Optimal Transformation Research Articles

Procrustes: A python library to find transformations that maximize the similarity between matrices

We have developed Procrustes, a free, open-source, cross-platform, and user-friendly Python library implementing a wide-range of algorithmic solutions to Procrustes problems. The goal of Procrustes analysis is to find an optimal transformation that makes two matrices as close as possible to each other, where the matrices are often (but need not always be) a list of multidimensional points specifying the systems of interest. We demonstrate the functionality of the package through various examples, mostly from cheminformatics. However, Procrustes analysis has broad applicability including image recognition, signal processing, data science, machine learning, computational biology, chemistry, and physics. Our library includes methods for one-sided Procrustes problems using orthogonal, rotational, symmetric, and permutation transformation matrices, as well as two-sided Procrustes problems using orthogonal and permutation transformation matrices. For the two-sided permutation Procrustes problem, we include heuristic algorithms along with a rigorous (but slow) method based on softassign. In addition, we include a general formulation of the Procrustes problem. The Procrustes source code and documentation is hosted on GitHub (https://github.com/theochem/procrustes). Program summaryProgram Title:ProcrustesCPC Library link to program files:https://doi.org/10.17632/57dkchhjbp.1Developer's repository link:https://github.com/theochem/procrustesLicensing provisions: GNU General Public License v3.0Programming language: PythonSupplementary material: Summary of Implemented Procrustes AlgorithmsNature of problem: The generic Procrustes problem aims to find the transformation (e.g., rotation, permutation, scaling, etc.) of a matrix (often constructed as a list of data points) which minimizes its distance to another matrix. This quantifies the “true” similarity between the two entities represented by the matrices. While this mathematical problem occurs in many contexts, it is most prevalent in the context of point-set registration, where two sets of points are aligned by rotating (and/or permuting) one set of points. Other applications include the traditional (linear) assignment problem and the quadratic assignment problem, where the transformation matrix is a permutation. The Kabsch algorithm for molecular structure alignment is also equivalent to rotational Procrustes.Solution method: The Procrustes library implements explicit solutions for the one-sided orthogonal, rotational, and symmetric Procrustes problems and uses the Hungarian algorithm for the one-sided permutation Procrustes problem. In addition to the explicit solution for the two-sided orthogonal Procrustes with two transformations, approximate algorithms for the two-sided orthogonal Procrustes with one transformation and two-sided permutation Procrustes with one transformation are provided. For the two-sided permutation Procrustes with one transformation, several new heuristics are implemented and an accurate (but computationally slow) method based on softassign algorithm is provided. In addition, a brute-force combinatorial approach can be used, albeit only for small matrices. Translation, rotation and scaling of matrices can be automatically treated with Procrustes functionality.Additional comments including restrictions and unusual features: A very broad range of Procrustes problems is treated with a common framework, including some unconventional problems like symmetric Procrustes and two-sided Procrustes problems. Several new heuristics methods for the two-sided permutation Procrustes problem with one transformation are provided, along with a robust softassign approach. The software is intended to work for matrices of moderate size.

Efficient approach for dynamic reliability analysis based on uniform design method and Box-Cox transformation

This paper proposes a novel approach for dynamic reliability analysis of uncertain structures subjected to non-stationary stochastic excitations. This approach calculates the first-passage probabilities by evaluating the transformed extreme value distribution (TEVD) instead of the original extreme value distribution (EVD). The Box-Cox transformation is first used to symmetrize the extreme value, and then the generalized Gaussian distribution (GGD) is suggested to approximate the main body and tails of the TEVD. An absolute skewness minimization criterion is proposed to find the optimal Box-Cox transformation parameter. Furthermore, the random-function spectral representation method (RFSRM) and uniform design method (UDM) are successfully combined to estimate the first four central moments of the transformed extreme value with a small sample size. Two numerical examples involving linear and nonlinear shear-frame structures under nonstationary ground motions are investigated. The results indicate that the proposed method can be used for dynamic reliability analysis with high accuracy and efficiency.

