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Relevant bibliographies by topics / Affine and Conformal 2D Transformation

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Academic literature on the topic 'Affine and Conformal 2D Transformation'

Author: Grafiati

Published: 5 June 2025

Last updated: 11 July 2025

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Journal articles on the topic "Affine and Conformal 2D Transformation"

1

Kumi-Boateng, Bernard, and Yao Yevenyo Ziggah. "FEASIBILITY OF USING GROUP METHOD OF DATA HANDLING (GMDH) APPROACH FOR HORIZONTAL COORDINATE TRANSFORMATION." Geodesy and cartography 46, no. 2 (2020): 55–66. http://dx.doi.org/10.3846/gac.2020.10486.

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Machine learning algorithms have emerged as a new paradigm shift in geoscience computations and applications. The present study aims to assess the suitability of Group Method of Data Handling (GMDH) in coordinate transformation. The data used for the coordinate transformation constitute the Ghana national triangulation network which is based on the two-horizontal geodetic datums (Accra 1929 and Leigon 1977) utilised for geospatial applications in Ghana. The GMDH result was compared with other standard methods such as Backpropagation Neural Network (BPNN), Radial Basis Function Neural Network (RBFNN), 2D conformal, and 2D affine. It was observed that the proposed GMDH approach is very efficient in transforming coordinates from the Leigon 1977 datum to the official mapping datum of Ghana, i.e. Accra 1929 datum. It was also found that GMDH could produce comparable and satisfactory results just like the widely used BPNN and RBFNN. However, the classical transformation methods (2D affine and 2D conformal) performed poorly when compared with the machine learning models (GMDH, BPNN and RBFNN). The computational strength of the machine learning models’ is attributed to its self-adaptive capability to detect patterns in data set without considering the existence of functional relationships between the input and output variables. To this end, the proposed GMDH model could be used as a supplementary computational tool to the existing transformation procedures used in the Ghana geodetic reference network.

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2

Pinz, Axel, Manfred Prantl, and Harald Ganster. "A Robust Affine Matching Algorithm Using an Exponentially Decreasing Distance Function." JUCS - Journal of Universal Computer Science 1, no. (8) (1995): 614–31. https://doi.org/10.3217/jucs-001-08-0614.

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We describe a robust method for spatial registration, which relies on the coarse correspondence of structures extracted from images, avoiding the establishment of point correspondences. These structures (tokens) are points, chains, polygons and regions at the level of intermediate symbolic representation (ISR). The algorithm recovers conformal transformations (4 affine parameters), so that 2-dimensional scenes as well as planar structures in 3D scenes can be handled. The affine transformation between two different tokensets is found by minimization of an exponentially decreasing distance function. As long as the tokensets are kept sparse, the method is very robust against a broad variety of common disturbances (e.g. incomplete segmentations, missing tokens, partial overlap). The performance of the algorithm is demonstrated using simple 2D shapes, medical, and remote sensing satellite images. The complexity of the algorithm is quadratic on the number of affine parameters.

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Mustafa M. Amami. "Multi and single epipolar geometry-based filters vs. affine and conformal 2D transformation-based filters." Global Journal of Engineering and Technology Advances 10, no. 3 (2022): 032–51. http://dx.doi.org/10.30574/gjeta.2022.10.3.0047.

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The accuracy of Optical Robot Navigation (ORN) depends mainly on the quality of the Automatic Image Matching (AIM) results. Conformal 2D transformation-based Filter (C-2DF), affine 2D transformation-based Filter (A-2DF) and Single Epipolar Geometry-based Filter (S-EGF) are common filters used in ORN. Multi-Epipolar Geometry-based Filter (M-EGF) has been introduced, tested and evaluated by the author and compared by each filter of those mentioned above in separate research papers. This paper comes to include all these individually comparisons, with additional details, showing the advantages and limitations of all filters comparing to each other. Tests show that C-2DF and A-2DF have failed to deal with AIM results in areas with open, narrow, and confused DOF. Also, they have failed to find out the right mathematical model in data with high rate of mismatched points and data obtained from images with difficult view angles. With limited DOF and low rate of errors, C-2DF and A-2DF have provided relatively sufficient results, which can be used for ORN applications that do not require precision. A-2DF is relatively better than C-2DF due to its flexibility to deal with figures including different scales, which is the case when dealing with different levels of DOF and different capturing angles between the cameras. The processing time is another disadvantage of C-2DF and A-2DF, where these are based on iterative estimation methods. Tests display how A-2DF is slowest, which keeps it away from using with real time ORN applications. Tests show that S-EGF and M-EGF are timesaving and able to deal with any AIM results, regardless the DOF, view angle and errors rate in observations. S-EGF is affected in areas including lines parallel to the cameras base line. M-EGF has offered the best results in terms of providing error-free filtered matched points in all tests. This can be attributed to the high restriction level of this filter, where the probability for the mismatched point to pass throughput the three co-planarity equations is nearly zero. M-EGF and S-EGF are affected by the quality of the Interior Orientation Elements (IOEs) and Exterior Orientation Parameters (EOPs) of the three cameras, leading to rejection a small number of corrected matched points, which can be avoided with professionally manufactured ORN systems. Tests illustrated that S-EGF and M-EGF are extremely high-speed and S-EGF is the faster and M-EGF, C-2DF, and A-2DF comes after, respectively. All results indicated that M-EGF is the best, as it is fast, restricted, reliable, and error-free technique and is suitable for real-time precise ORN applications.

