature space. It is achieved by considering a gradient histogram as a continuous angular signal which can be well represented by the spherical harmonics. The rotation-invariance is established based on the Fourier-based analysis, in which high-frequency signals can be filtered out. This makes the extracted features robust to noises and outliers. Then, with the extracted features, pairwise correspondence can be found by the fast search. Finally, the transformation parameters can be estimated by fitting the rigid transformation model using the corresponding points and RANSAC algorithm. Experiments are conducted to prove the effectiveness of our proposed method in the task of point cloud registration. Regarding the experimental results of the point cloud registration using two TLS benchmark point cloud datasets, featuring with limited overlaps and uneven point densities and covering different urban scenes, our proposed method can achieve a fast coarse registration with rotation errors of less than 1 degree and translation errors of less than 1m.

Application of simulated annealing algorithm for 3D coordinate transformation problem solution

Transformation of spatial coordinates (3D) is a common computational task in photogrammetry, engineering geodesy, geographical information systems or computer vision. In the most frequently used variant, transformation of point coordinates requires knowledge of seven transformation parameters, of which three determine translation, another three rotation and one change in scale. As these parameters are commonly determined through iterative methods, it is essential to know their initial approximation. While determining approximate values of the parameters describing translation or scale change is relatively easy, determination of rotation requires more advanced methods. This study proposes an original, two-step procedure of estimating transformation parameters. In the initial step, a modified version of simulated annealing algorithm is used for identifying the approximate value of the rotation parameter. In the second stage, traditional least squares method is applied to obtain the most probable values of transformation parameters. The way the algorithm works was checked on two numerical examples. The computational experiments proved that proposed algorithm is efficient even in cases characterised by very disadvantageous configuration of common points.