STranGAN: Adversarially-learnt Spatial Transformer for scalable human activity recognition

We tackle the problem of domain adaptation for inertial sensing-based human activity recognition (HAR) applications -i.e., in developing mechanisms that allow a classifier trained on sensor samples collected under a certain narrow context to continue to achieve high activity recognition accuracy even when applied to other contexts. This is a problem of high practical importance as the current requirement of labeled training data for adapting such classifiers to every new individual, device, or on-body location is a major roadblock to community-scale adoption of HAR-based applications. We particularly investigate the possibility of ensuring robust classifier operation, without requiring any new labeled training data, under changes to (a) the individual performing the activity, and (b) the on-body position where the sensor-embedded mobile or wearable device is placed. We propose STranGAN, a framework that explicitly decouples the domain adaptation functionality from the classification model by learning and applying a set of optimal spatial affine transformations on the target domain inertial sensor data stream by employing adversarial learning, which only requires collecting raw data samples (but no accompanying activity labels) from both source and target domains. STranGAN’s uniqueness lies in its ability to perform practically useful adaptation (a) without any labeled training data and without requiring paired, synchronized generation of source and target domain samples, and (b) without requiring any changes to a pre-trained HAR classifier. Empirical results using three publicly available benchmark datasets indicate that STranGAN(a) is particularly effective in handling on-body position heterogeneity(achieving a 5% improvement in classification F1 score compared to state-of-the-art baselines), (b) offers competitive performance for handling cross-individual variations, and (c) the affine transformation parameters can be analyzed to gain interpretable insights on the domain heterogeneity.

Transformations of Multi-Player Normal form Games by Preplay Offers between Players

The paper deals with multiplayer normal form games which are preceded by a ‘preplay negotiation phase’ consisting of exchange of preplay offers by players for payments of utility to other players conditional on them playing designated in the offers strategies. The game-theoretic effect of such preplay offers is a transformation of the payoff matrix of the game, obtained by transferring the offered payments between the payoffs of the respective players; thus, certain groups of game matrix transformations naturally emerge. The main result is an explicit and rather transparent algebraic characterization of the possible transformations of the payoff matrix of any given N-person normal form game induced by preplay offers for transfer of payments. That result can be used to describe the ‘bargaining space’ of the game and to determine the mutually optimal game transformations that rational players can achieve by exchange of preplay offers.

DAMR: A deep gaussian mixture point cloud registration method with the dual attention mechanism

Point cloud registration is important for the processing of 3D model reconstruction, but with the challenge of low registration accuracy. In order to overcome this obstacle, this paper proposed a dual attention mechanism registration (DAMR) method for the point cloud registration. Firstly, the dual attention mechanism is utilized to extract key point features with different dimensions via assigning weights to the input point clouds. Secondly, the matching parameters are obtained by estimating the position correspondence between feature points and gaussian mixture model. Finally, the parameter unit blocks of two models are applied to recover the optimal transformation by matching parameters. In order to test the performance of our method, four groups of datasets include public data models and cultural relic models are adopted, respectively. Compared with traditional methods, our method has shown better performance to effectively ensured the registration accuracy of 3D point cloud models.

Assessment of Thermophysical Performance of Ester-Based Nanofluids for Enhanced Insulation Cooling in Transformers

Nanotechnology provides an effective way to upgrade the thermophysical characteristics of dielectric oils and creates optimal transformer design. The properties of insulation materials have a significant effect on the optimal transformer design. Ester-based nanofluids (NF) are introduced as an energy-efficient alternative to conventional mineral oils, prepared by dispersing nanoparticles in the base oil. This study presents the effect of nanoparticles on the thermophysical properties of pure natural ester (NE) and synthetic ester (SE) oils with temperature varied from ambient temperature up to 80 °C. A range of concentrations of graphene oxide (GO) and TiO2 nanoparticles were used in the study to upgrade the thermophysical properties of ester-based oils. The experiments for thermal conductivity and viscosity were performed using a TC-4 apparatus that follows Debby’s concept and a redwood viscometer apparatus that follows the ASTM-D445 experimental standard, respectively. The experimental results show that nanoparticles have a positive effect on the thermal conductivity and viscosity of oils which reduces with an increase in temperature.