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4

Mustafa, M. Amami. "Multi and single epipolar geometry-based filters vs. affine and conformal 2D transformation-based filters." Global Journal of Engineering and Technology Advances 10, no. 3 (2022): 032–51. https://doi.org/10.5281/zenodo.6402367.

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The accuracy of Optical Robot Navigation (ORN) depends mainly on the quality of the Automatic Image Matching (AIM) results. Conformal 2D transformation-based Filter (C-2DF), affine 2D transformation-based Filter (A-2DF) and Single Epipolar Geometry-based Filter (S-EGF) are common filters used in ORN. Multi-Epipolar Geometry-based Filter (M-EGF) has been introduced, tested and evaluated by the author and compared by each filter of those mentioned above in separate research papers. This paper comes to include all these individually comparisons, with additional details, showing the advantages and limitations of all filters comparing to each other. Tests show that C-2DF and A-2DF have failed to deal with AIM results in areas with open, narrow, and confused DOF. Also, they have failed to find out the right mathematical model in data with high rate of mismatched points and data obtained from images with difficult view angles. With limited DOF and low rate of errors, C-2DF and A-2DF have provided relatively sufficient results, which can be used for ORN applications that do not require precision. A-2DF is relatively better than C-2DF due to its flexibility to deal with figures including different scales, which is the case when dealing with different levels of DOF and different capturing angles between the cameras. The processing time is another disadvantage of C-2DF and A-2DF, where these are based on iterative estimation methods. Tests display how A-2DF is slowest, which keeps it away from using with real time ORN applications. Tests show that S-EGF and M-EGF are timesaving and able to deal with any AIM results, regardless the DOF, view angle and errors rate in observations. S-EGF is affected in areas including lines parallel to the cameras base line. M-EGF has offered the best results in terms of providing error-free filtered matched points in all tests. This can be attributed to the high restriction level of this filter, where the probability for the mismatched point to pass throughput the three co-planarity equations is nearly zero. M-EGF and S-EGF are affected by the quality of the Interior Orientation Elements (IOEs) and Exterior Orientation Parameters (EOPs) of the three cameras, leading to rejection a small number of corrected matched points, which can be avoided with professionally manufactured ORN systems. Tests illustrated that S-EGF and M-EGF are extremely high-speed and S-EGF is the faster and M-EGF, C-2DF, and A-2DF comes after, respectively. All results indicated that M-EGF is the best, as it is fast, restricted, reliable, and error-free technique and is suitable for real-time precise ORN applications.

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5

Ziggah, Yao Yevenyo, Youjina Hu, Yakubu Issaka, and Prosper Basommi Laari. "LEAST SQUARES SUPPORT VECTOR MACHINE MODEL FOR COORDINATE TRANSFORMATION." Geodesy and cartography 45, no. 5 (2019): 16–27. http://dx.doi.org/10.3846/gac.2019.6053.

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In coordinate transformation, the main purpose is to provide a mathematical relationship between coordinates related to different geodetic reference frames. This gives the geospatial professionals the opportunity to link different datums together. Review of previous studies indicates that empirical and soft computing models have been proposed in recent times for coordinate transformation. The main aim of this study is to present the applicability and performance of Least Squares Support Vector Machine (LS-SVM) which is an extension of the Support Vector Machine (SVM) for coordinate transformation. For comparison purpose, the SVM and the widely used Backpropagation Neural Network (BPNN), Radial Basis Function Neural Network (RBFNN), 2D conformal and affine methods were also employed. To assess how well the transformation results fit the observed data, the root mean square of the residual horizontal distances and standard deviation were used. From the results obtained, the LS-SVM and RBFNN had comparable results and were better than the other methods. The overall statistical findings produced by LS-SVM met the accuracy requirement for cadastral surveying applications in Ghana. To this end, the proposed LS-SVM is known to possess promising predictive capabilities and could efficiently be used as a supplementary technique for coordinate transformation.

