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Fernando De La Torre - One of the best experts on this subject based on the ideXlab platform.
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Subspace Procrustes Analysis
International Journal of Computer Vision, 2017Co-Authors: Xavier Perez-sala, Fernando De La Torre, Laura Igual, Sergio Escalera, Cecilio AnguloAbstract:Procrustes Analysis (PA) has been a popular technique to align and build 2-D statistical models of shapes. Given a set of 2-D shapes PA is applied to remove rigid transformations. Later, a non-rigid 2-D model is computed by modeling the residual (e.g., PCA). Although PA has been widely used, it has several limitations for modeling 2-D shapes: occluded landmarks and missing data can result in local minima solutions, and there is no guarantee that the 2-D shapes provide a uniform sampling of the 3-D space of rotations for the object. To address previous issues, this paper proposes subspace PA (SPA). Given several instances of a 3-D object, SPA computes the mean and a 2-D subspace that can model rigid and non-rigid deformations of the 3-D object. We propose a discrete (DSPA) and continuous (CSPA) formulation for SPA, assuming that 3-D samples of an object are provided. DSPA extends the traditional PA, and produces unbiased 2-D models by uniformly sampling different views of the 3-D object. CSPA provides a continuous approach to uniformly sample the space of 3-D rotations, being more efficient in space and time. We illustrate the benefits of SPA in two different applications. First, SPA is used to learn 2-D face and body models from 3-D datasets. Experiments on the FaceWarehouse and CMU motion capture (MoCap) datasets show the benefits of our 2-D models against the state-of-the-art PA approaches and conventional 3-D models. Second, SPA learns an unbiased 2-D model from CMU MoCap dataset and it is used to estimate the human pose on the Leeds Sports dataset.
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subspace Procrustes Analysis
European Conference on Computer Vision, 2014Co-Authors: Xavier Perezsala, Fernando De La Torre, Laura Igual, Sergio Escalera, Cecilio AnguloAbstract:Procrustes Analysis (PA) has been a popular technique to align and build 2-D statistical models of shapes. Given a set of 2-D shapes PA is applied to remove rigid transformations. Then, a non-rigid 2-D model is computed by modeling (e.g., PCA) the residual. Although PA has been widely used, it has several limitations for modeling 2-D shapes: occluded landmarks and missing data can result in local minima solutions, and there is no guarantee that the 2-D shapes provide a uniform sampling of the 3-D space of rotations for the object. To address previous issues, this paper proposes Subspace PA (SPA). Given several instances of a 3-D object, SPA computes the mean and a 2-D subspace that can simultaneously model all rigid and non-rigid deformations of the 3-D object. We propose a discrete (DSPA) and continuous (CSPA) formulation for SPA, assuming that 3-D samples of an object are provided. DSPA extends the traditional PA, and produces unbiased 2-D models by uniformly sampling different views of the 3-D object. CSPA provides a continuous approach to uniformly sample the space of 3-D rotations, being more effcient in space and time. Experiments using SPA to learn 2-D models of bodies from motion capture data illustrate the benefits of our approach.
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ECCV Workshops (1) - Subspace Procrustes Analysis
Computer Vision - ECCV 2014 Workshops, 2014Co-Authors: Xavier Perez-sala, Fernando De La Torre, Laura Igual, Sergio Escalera, Cecilio AnguloAbstract:Procrustes Analysis (PA) has been a popular technique to align and build 2-D statistical models of shapes. Given a set of 2-D shapes PA is applied to remove rigid transformations. Then, a non-rigid 2-D model is computed by modeling (e.g., PCA) the residual. Although PA has been widely used, it has several limitations for modeling 2-D shapes: occluded landmarks and missing data can result in local minima solutions, and there is no guarantee that the 2-D shapes provide a uniform sampling of the 3-D space of rotations for the object. To address previous issues, this paper proposes Subspace PA (SPA). Given several instances of a 3-D object, SPA computes the mean and a 2-D subspace that can simultaneously model all rigid and non-rigid deformations of the 3-D object. We propose a discrete (DSPA) and continuous (CSPA) formulation for SPA, assuming that 3-D samples of an object are provided. DSPA extends the traditional PA, and produces unbiased 2-D models by uniformly sampling different views of the 3-D object. CSPA provides a continuous approach to uniformly sample the space of 3-D rotations, being more effcient in space and time. Experiments using SPA to learn 2-D models of bodies from motion capture data illustrate the benefits of our approach.