Histological and cytological study on meristematic nodule induction and shoot organogenesis in Paeonia ostii ‘Feng Dan’

This is the first report concerning the sequence of histological and cytological events occurring during organogenesis from cotyledon-derived meristematic nodules (MNs) in Paeonia ostii ‘Feng Dan’. Sections were made and studies were carried out with dissecting microscope, light microscope, scanning electron microscopy (SEM) and transmission electron microscopy observation. Histological studies revealed a complex developmental process of morphogenesis including five stages: (1) callus originated from cell division in both cambial and cortical regions; type I—yellow compact callus with densely arranged clumps was identified as embryogenic callus. (2) pre-nodular structure consisted of organization center (a central area of vascularization surrounded by meristematic cell layers) and an epidermis-like layer; (3) independent MNs comprised of organization center, a cortical-like area of parenchymatous cells and an epidermal-like area; (4) nodular clusters displayed vigorously internal meristematic cell division and generated a relative movement towards the nodules periphery, establishing vascular connection with primordia; (5) successive new elongated shoots with axillary bud primordia were developed. SEM observations showed three types of extracellular matrix, a smooth membranous layer, fibrillar structures and granular mucilage-like secretions on embryogenic callus, demonstrating its dynamic morphological changes. Ultrastructural analysis revealed striking changes of chloroplast morphology and starch content during MNs morphogenesis. This study allows a better understanding of in vitro regeneration via MN culture and provides references for protocol optimization and genetic transformation.

A Fuzzy Collaborative Intelligence Approach to Group Decision-Making: a Case Study of Post-COVID-19 Restaurant Transformation.

In a fuzzy group decision-making task, when decision makers lack consensus, existing methods either ignore this fact or force a decision maker to modify his/her judgment. However, these actions may be unreasonable. In this study, a fuzzy collaborative intelligence approach that seeks the consensus among experts in a novel way is proposed. Fuzzy collaborative intelligence is the application of biologically inspired fuzzy logic to a group task. The proposed methodology is based on the fact that a decision maker must make a choice even if he/she is uncertain. As a result, the decision maker’s fuzzy judgment matrix may not be able to represent his/her judgment. To solve such a problem, the fuzzy judgment matrix of each decision maker is decomposed into several fuzzy judgment submatrices. From the fuzzy judgment submatrices of all decision makers, a consensus can be easily identified. The proposed fuzzy collaborative intelligence approach and several existing methods have been applied to the case of the post-COVID-19 transformation of a Japanese restaurant in Taiwan. Because such transformation was beyond the expectation of the Japanese restaurant, the employees lacked consensus if existing methods were applied to identify their consensus. The proposed methodology solved this problem. The optimal transformation plan involved increasing the distance between tables, erecting screens between tables, and improving air circulation. In a fuzzy group decision-making task, an acceptable decision cannot be made without the consensus among decision makers. Ignoring this or forcing decision makers to modify their preferences is unreasonable. Identifying the consensus among experts from another point of view is a viable treatment.

Computational Resolution of a Boolean Equation of 21 Variables

The Alienor method has been elaborated at the beginning of the 1980s by Yves Cherruault and Arthur Guillez (1983). The following people have also greatly contributed to the improvement of this new optimization method: Blaise Somé, Gaspar Mora, Balira Konfé, Jean Claude Mazza and Esther Claudine Bityé Mvondo. The basic idea consists in using a reducing transformation allowing us to simplify a multivariable optimization problem to a new optimization problem according to a single variable. The rational gestion of enterprises leads generally to the use of Operational Research, often called management science. The term Operational Research means a scientific approach to decision making, that seeks optimization in a system. Consequently, it is better to take the right decisions. Otherwise, fatal consequences can occur instantaneously [1]. Generally, we have to maximize the global profit margin, taking into account some constraints. For instance, in an integer programming problem, some or all the variables are required to be nonnegative integers. In this paper, we present new reducing transformations for global optimization in integer, binary and mixed variables as well as the applications in Boolean algebra by solving a Boolean Equation of 21 variables. The applications in Operational Research are presented on various examples, resolved by using the tabulator Excel of Microsoft.

Synchrosqueezing Optimal Basic Wavelet Transform and Its Application on Sedimentary Cycle Division