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Amami, Mustafa M. "Comparison between Multi Epipolar Geometry & Affine 2d Transformation-Based Filters for Optical Robot Navigation." International Journal for Research in Applied Science and Engineering Technology 10, no. 3 (2022): 399–409. http://dx.doi.org/10.22214/ijraset.2022.40652.

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Abstract: In previous research papers, Multi Epipolar Geometry-based Filter (M-EGF) has proven its high capability to overcome Single Epipolar Geometry-based Filter (S-EGF) as well as with conformal 2D Transformation-based Filter (C-2DF) in terms of providing precise, trusted, outlier-free, and real time Automatic Image Matching (AIM) results for Optical Robot Navigation (ORN) applications. This paper comes in a series of comparing M-EGF with the most common filters extensively used in ORN. Affine 2D Transformation-based Filter (A-2DF) is another familiar filter used for detecting outliers in AIM results and regards as the advanced version of C-2DF, where it can deal with any changing or distortion in image scales in X and Y directions. In this paper, M-EGF has been compared with A-2DF using the same system, tests, tracks and images and the same evaluation techniques used for comparing M-EGF to S-EGF and C-2DF in the related research papers. Tests show that A-2DF is similar to C-2DF in terms of its disability to filter AIM results in areas with open, narrow, and confused Depth Of Field (DOF). A-2DF is also limited in terms of finding out the 6 correct parameters for its mathematical model when AIM results includes a significant number of mismatching points. Difficult view angles has also a noted effect on the performance of A-2DF, but less than that of C-2DF due to its ability to work with different scales. In tests including limited DOF and low level of outliers, A-2DF has shown comparatively adequate outcomes, that is suitable for non-sensitive applications, in which the error does not entail any serious consequences. A-2DF is independent of the errors in Exterior Orientation Parameters (EOP) and Interior Orientation Elements (IOE) of cameras, where it is image points dependent estimation filter. Tests show that M-EGF is time- effective, efficient with any AIM findings, regardless DOF, capturing angle, outliers rate in observations, type of features and tracks. Unlike, A-2DF, tests show that the performance of M-EGF can affect by the quality of IOEs and EOPs, as a number of correctly matched points might be rejected, and this limitation is not related to the filter mathematical design but the professionalism of cameras calibration and EOP determination. in terms of processing time, A-2DF is considerably slow comparing with M-EGF due to its iterative and repeatability design, which makes it, unlike MEGF, unsuitable for real-time precise ORN applications. Keywords: Optical Robot Navigation, Epipolar Geometry, Automatic Image Matching, Co-planarity Equation, Real Time Applications, Affine 2D Transformation

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HOU, BO-YU, and WEN-LI YANG. "THE DRESSING TRANSFORMATION OF THE CONFORMAL AFFINE TODA." International Journal of Modern Physics A 09, no. 17 (1994): 2997–3006. http://dx.doi.org/10.1142/s0217751x94001187.

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We study the dressing transformations of the conformal affine [Formula: see text] Todal which can be obtained from a Hamiltonian reduction. As a special case, we obtain the dressing transformations of the sinh-Gordon model. We will show that the dressing group is the semiclassical limit of the quantum group [Formula: see text]. We will also obtain the algebra of the charges which generate the infinitesimal dressing transformations.

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BABARO, JUAN PABLO, and GASTON GIRIBET. "ON THE DESCRIPTION OF SURFACE OPERATORS IN ${\mathcal N} = 2^*$ SYM." Modern Physics Letters A 28, no. 06 (2013): 1330003. http://dx.doi.org/10.1142/s0217732313300036.

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Alday and Tachikawa [Lett. Math. Phys.94, 87 (2010)] observed that the Nekrasov partition function of [Formula: see text] superconformal gauge theories in the presence of fundamental surface operators can be associated to conformal blocks of a 2D CFT with affine sl(2) symmetry. This can be interpreted as the insertion of a fundamental surface operator changing the conformal symmetry from the Virasoro symmetry discovered in Ref. 2 to the affine Kac–Moody symmetry. A natural question arises as to how such a 2D CFT description can be extended to the case of non-fundamental surface operators. Motivated by this question, we review the results [Y. Hikida and V. Schomerus, JHEP0710, 064 (2007); S. Ribault, JHEP0805, 073 (2008)] and put them together to suggest a way to address the problem: It follows from this analysis that the expectation value of a non-fundamental surface operator in the SU(2) [Formula: see text] super Yang–Mills (YM) theory would be in correspondence with the expectation value of a single vertex operator in a two-dimensional CFT with reduced affine symmetry and whose central charge is parametrized by the integer number that labels the type of singularity of the surface operator.