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continuous generalized Procrustes Analysis
Pattern Recognition, 2014Co-Authors: Laura Igual, Xavier Perezsala, Sergio Escalera, Cecilio Angulo, Fernando De La TorreAbstract:Two-dimensional shape models have been successfully applied to solve many problems in computer vision, such as object tracking, recognition, and segmentation. Typically, 2D shape models are learned from a discrete set of image landmarks (corresponding to projection of 3D points of an object), after applying Generalized Procustes Analysis (GPA) to remove 2D rigid transformations. However, the standard GPA process suffers from three main limitations. Firstly, the 2D training samples do not necessarily cover a uniform sampling of all the 3D transformations of an object. This can bias the estimate of the shape model. Secondly, it can be computationally expensive to learn the shape model by sampling 3D transformations. Thirdly, standard GPA methods use only one reference shape, which can might be insufficient to capture large structural variability of some objects.To address these drawbacks, this paper proposes continuous generalized Procrustes Analysis (CGPA). CGPA uses a continuous formulation that avoids the need to generate 2D projections from all the rigid 3D transformations. It builds an efficient (in space and time) non-biased 2D shape model from a set of 3D model of objects. A major challenge in CGPA is the need to integrate over the space of 3D rotations, especially when the rotations are parameterized with Euler angles. To address this problem, we introduce the use of the Haar measure. Finally, we extended CGPA to incorporate several reference shapes. Experimental results on synthetic and real experiments show the benefits of CGPA over GPA. HighlightsContinuous formulation of the generalized Procrustes Analysis.CGPA avoids the need to generate 2D projections from all 3D rigid transformations.CGPA builds an efficient non-biased 2D shape model from 3D objects.CGPA uses the Haar measure to integrate over the space of 3D rotations.Experimental results building 2D shape models for different public datasets.
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continuous Procrustes Analysis to learn 2d shape models from 3d objects
Computer Vision and Pattern Recognition, 2010Co-Authors: Laura Igual, Fernando De La TorreAbstract:Two dimensional shape models have been successfully applied to solve many problems in computer vision such as object tracking, recognition and segmentation. Typically, 2D shape models (e.g. Point Distribution Models, Active Shape Models) are learned from a discrete set of image landmarks once the rigid transformations are removed applying Procrustes Analysis (PA). However, the standard PA process suffers from two main limitations: (i) the 2D training samples do not necessarily cover a uniform sampling of all 3D transformations of an object. This can bias the estimate of the shape model; (ii) it can be computationally expensive to learn the shape model by sampling 3D transformations; To solve these problems, we propose Continuous Procrustes Analysis (CPA). CPA uses a continuous formulation that avoids the need to generate 2D projections from all 3D rigid transformations. Furthermore, it builds an efficient (space and time) non-biased 2D shape model from a 3D model of an object. Preliminary experimental results to build 2D shape models of objects and faces show the benefits of CPA over PA.
Laura Igual - One of the best experts on this subject based on the ideXlab platform.
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Subspace Procrustes Analysis
International Journal of Computer Vision, 2017Co-Authors: Xavier Perez-sala, Fernando De La Torre, Laura Igual, Sergio Escalera, Cecilio AnguloAbstract:Procrustes Analysis (PA) has been a popular technique to align and build 2-D statistical models of shapes. Given a set of 2-D shapes PA is applied to remove rigid transformations. Later, a non-rigid 2-D model is computed by modeling the residual (e.g., PCA). Although PA has been widely used, it has several limitations for modeling 2-D shapes: occluded landmarks and missing data can result in local minima solutions, and there is no guarantee that the 2-D shapes provide a uniform sampling of the 3-D space of rotations for the object. To address previous issues, this paper proposes subspace PA (SPA). Given several instances of a 3-D object, SPA computes the mean and a 2-D subspace that can model rigid and non-rigid deformations of the 3-D object. We propose a discrete (DSPA) and continuous (CSPA) formulation for SPA, assuming that 3-D samples of an object are provided. DSPA extends the traditional PA, and produces unbiased 2-D models by uniformly sampling different views of the 3-D object. CSPA provides a continuous approach to uniformly sample the space of 3-D rotations, being more efficient in space and time. We illustrate the benefits of SPA in two different applications. First, SPA is used to learn 2-D face and body models from 3-D datasets. Experiments on the FaceWarehouse and CMU motion capture (MoCap) datasets show the benefits of our 2-D models against the state-of-the-art PA approaches and conventional 3-D models. Second, SPA learns an unbiased 2-D model from CMU MoCap dataset and it is used to estimate the human pose on the Leeds Sports dataset.