Sedimentary cycle division is an important step for sequence stratigraphy analysis. For the division of sedimentary cycle using seismic data, a key issue is characterizing the changes of dominant frequencies caused by the changes of stratum thickness with high accuracy and high resolution. The synchrosqueezing transform (SST) can provide a time–frequency (TF) representation with high resolution by synchrosqueezing the TF spectrum, which helps the sedimentary cycle identification. Unfortunately, it is a hard task to choose an appropriate basic wavelet, which influences the accuracy of the SST to characterize the sedimentary cycle. To solve this issue, we construct a synchrosqueezing optimal basic wavelet transform (SOBWT) to optimally characterize the sedimentary cycle. We first propose a criterion to construct the basic wavelet of SST by deriving the dominant frequency location condition and defining the similarity coefficient condition of the basic wavelet. Then, we introduce the optimal basic wavelet (OBW) to construct the basic wavelet that satisfies the dominant frequency location condition and the similarity coefficient condition. Note that we term the SST with a basic wavelet that satisfies the dominant frequency location condition and the similarity coefficient condition as the SOBWT. Finally, we apply the proposed SOBWT to synthetic and field data to testify its validity and effectiveness and compare it with conventional SST-based methods. The application results illustrate that it is much more convenient and easier for the sedimentary cycle division based on the SOBWT results.

The Multisynchrosqueezing Optimal Basic Wavelet Transform and Applications to Sedimentary Cycle Division

The time-frequency (TF) analysis (TFA) tools are usually used to analyze the seismic reflection signals to assist the sedimentary cycle division. The high-resolution TFA results are beneficial to characterize the dominant frequency changes caused by the variations of the stratum thickness. The multisynchrosqueezing transform (MSST) is an iterative version of the synchrosqueezing transform (SST), which provides a more concentrated TF representation than the SST. So, the MSST is suitable for the sedimentary cycle characterization. However, it is a hard task to construct an appropriate basic wavelet. In this study, by combining the MSST and optimal basic wavelet (OBW), we proposed a multisynchrosqueezing OBW transform (MSOBWT) to help the sedimentary cycle division. The proposed method first defines the dominant frequency location condition (DFLC) that ensures the MSST to reassign the TF spectrum to the dominant frequencies position. Further, the OBW is introduced to construct the basic wavelet that satisfies the DFLC. Finally, the synthetic traces and field data are used to testify its effectiveness for the sedimentary cycle division.

Genotype Screening of Recipient Resources with High Regeneration and Transformation Efficiency in Chrysanthemum

Genetic transformation is one of the key steps in the molecular breeding of chrysanthemum, which relies on an optimal regeneration and transformation system. However, the regeneration system of different chrysanthemum cultivars varies, and the regeneration time of most cultivars is long. To screen cultivars with highly efficient regeneration, leaves and shoot tip thin cell layers (tTCL) from eight chrysanthemum cultivars with different flower colors and flower types were cultured on Murashige and Skoog media (MS) supplemented with 1.0–5.0 mg L−1 6-benzylaminopurine (6-BA) and 0.1–1.0 mg L−1 α-naphthaleneacetic (NAA). The results showed that the most efficient regeneration media were MS + 6-BA 1.0 mg L−1 + NAA 0.5 mg L−1 for leaf explants and MS + 6-BA 5.0 mg L−1 + NAA 0.1 mg L−1 for tTCL explants. Subsequently, another 13 chrysanthemum cultivars were screened by using the media, and finally, three cultivars with high regeneration efficiency were obtained from 21 cultivars. Among these, C1 had the highest regeneration efficiency: the regeneration rate of leaf explants reached 80.0% after 42 days of culture, and the regeneration rate of tTCL explants reached 100% after 31 days of culture. Furthermore, we also established the transformation system for C1 as follows: preculturing for one day, infecting with Agrobacterium suspension (OD600 = 0.6) for 10 min, and cultivating in the regeneration medium with 350 mg L−1 carbenicillin and 10 mg L−1 kanamycin, thus ultimately achieving a transformation rate of 4.0%. In this study, a new chrysanthemum cultivar with an efficient regeneration and transformation system was screened, which is beneficial to enrich the flower color of chrysanthemum transgenic plant recipients and to the functional research of flower color or type-related genes.

Hierarchical NiFeV hydroxide nanotubes: synthesis, topotactic transformation and electrocatalysis towards the oxygen evolution reaction

Hierarchical NiFeV hydroxide nanotubes were prepared through a facile sacrificial template method. Composition optimization and subsequent topotactic transformation into phosphides were conducted for further enhanced electrocatalytic activity.