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Mihai, I., A. Oiagă, and R. Rosca. "On a class of even-dimensional manifolds structured by an affine connection." International Journal of Mathematics and Mathematical Sciences 29, no. 11 (2002): 681–86. http://dx.doi.org/10.1155/s0161171202011390.

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We deal with a2m-dimensional Riemannian manifold(M,g)structured by an affine connection and a vector field𝒯, defining a𝒯-parallel connection. It is proved that𝒯is both a torse forming vector field and an exterior concurrent vector field. Properties of the curvature2-forms are established. It is shown thatMis endowed with a conformal symplectic structureΩand𝒯defines a relative conformal transformation ofΩ.

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BELGIORNO, F., A. S. CATTANEO, F. FUCITO, and M. MARTELLINI. "A CONFORMAL AFFINE TODA MODEL OF 2D BLACK HOLES: A QUANTUM STUDY OF THE EVAPORATION END POINT." Modern Physics Letters A 08, no. 27 (1993): 2593–605. http://dx.doi.org/10.1142/s021773239300297x.

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In this paper we reformulate the dilaton-gravity theory of Callan et al. as a new effective conformal field theory which turns out to be a generalization of the so-called SL 2-conformal affine Toda (CAT) theory studied some time ago by Babelon and Bonora. We quantize this model, thus keeping in account the dilaton-gravity quantum effects. We then implement a Renormalization Group analysis to study the black hole thermodynamics and the final state of the Hawking evaporation.

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Book chapters on the topic "Affine and Conformal 2D Transformation"

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Kobayashi, Shoshichi. "Affine, Conformal and Projective Transformations." In Transformation Groups in Differential Geometry. Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-61981-6_4.

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Anjyo, Ken, and Hiroyuki Ochiai. "2D Affine Transformation between Two Triangles." In Mathematical Basics of Motion and Deformation in Computer Graphics, Second Edition. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-031-02592-1_5.

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Anjyo, Ken, and Hiroyuki Ochiai. "2D Affine Transformation between Two Triangles." In Mathematical Basics of Motion and Deformation in Computer Graphics. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-031-79561-9_5.

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Conference papers on the topic "Affine and Conformal 2D Transformation"

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Ou, Junhai, and Jiangqun Ni. "Blind estimation of affine transformation using 2D cyclostationarity of resampled images." In Ninth International Symposium on Multispectral Image Processing and Pattern Recognition (MIPPR2015), edited by Zhiguo Cao, Jayaram K. Udupa, and Henri Maître. SPIE, 2015. http://dx.doi.org/10.1117/12.2205468.

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Pan, Yijie, Yongtian Wang, Juan Liu, Xin Li, and Jia Jia. "Fast polygon-based method using 2D Fourier analysis of 3D affine transformation." In Digital Holography and Three-Dimensional Imaging. OSA, 2013. http://dx.doi.org/10.1364/dh.2013.dtu1a.3.

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Wakahara, Toru, and Seiichi Uchida. "Hierarchical Decomposition of Handwriting Deformation Vector Field Using 2D Warping and Global/Local Affine Transformation." In 2009 10th International Conference on Document Analysis and Recognition. IEEE, 2009. http://dx.doi.org/10.1109/icdar.2009.33.

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Shults, Roman, Asset Urazaliev, Andriy Annenkov, Olena Nesterenko, Oksana Kucherenko, and Kateryna Kim. "Different Approaches to Coordinate Transformation Parameters Determination of Nonhomogeneous Coordinate Systems." In 11th International Conference “Environmental Engineering”. VGTU Technika, 2020. http://dx.doi.org/10.3846/enviro.2020.687.

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During reconstruction and restoration of city geodetic networks, there is quite a common problem that is related to the nonhomogeneity of existing geodetic networks. In any city, local authorities operate with their coordinate systems. Such conditions lead to inconsistency between data of different services. There is only one way how to overcome the problem that lies in the creation and deployment of the new common coordinate system for the whole city. But such an approach has a lack connected with the necessity of transformation parameters acquisition for the latest and old coordinate systems. Insofar as old coordinate systems had been created with different accuracy, using various equipment, and measuring technologies, it is not possible to consider them as homogeneous. It means that we cannot use a classical conformal Helmert transformation to link different coordinate systems. In the presented paper were studied the different approaches for transformation parameters acquisition. A case study of the Almaty city coordinate system was researched and compared the following methods: Helmert transformation, bilinear transformation, the second and third-order regression transformation, and the fourth-order conformal polynomial transformation. It was found out that neither of the considered methods maintains the necessary transformation accuracy (>5 cm). That is why the creation of the transformation field using the finite element method (FEM) was suggested. The whole city was divided into triangles using Delaunay triangulation. For each triangle, the transformation parameters were found using affine transformation with the necessary accuracy.