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subspace Procrustes Analysis
European Conference on Computer Vision, 2014Co-Authors: Xavier Perezsala, Fernando De La Torre, Laura Igual, Sergio Escalera, Cecilio AnguloAbstract:Procrustes Analysis (PA) has been a popular technique to align and build 2-D statistical models of shapes. Given a set of 2-D shapes PA is applied to remove rigid transformations. Then, a non-rigid 2-D model is computed by modeling (e.g., PCA) the residual. Although PA has been widely used, it has several limitations for modeling 2-D shapes: occluded landmarks and missing data can result in local minima solutions, and there is no guarantee that the 2-D shapes provide a uniform sampling of the 3-D space of rotations for the object. To address previous issues, this paper proposes Subspace PA (SPA). Given several instances of a 3-D object, SPA computes the mean and a 2-D subspace that can simultaneously model all rigid and non-rigid deformations of the 3-D object. We propose a discrete (DSPA) and continuous (CSPA) formulation for SPA, assuming that 3-D samples of an object are provided. DSPA extends the traditional PA, and produces unbiased 2-D models by uniformly sampling different views of the 3-D object. CSPA provides a continuous approach to uniformly sample the space of 3-D rotations, being more effcient in space and time. Experiments using SPA to learn 2-D models of bodies from motion capture data illustrate the benefits of our approach.
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ECCV Workshops (1) - Subspace Procrustes Analysis
Computer Vision - ECCV 2014 Workshops, 2014Co-Authors: Xavier Perez-sala, Fernando De La Torre, Laura Igual, Sergio Escalera, Cecilio AnguloAbstract:Procrustes Analysis (PA) has been a popular technique to align and build 2-D statistical models of shapes. Given a set of 2-D shapes PA is applied to remove rigid transformations. Then, a non-rigid 2-D model is computed by modeling (e.g., PCA) the residual. Although PA has been widely used, it has several limitations for modeling 2-D shapes: occluded landmarks and missing data can result in local minima solutions, and there is no guarantee that the 2-D shapes provide a uniform sampling of the 3-D space of rotations for the object. To address previous issues, this paper proposes Subspace PA (SPA). Given several instances of a 3-D object, SPA computes the mean and a 2-D subspace that can simultaneously model all rigid and non-rigid deformations of the 3-D object. We propose a discrete (DSPA) and continuous (CSPA) formulation for SPA, assuming that 3-D samples of an object are provided. DSPA extends the traditional PA, and produces unbiased 2-D models by uniformly sampling different views of the 3-D object. CSPA provides a continuous approach to uniformly sample the space of 3-D rotations, being more effcient in space and time. Experiments using SPA to learn 2-D models of bodies from motion capture data illustrate the benefits of our approach.
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continuous generalized Procrustes Analysis
Pattern Recognition, 2014Co-Authors: Laura Igual, Xavier Perezsala, Sergio Escalera, Cecilio Angulo, Fernando De La TorreAbstract:Two-dimensional shape models have been successfully applied to solve many problems in computer vision, such as object tracking, recognition, and segmentation. Typically, 2D shape models are learned from a discrete set of image landmarks (corresponding to projection of 3D points of an object), after applying Generalized Procustes Analysis (GPA) to remove 2D rigid transformations. However, the standard GPA process suffers from three main limitations. Firstly, the 2D training samples do not necessarily cover a uniform sampling of all the 3D transformations of an object. This can bias the estimate of the shape model. Secondly, it can be computationally expensive to learn the shape model by sampling 3D transformations. Thirdly, standard GPA methods use only one reference shape, which can might be insufficient to capture large structural variability of some objects.To address these drawbacks, this paper proposes continuous generalized Procrustes Analysis (CGPA). CGPA uses a continuous formulation that avoids the need to generate 2D projections from all the rigid 3D transformations. It builds an efficient (in space and time) non-biased 2D shape model from a set of 3D model of objects. A major challenge in CGPA is the need to integrate over the space of 3D rotations, especially when the rotations are parameterized with Euler angles. To address this problem, we introduce the use of the Haar measure. Finally, we extended CGPA to incorporate several reference shapes. Experimental results on synthetic and real experiments show the benefits of CGPA over GPA. HighlightsContinuous formulation of the generalized Procrustes Analysis.CGPA avoids the need to generate 2D projections from all 3D rigid transformations.CGPA builds an efficient non-biased 2D shape model from 3D objects.CGPA uses the Haar measure to integrate over the space of 3D rotations.Experimental results building 2D shape models for different public datasets.
