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Procrustes Analysis (PA) has been a popular technique to align and build -D statistical models of shapes. Given a set of -D shapes PA is applied to remove rigid transformations. Then, a non-rigid -D model is computed by modeling (e.g., PCA) the residual. Although PA has been widely used, it has several limitations for modeling -D shapes: occluded landmarks and missing data can result in local minima solutions, and there is no guarantee that the -D shapes provide a uniform sampling of the -D space of rotations for the object. To address previous issues, this paper proposes Subspace PA (SPA). Given several instances of a -D object, SPA computes the mean and a -D subspace that can simultaneously model all rigid and non-rigid deformations of the -D object. We propose a discrete (DSPA) and continuous (CSPA) formulation for SPA, assuming that -D samples of an object are provided. DSPA extends the traditional PA, and produces unbiased -D models by uniformly sampling different views of the -D object. CSPA provides a continuous approach to uniformly sample the space of -D rotations, being more efficient in space and time. Experiments using SPA to learn -D models of bodies from motion capture data illustrate the benefits of our approach. Subspace Procrustes Analysis Xavier Perez-Sala1,3,4(B), Fernando De la Torre, Laura Igual, Sergio Escalera, and Cecilio Angulo 1 Fundació Privada Sant Antoni Abat, 08800 Vilanova i la Geltrú, Spain xavier.perez-sala@upc.edu 2 Robotics Institute, Carnegie Mellon University, Pittsburgh, PA 15213, USA 3 Computer Vision Center, Universitat Autònoma de Barcelona, Bellaterra, Spain 4 Universitat Politècnica de Catalunya, 08800 Vilanova i la Geltrú, Spain 5 Universitat de Barcelona, 08007 Barcelona, Spain Abstract. 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 efficient in space and time. Experiments using SPA to learn 2-D models of bodies from motion capture data illustrate the benefits of our approach. 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 efficient in space and time. Experiments using SPA to learn 2-D models of bodies from motion capture data illustrate the benefits of our approach.