Tutorials
https://diglib.eg.org:443/handle/10.2312/302
Eurographics 2013 - Tutorials2019-06-18T17:08:17ZSymmetry in Shapes - Theory and Practice
https://diglib.eg.org:443/handle/10.2312/conf.EG2013.tutorials.t9
Symmetry in Shapes - Theory and Practice
Mitra, Niloy; Ovsjanikov, Maksim; Pauly, Mark; Wand, Michael; Ceylan, Duygu
Diego Gutierrez and Karol Myszkowski
Part I: What is symmetry? Part II: Extrinsic symmetry detection Part III: Intrinsic symmetries Part IV: Representations and applications Conclusions, wrap-up
2013-01-01T00:00:00ZNatural Image Statistics: Foundations and Applications
https://diglib.eg.org:443/handle/10.2312/conf.EG2013.tutorials.t8
Natural Image Statistics: Foundations and Applications
Pouli, Tania; Cunningham, Douglas; Reinhard, Erik
Diego Gutierrez and Karol Myszkowski
Natural images exhibit statistical regularities that differentiate them from random collections of pixels. Moreover, the human visual system appears to have evolved to exploit such statistical regularities. As computer graphics is concernedwith producing imagery for observation by humans, it would be prudent to understandwhich statistical regularities occur in nature, so they can be emulated by image synthesis methods. In this tutorial we introduce all aspects of natural image statistics, ranging from data collection to analysis and finally their applications in computer graphics, computational photography, image processing and art.
2013-01-01T00:00:00ZProjective Geometry, Duality and Precision of Computation in Computer Graphics, Visualization and Games
https://diglib.eg.org:443/handle/10.2312/conf.EG2013.tutorials.t7
Projective Geometry, Duality and Precision of Computation in Computer Graphics, Visualization and Games
Skala, Vaclav
Diego Gutierrez and Karol Myszkowski
Homogeneous coordinates and projective geometry are mostly connected with geometric transformations only. However the projective extension of the Euclidean system allows reformulation of geometrical problems which can be easily solved. In many cases quite complicated formulae are becoming simple from the geometrical and computational point of view. In addition they lead to simple parallelization and to matrix-vector operations which are convenient for matrix-vector hardwarearchitecture like GPU. In this short tutorial we will introduce "practical theory" of the projective space and homogeneous coordinates. We will show that a solution of linear system of equations is equivalent to generalized cross product and how this influences basic geometrical algorithms. The projective formulation is also convenient for computation of barycentric coordinates, as it is actually one crossproduct implemented as one clock instruction on GPU. Additional speed up can be expected, too.Moreover use of projective representation enables to postpone division operations in many geometrical problems, which increases robustness and stability of algorithms. There is no need to convert coordinates of points from the homogeneous coordinates to the Euclidean ones as the projective formulation supports homogeneous coordinates natively. The presented approach can be applied in computational problems, games and visualization applications as well.
2013-01-01T00:00:00ZTensor Approximation in Visualization and Computer Graphics
https://diglib.eg.org:443/handle/10.2312/conf.EG2013.tutorials.t6
Tensor Approximation in Visualization and Computer Graphics
Pajarola, Renato; Suter, Susanne K.; Ruiters, Roland
Diego Gutierrez and Karol Myszkowski
In this course, we will introduce the basic concepts of tensor approximation (TA) - a higher-order generalization of the SVD and PCA methods - as well as its applications to visual data representation, analysis and visualization, and bring the TA framework closer to visualization and computer graphics researchers and practitioners. The course will cover the theoretical background of TA methods, their properties and how to compute them, as well as practical applications of TA methods in visualization and computer graphics contexts. In a first theoretical part, the attendees will be instructed on the necessary mathematical background of TA methods to learn the basics skills of using and applying these new tools in the context of the representation of large multidimensional visual data. Specific and very noteworthy features of the TA framework are highlighted which can effectively be exploited for spatio-temporal multidimensional data representation and visualization purposes. In two application oriented sessions, compact TA data representation in scientific visualization and computer graphics as well as decomposition and reconstruction algorithms will be demonstrated. At the end of the course, the participants will have a good basic knowledge of TA methods along with a practical understanding of its potential application in visualization and graphics related projects.
2013-01-01T00:00:00Z