Information Theory Tools for Viewpoint Selection, Mesh Saliency and Geometry Simplification Mateu Sbert, Miquel Feixas, Pascual Castell´ o and Miguel Chover Abstract In this chapter we review the use of an information channel as a unified framework for viewpoint selection, mesh saliency and geometry simplification. Tak- ing the viewpoint distribution as input and object mesh polygons as output vectors, the channel is given by the projected areas of the polygons over the different view- points. From this channel, viewpoint entropy and viewpoint mutual information can be defined in a natural way. Reversing this channel, polygonal mutual information is obtained, which is interpreted as an ambient occlusion-like quantity, and from the variation of this polygonal mutual information mesh saliency is defined. Viewpoint entropy, viewpoint Kullback-Leibler distance, and viewpoint mutual information are then applied to mesh simplification, and shown to compare well with a classical geometrical simplification method. 1 Introduction In computer graphics, several viewpoint quality measures have been applied in areas such as scene understanding [29, 36, 30, 9], scene exploration [15, 33], image-based Mateu Sbert Graphics and Imaging Laboratory, Universitat de Girona, Building P4, Campus Montilivi, 17071- Girona, Spain, e-mail: mateu@ima.udg.edu Miquel Feixas Graphics and Imaging Laboratory, Universitat de Girona, Building P4, Campus Montilivi, 17071- Girona, Spain, e-mail: feixas@ima.udg.edu Pascual Castell´ o Computer Graphics Group, Universitat Jaume I, Campus Riu Sec, 12071-Castell´ o, Spain, e-mail: castellp@lsi.uji.es Miguel Chover Computer Graphics Group, Universitat Jaume I, Campus Riu Sec, 12071-Castell´ o, Spain, e-mail: chover@lsi.uji.es 1