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continuous Procrustes Analysis to learn 2d shape models from 3d objects
Computer Vision and Pattern Recognition, 2010Co-Authors: Laura Igual, Fernando De La TorreAbstract:Two dimensional shape models have been successfully applied to solve many problems in computer vision such as object tracking, recognition and segmentation. Typically, 2D shape models (e.g. Point Distribution Models, Active Shape Models) are learned from a discrete set of image landmarks once the rigid transformations are removed applying Procrustes Analysis (PA). However, the standard PA process suffers from two main limitations: (i) the 2D training samples do not necessarily cover a uniform sampling of all 3D transformations of an object. This can bias the estimate of the shape model; (ii) it can be computationally expensive to learn the shape model by sampling 3D transformations; To solve these problems, we propose Continuous Procrustes Analysis (CPA). CPA uses a continuous formulation that avoids the need to generate 2D projections from all 3D rigid transformations. Furthermore, it builds an efficient (space and time) non-biased 2D shape model from a 3D model of an object. Preliminary experimental results to build 2D shape models of objects and faces show the benefits of CPA over PA.
Fabio Crosilla - One of the best experts on this subject based on the ideXlab platform.
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Procrustes Analysis for the virtual trial assembly of large-size elements
Robotics and Computer-integrated Manufacturing, 2020Co-Authors: Eleonora Maset, Fabio Crosilla, L. Scalera, D. Zonta, I.m. Alba, Andrea FusielloAbstract:Abstract Virtual assembly is an essential method to increase efficiency and to identify potential issues of the assembly process in several manufacturing fields, as for instance robotized assembly. The paper presents a novel procedure based on Affine Procrustes Analysis for the Virtual Trial Assembly (VTA) of large-size elements. This approach to virtual assembly allows to identify possible discrepancies between the workpieces and their nominal specifications, and to automatically define shape and dimensions of the potential corrective elements needed to achieve the designed assembly. The method is a variation of the classical Extended Orthogonal Procrustes Analysis (a tool that provides the least squares alignment among corresponding points), and permits to easily verify the parallelism condition of planes of large-size elements and the satisfaction of the alignment tolerances in the components to be assembled. Furthermore, the method implicitly takes into account the presence of corrective elements, avoiding assembly errors propagation. Experiments show the feasibility of the proposed approach and its advantages with respect to the classical one. The novel method is applied to the challenging assembly of dogbones elements of Vessel in New York.
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Orthogonal Procrustes Analysis
Advanced Procrustes Analysis Models in Photogrammetric Computer Vision, 2019Co-Authors: Fabio Crosilla, Alberto Beinat, Andrea Fusiello, Eleonora Maset, Domenico VisintiniAbstract:The terms Procrustes Analysis and Procrustes Techniques are referred to a set of least squares mathematical models used to perform transformations among corresponding points belonging to a generic k-dimensional space, in order to satisfy their maximum agreement.
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Applications of Anisotropic Procrustes Analysis
Advanced Procrustes Analysis Models in Photogrammetric Computer Vision, 2019Co-Authors: Fabio Crosilla, Alberto Beinat, Andrea Fusiello, Eleonora Maset, Domenico VisintiniAbstract:As extensively shown in the previous chapters, Procrustes Analysis allows to easily perform transformations among corresponding point coordinates belonging to a generic k-dimensional space and it is therefore suited to solve problems encountered in geodesy, photogrammetric computer vision, and laser scanning.
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errors in variables anisotropic extended orthogonal Procrustes Analysis
IEEE Geoscience and Remote Sensing Letters, 2017Co-Authors: Eleonora Maset, Fabio Crosilla, Andrea FusielloAbstract:This letter presents a novel total least squares (TLS) solution of the anisotropic row-scaling Procrustes problem. The ordinary LS Procrustes approach finds the transformation parameters between origin and destination sets of observations minimizing errors affecting only the destination one. In this letter, we introduce the errors-in-variables model in the anisotropic Procrustes Analysis problem and present a solution that can deal with the uncertainty affecting both sets of observations. The algorithm is applied to solve the image exterior orientation problem. Experiments show that the proposed TLS method leads to an accuracy in the parameters estimation that is higher than the one reached with the ordinary LS anisotropic Procrustes solution when the number of points, whose coordinates are known in both the image and the external systems, is small.