Super-Resolution Optimal Basic Wavelet Transform and Its Application in Thin-Bed Thickness Characterization

Continuous wavelet transform (CWT) is often used to extract the peak frequency attribute for characterizing the thin-bed thickness. Good joint time-frequency (TF) resolution is beneficial for the extraction of peak frequency. However, due to the Heisenberg’s uncertain principle, the time and frequency resolution of CWT cannot be obtained simultaneously. In this paper, combining the adaptive superlet transform and the optimal basic wavelet, a super-resolution optimal basic wavelet transform (SROBWT) is proposed to obtain the best joint TF resolution. The optimal basic wavelet matching the seismic wavelet is constructed as a basic wavelet of the adaptive superlet transform. Herein, taking the best joint TF resolution of the seismic wavelet as the target, a parameter selection method is proposed for the adaptive superlet transform. Furthermore, based on the proposed SROBWT and wedge model, a workflow is proposed to characterize the thin-bed thickness. The synthetic and field seismic data are employed to demonstrate the validity of the proposed methods. All the corresponding results show that the SROBWT has a better joint TF resolution than the conventional methods and the proposed workflow can correctly characterize the spatial variation of the thin-bed thickness, which is beneficial for further sediment sources analysis and reservoir prediction.

Research on Programming Model and Compilation Optimization Technology of Multi-Core GPU

GPGPU (General Purpose Computing on Graphics Processing Units) has been widely applied to high performance computing. However, GPU architecture and programming model are different from that of traditional CPU. Accordingly, it is rather challenging to develop efficient GPU applications. This paper focuses on the key techniques of programming model and compiler optimization for many-core GPU, and addresses a number of key theoretical and technical issues. This paper proposes a many-threaded programming model ab-Stream, which would transparentize architecture differences and provide an easy to parallel, easy to program, easy to extend and easy to tune programming model. In addition, this paper proposes memory optimization and data transfer transformation according to data classification. Firstly, this paper proposes data layout pruning based on classification memory, and then proposes Ta T (Transfer after Transformed) for transferring Strided data between CPU and GPU. Experimental results demonstrate that proposed techniques would significantly improve performance for GPGPU applications.

Using 2-Lines Congruent Sets for Coarse Registration of Terrestrial Point Clouds in Urban Scenes

The registration of terrestrial point clouds is a crucial technique to obtaining the entire scene geometry. However, urban scenes, characterized by repetitive components, symmetrical structures, and object occlusion, pose ambiguity challenge of matches in the accurate registration of terrestrial point clouds. This article proposes a coarse registration approach using 2-lines congruent sets (2LCS) for urban point clouds. 3-D line features are extracted in the point clouds and classified into two categories according to directions. With that, a pair of 3-D line features from different categories is selected in the target point cloud to construct the 2-lines base with significant geometric characteristics. Next, the congruent 2-lines bases are identified in the source point cloud using geometric constraints, leading to the 2LCS. The 2LCS are then used to estimate the rigid motion between pairwise point cloud, leading to a set of candidate transformation parameters. The largest common point (LCP) set and maximum line structure consistency (MLSC) are integrated to evaluate the transformations. Finally, the procedure is repeated based on the RANSAC scheme to achieve optimal transformation values. We applied the proposed method to nine urban scenes with varying conditions and compared its performance with other state-of-the-art methods. The results show that our proposed approach is more robust for registering terrestrial point clouds in urban scenes with repetitive components, symmetrical structures, and limited overlap, leading to optimal or near-optimal results after fine registration optimization.

Designing the technological transformation toward sustainable steelmaking: A framework to provide decision support to industrial practitioners

Climate change and the resultant requirement to reduce greenhouse gas emissions have become one of society’s main challenges. High emissions occur in the industrial sector and particularly in steelmaking. Due to energy-intensive carbon-based production processes, there is a significant potential to reduce greenhouse gas emissions in the steel industry. In this context, a promising technology is the hydrogen-based direct reduction of iron ore that can be used instead of coal-based blast furnaces. However, the transformation toward sustainable steelmaking implies various regulatory, technological, and economic challenges. For example, decision-makers must decide about strategic investments in the context of an uncertain political environment and unpredictable development pathways of future technologies. These courses have a direct impact on the competitiveness of steelmaking corporations. Consequently, decision-makers in industrial practice waver to design and evaluate advantageous transformation pathways for their corporations. We propose a framework of a decision support tool to design and evaluate the transformation toward sustainable steelmaking. To this end, we model the relevant steelmaking processes based on activity analysis and link them to optimization packages. Decision-makers can evaluate alternative future market scenarios and determine the optimal transformation pathway for their corporation. We discussed our framework with decision-makers from steelmaking. They confirm the effectiveness of our approach to support them in evaluating advantageous transformation pathways for their corporation.