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Haoge, Liu, Md Motiur Rahman, and Jing Lu. "Analytical Solution of Stress State Wellbore Instability Due to Collapse Washout and Induced Fractures." In IADC/SPE Asia Pacific Drilling Technology Conference. SPE, 2021. http://dx.doi.org/10.2118/201021-ms.

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Abstract Wellbore suffers from washout, partial collapse and induced fractures, making it more likely to be elliptical rather than circular. The classic stress analysis of a wellbore, which regards the wellbore as circular, is actually not so suitable. Based on the linear elasticity, this paper introduces the 2D analytical solution of stress state for wellbore instability. Analytical results, compared to numerical, show how the wellbore pressure would be maintained to prevent wellbore instability while drilling. Analytical solution of stress analysis is proposed for complicated models where the wellbore is regarded as non-circular. Stress problems of a 2D linear elastic model are simplified with mathematical equations. Muskhelishvili theory is used for complex analyses for stress analysis in elasticity. Then the stress state of the formation is obtained, where finding a suitable conformal transformation to map the formation area into a unit circle is crucial in the process. Finite Element Method (FEM) is also applied for the same case. Finally, the analytical result is compared to the numerical result, considering collapse, washout and induced fractures in wellbore. Typical data set are used for a vertical wellbore. By comparing to the numerical results (FEM), the simplicity for calculation and the correctness of the analytical solution is established whereas it is found that the intrinsic error of numerical solution cannot be eliminated. Results show that with larger boundary sizes, the FEM result become closer to the analytical result. A conformal transformation for the wellbore mapping with fractures was found. Trials have been done to the fractured wellbore, which can be regarded as a stress cage model, while two mathematical problems in solving the stress state analytically on the vertical wellbore with fractures were encountered. Trial and suggestions towards solving these two problems with results are introduced in details. Stress state of the formation has been calculated and plotted by using the analytical solution. Results show the stress contours plotted by analytical solution in Mathematica™, and the ones plotted by FEM with boundary size set as 2000 mm in Solidworks™. The stress states calculated by these two methods match quite well, which means the proposed analytical solution is correct. An insightful sensitivity analysis (with elliptical factor of wellbore and anisotropic factor of the tectonic stresses) will be presented. For decades, numerical method for stress analysis has been applied, ignoring the development of analytical method. It's the complexity of analytical solution that makes it difficult to handle. However, based on the same simplifications for an engineering problem, analytical method is always faster and more accurate compared to the numerical solution in many cases. The analytical solution provides the possibility for process control in real-time technologies and this can be applied to wellbore instability case of collapse, washout and fractures.

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Sahlabadi, Mohammad, Yao Zhao, Kyle Jezler, et al. "Polydopamine Coating for Thermal Insulation of Shape Memory Alloy Wires." In ASME 2016 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/smasis2016-9265.

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Shape memory alloy (SMA) materials, such as Nickel Titanium (NiTi), can generate stress and strain during phase transformation induced by thermomechanical stimulation. Therefore, they may be used to construct active actuating devices for various biomedical applications such as smart surgical tools. Since temperature rise during the operation of SMA devices may damage the surrounding tissue, it is important to thermally shield such devices. We propose to use polydopamine (PDA) as an insulating coating for NiTi-based smart needles. PDA is a biomolecule (dopamine) derived polymer that can form conformal coating on various materials including NiTi. It is hypothesized that the surface temperature of the PDA coated needle can be reduced by the low thermal conductivity of PDA and the thermal resistance of the PDA/NiTi interface. Our experiments conducted in ambient air at room temperature showed that the coating reduced the surface temperature by as much as 45%. In this paper, we will present the thermal insulating performance of the PDA coating on NiTi wires. An experimental setup where the wire is embedded inside a gel phantom/tissue has been developed to simulate needle-tissue interaction. Effects of the coating thickness (material thermal resistance) and the number of layers (interfacial thermal resistance) will be discussed. 2D finite element analyses (FEA) were performed using ABAQUS to investigate the thermal distribution around the coated NiTi wires and the tissue gel phantom. In addition, using thermal distribution, potential tissue damage was assessed.

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