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solving bundle block adjustment by generalized anisotropic Procrustes Analysis
Isprs Journal of Photogrammetry and Remote Sensing, 2015Co-Authors: Andrea Fusiello, Fabio CrosillaAbstract:Abstract The paper presents a new analytical tool to solve the classical photogrammetric bundle block adjustment. The analytical model is based on the generalized extension of the anisotropic row-scaling Procrustes Analysis, that has been recently proposed by the same authors to solve the image exterior orientation problem. The main advantage of the method is given by the fact that the problem solution does not require any approximate value of the unknown parameters, nor any linearization procedure. Moreover, the algorithm is exceedingly simple to describe and easy to implement. Empirical results indicate that a zero-information initialization of the iterative relaxation procedure leads almost always to the correct final least squares solution. Experiments confirm the accuracy of the proposed method, when compared to the results obtained by applying a classical photogrammetric bundle block adjustment.
Garmt Dijksterhuis - One of the best experts on this subject based on the ideXlab platform.
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generalised Procrustes Analysis with optimal scaling exploring data from a power supplier
Computational Statistics & Data Analysis, 2009Co-Authors: Jaap E Wieringa, Garmt Dijksterhuis, J. C. Gower, Frederieke Van PerloAbstract:Generalised Procrustes Analysis (GPA) is a method for matching several, possibly large, data sets by fitting them to each other using transformations, typically rotations. The linear version of GPA has been applied in a wide range of contexts. A non-linear extension of GPA is developed which uses Optimal Scaling (OS). The approach is suited to match data sets that contain nominal variables. A database of a Dutch power supplier that contains many categorical variables unfit for the usual linear GPA methodology is used to illustrate the approach.
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Procrustes Analysis in studying sensory instrumental relations
Food Quality and Preference, 1994Co-Authors: Garmt DijksterhuisAbstract:In this paper the relation between a sensory and an instrumental dataset is studied by means of Procrustes Analysis. The method is introduced with emphasis on its application to match two datasets. First the structure of each dataset is studied separately by means of Principal Component Analysis. After standardising the two datasets Procrustes Analysis is used to match the two sets. It is concluded that, though not often used to this end, Procrustes Analysis is a suitable method to study the relations between sensory and instrumental data.
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Multivariate Data Analysis in Sensory and Consumer Science - Procrustes Analysis in studying sensory-instrumental relations
Food Quality and Preference, 1994Co-Authors: Garmt DijksterhuisAbstract:In this paper the relation between a sensory and an instrumental dataset is studied by means of Procrustes Analysis. The method is introduced with emphasis on its application to match two datasets. First the structure of each dataset is studied separately by means of Principal Component Analysis. After standardising the two datasets Procrustes Analysis is used to match the two sets. It is concluded that, though not often used to this end, Procrustes Analysis is a suitable method to study the relations between sensory and instrumental data.
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the interpretation of generalized Procrustes Analysis and allied methods
Food Quality and Preference, 1991Co-Authors: Garmt Dijksterhuis, J. C. GowerAbstract:We discuss various issues surrounding the use and interpretation of Generalized Procrustes Analysis and related methods. Included are considerations that have to be made before starting an Analysis, how to handle different dimensionalities of data, when to consider fitting scaling factors and when not to, and the distinction between the number of dimensions that are needed to give an adequate fit and the number of dimensions needed for graphical representation. The distinction between signal and noise plays an important part in explaining how different methods are suitable for exploring different aspects of the data, rather than being viewed as competing methods with the same general objectives. Explanations are largely set in a geometrical context, thus keeping technical mathematics to a minimum; a common Analysis of Variance framework allows all the methods to be considered in a unified way and suggests some new ways in which these kinds of data may be analysed. The whole is illustrated by example analyses.
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interpreting generalized Procrustes Analysis Analysis of variance tables
Food Quality and Preference, 1990Co-Authors: Garmt Dijksterhuis, Pieter PunterAbstract:Abstract Two different methods for generalized Procrustes Analysis are introduced. One of the methods is used to illustrate the interpretation of the results of a conventional and of a free choice profiling experiment. The different sources of variance are partitioned over the products and judges. A relative measure corresponding to the percentage ‘variance accounted for’ is proposed as an alternative to the variance measures usually reported with GPA analyses. This relative measure is easy to interpret, graphical display of the measures helps in interpreting the ‘Analysis of variance’ tables.