Optimal Transformer Modeling by Space Embedding for Ionospheric Total Electron Content Prediction

Prediction of ionospheric total electron content (TEC) enables accurate ionospheric delay correction for global navigation satellite system services. Thus, it is crucial to extract the characteristics of the temporal periodicity and spatial correlation for TEC modeling and prediction. The self-attention mechanism of the transformer structure is utilized to capture the long-term characteristics of the TEC in China. The gate recurrent unit (GRU) network and long short-term memory (LSTM) were chosen for comparison because of their capability for non-linear time series modeling. The results indicate that the proposed model outperforms LSTM by 23% from 2016 to 2018 and GRU by more than 4% from 2016 to 2017. In terms of small, moderate, and intense geomagnetic storms, the relative error at all involved latitude levels was reduced by 40%, 39%, and 5%, respectively, compared with GRU, as well as 44%, 47%, and 12%, respectively, compared with LSTM. Furthermore, the ensemble model (Ense-Trans) based on two proposed spatially embedded transformer models (Trans), compared with the original Trans model, reduced the relative error by 11.38%, 8.78%, and 11.78% in the summer, autumn, and winter of 2018, respectively. It is concluded that Trans has much better performance than GRU and LSTM, and Ense-Trans is better than Trans itself in terms of TEC prediction. This study will be of great significance for ionospheric real-time research and other space weather applications in the future.

A Stepwise Minimum Spanning Tree Matching Method for Registering Vehicle-Borne and Backpack LiDAR Point Clouds

Vehicle-borne Laser Scanning (VLS) and Backpack Laser Scanning (BLS) are two emerging mobile mapping technologies for capturing detailed spatial information near ground in urban built environments. BLS has flexible mobility and usually provides point clouds in a local coordinate system. Therefore, a mismatch between VLS and BLS point clouds data is quite common. Fusing VLS and BLS data in different coordinate systems could provide a comprehensive survey of urban built environments. Because of the complexity of urban road environments and the difference in data acquisition methods, traditional registration approaches based on point-level correspondences are likely to fail and sometimes involve substantial manual efforts. In this paper, we propose a novel registration approach that finds the optimal transformation between the respective point clouds based on a unique tree distribution pattern defined by tree trunk centers. The proposed method consists of three key steps, i.e., trunk center extraction, stepwise minimum spanning tree (MST) matching, and transformation estimation. Stepwise MST matching is an essential step in finding the one-to-one correspondences using a topological similarity between the two LiDAR datasets. We evaluated our method with five real-world datasets collected in the Shanghai city, China. The results showed that the proposed method performed well in all five experiment sites with an average rotation error of less than 0.06° and an average translation error of less than 0.05 m. Moreover, the reported mean position deviation in the five sites are 0.112 m, 0.144 m, 0.176 m, 0.148 m, and 0.184 m, respectively. Our proposed method has a great potential for registering multiplatform LiDAR data that could provide comprehensive and essential 3D information for numerous urban applications.

Automatic Registration of Very Low Overlapping Array InSAR Point Clouds in Urban Scenes

Array interferometric synthetic aperture radar (Array InSAR) has a 3-D resolution capability and solves the layover problem in interferometric SAR (InSAR) by arranging multiple antennas in the cross-orbit direction. Airborne Array InSAR point clouds are obtained from two scans for complete building information in urban areas, resulting in very low overlapping point cloud. The existing methods are difficult to extract the identical features for the registration of Array InSAR point clouds. To this end, a robust registration approach Array InSAR point clouds in urban areas is proposed in this study. The main contribution of this article is raising the theoretically optimal transformation for achieving point cloud registration, considering the constraint from parallel facades of a certain building. Point density estimation is adopted to retain building facade points for initial registration. The facade pairs of a specific building are then matched and divided into two categories by judging whether one contains the concave–convex features or not, for performing rotation rectification and fine shift fixation, respectively. Experimental results of both simulated and real data validate the feasibility and reliability of our approach. For the simulated data, the results reach an average rotation error of about 0.01° and an average translation error of less than 0.8 m. For the real data, two evaluation criteria are designed for the lack of reference data. The results reach an average of 0.4° of the defined angle difference and less 0.8-m distance difference from the source facades center to the normal extension of the target facades.