Rigid Shape Interpolation Using Normal Equations

International audienceIn this paper we provide a new compact formulation of rigid shape interpolation in terms of normal equations, and propose several enhancements to previous techniques. Specifically, we propose 1) a way to improve mesh independence, making the interpolation result less influenced by variations in tessellation, 2) a faster way to make the interpolation symmetric, and 3) simple modifications to enable controllable interpolation. Finally we also identify 4) a failure mode related to large rotations that is easily triggered in practical use, and we present a solution for this as well

Mathematical Progress in Expressive Image Synthesis I

This book presents revised versions of the best papers selected from the symposium “Mathematical Progress in Expressive Image Synthesis” (MEIS2013) held in Fukuoka, Japan, in 2013. The topics cover various areas of computer graphics (CG), such as surface deformation/editing, character animation, visual simulation of fluids, texture and sound synthesis, and photorealistic rendering. From a mathematical point of view, the book also presents papers addressing discrete differential geometry, Lie theory, computational fluid dynamics, function interpolation, and learning theory. This book showcases the latest joint efforts between mathematicians, CG researchers, and practitioners exploring important issues in graphics and visual perception. The book provides a valuable resource for all computer graphics researchers seeking open problem areas, especially those now entering the field who have not yet selected a research direction

Mathematical Basics of Motion and Deformation in Computer Graphics, Second Edition

Buku ini memberikan informasi mengenai penerapan model jaringan saraf ke data bahasa alami. Buku (Bagian I dan II) mencakup dasar-dasar pembelajaran mesin yang diawasi dan jaringan saraf umpan-maju, dasar-dasar bekerja dengan pembelajaran mesin melalui data bahasa, dan penggunaan berbasis vektor daripada representasi simbolis untuk kata-kata, termasuk abstraksi grafik-komputasi, yang memungkinkan untuk dengan mudah mendefinisikan dan melatih jaringan saraf arbitrer, dan merupakan dasar di balik desain perpustakaan perangkat lunak jaringan saraf kontemporer

Mathematical Progress in Expressive Image Synthesis II

The material included in this book provides selected presentations given at the international symposium MEIS2014. The book aims to provide a unique venue where various issues in computer graphics (CG) application fields are discussed by mathematicians as well as CG researchers and practitioners. The target audience is not limited to researchers in academia but also those in industries with a strong interest in digital media creation, scientific visualization, and visual engineering. 

Finite-dimensional RKHS for Solving Computer Graphics Problems

1.Introduction 2.Mathematical background 3.RKHS and Bayesian estimates 4.RKHS for superresolution 5.Concluding remarkWe present a few computationally tractable models of finite-dimensional Reproducing Kernel Hilbert Spaces (RKHS) that give a theoretical foundation of the techniques we have developed to solve several problems in computer graphics. The problems we deal with in this paper are signal and geometry interpolation/extrapolation as well as solving an inverse problem in animation

Compatible Embedding for 2D Shape Animation

Abstract—We present new algorithms for the compatible embedding of 2D shapes. Such embeddings offer a convenient way to interpolate shapes having complex, detailed features. Compared to existing techniques, our approach requires less user input, is faster, more robust, and simpler to implement, making it ideal for interactive use in practical applications. Our new approach consists of three parts. First, our boundary matching algorithm locates salient features using the perceptually-motivated principles of scalespace and uses these as automatic correspondences to guide an elastic curve matching algorithm. Second, we simplify boundaries while maintaining their parametric correspondence and the embedding of the original shapes. Finally, we extend the mapping to shapes ’ interiors via a new compatible triangulation algorithm. The combination of our algorithms allows us to demonstrate 2D shape interpolation with instant feedback. The proposed algorithms exhibit a combination of simplicity, speed, and accuracy that has not been achieved in previous work