Andrea Fusiello - One of the best experts on this subject based on the ideXlab platform.
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Procrustes Analysis for the virtual trial assembly of large-size elements
Robotics and Computer-integrated Manufacturing, 2020Co-Authors: Eleonora Maset, Fabio Crosilla, L. Scalera, D. Zonta, I.m. Alba, Andrea FusielloAbstract:Abstract Virtual assembly is an essential method to increase efficiency and to identify potential issues of the assembly process in several manufacturing fields, as for instance robotized assembly. The paper presents a novel procedure based on Affine Procrustes Analysis for the Virtual Trial Assembly (VTA) of large-size elements. This approach to virtual assembly allows to identify possible discrepancies between the workpieces and their nominal specifications, and to automatically define shape and dimensions of the potential corrective elements needed to achieve the designed assembly. The method is a variation of the classical Extended Orthogonal Procrustes Analysis (a tool that provides the least squares alignment among corresponding points), and permits to easily verify the parallelism condition of planes of large-size elements and the satisfaction of the alignment tolerances in the components to be assembled. Furthermore, the method implicitly takes into account the presence of corrective elements, avoiding assembly errors propagation. Experiments show the feasibility of the proposed approach and its advantages with respect to the classical one. The novel method is applied to the challenging assembly of dogbones elements of Vessel in New York.
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Orthogonal Procrustes Analysis
Advanced Procrustes Analysis Models in Photogrammetric Computer Vision, 2019Co-Authors: Fabio Crosilla, Alberto Beinat, Andrea Fusiello, Eleonora Maset, Domenico VisintiniAbstract:The terms Procrustes Analysis and Procrustes Techniques are referred to a set of least squares mathematical models used to perform transformations among corresponding points belonging to a generic k-dimensional space, in order to satisfy their maximum agreement.
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Applications of Anisotropic Procrustes Analysis
Advanced Procrustes Analysis Models in Photogrammetric Computer Vision, 2019Co-Authors: Fabio Crosilla, Alberto Beinat, Andrea Fusiello, Eleonora Maset, Domenico VisintiniAbstract:As extensively shown in the previous chapters, Procrustes Analysis allows to easily perform transformations among corresponding point coordinates belonging to a generic k-dimensional space and it is therefore suited to solve problems encountered in geodesy, photogrammetric computer vision, and laser scanning.
-
errors in variables anisotropic extended orthogonal Procrustes Analysis
IEEE Geoscience and Remote Sensing Letters, 2017Co-Authors: Eleonora Maset, Fabio Crosilla, Andrea FusielloAbstract:This letter presents a novel total least squares (TLS) solution of the anisotropic row-scaling Procrustes problem. The ordinary LS Procrustes approach finds the transformation parameters between origin and destination sets of observations minimizing errors affecting only the destination one. In this letter, we introduce the errors-in-variables model in the anisotropic Procrustes Analysis problem and present a solution that can deal with the uncertainty affecting both sets of observations. The algorithm is applied to solve the image exterior orientation problem. Experiments show that the proposed TLS method leads to an accuracy in the parameters estimation that is higher than the one reached with the ordinary LS anisotropic Procrustes solution when the number of points, whose coordinates are known in both the image and the external systems, is small.
-
solving bundle block adjustment by generalized anisotropic Procrustes Analysis
Isprs Journal of Photogrammetry and Remote Sensing, 2015Co-Authors: Andrea Fusiello, Fabio CrosillaAbstract:Abstract The paper presents a new analytical tool to solve the classical photogrammetric bundle block adjustment. The analytical model is based on the generalized extension of the anisotropic row-scaling Procrustes Analysis, that has been recently proposed by the same authors to solve the image exterior orientation problem. The main advantage of the method is given by the fact that the problem solution does not require any approximate value of the unknown parameters, nor any linearization procedure. Moreover, the algorithm is exceedingly simple to describe and easy to implement. Empirical results indicate that a zero-information initialization of the iterative relaxation procedure leads almost always to the correct final least squares solution. Experiments confirm the accuracy of the proposed method, when compared to the results obtained by applying a classical photogrammetric bundle block adjustment.
