Tag Archives: Algorithms

Backward induction versus forward induction reasoning

In this paper we want to shed some light on what we mean by backward induction and forward induction reasoning in dynamic games. To that purpose, we take the concepts of common belief in future rationality (Perea [1]) and extensive form rationalizability (Pearce [2], Battigalli [3], Battigalli and Siniscalchi [4]) as possible representatives for backward induction and forward induction reasoning. We compare both concepts on a conceptual, epistemic and an algorithm level, thereby highlighting some of the crucial  differences between backward and forward induction reasoning in dynamic games.

© The authors. Article originally published in ‘Games’, V. 1 (2010), pp. 168-188, as open access article, distributed under the terms of the Creative Commons Attribution License

View full Article in PDF

Character animation from 2D pictures and 3D motion data

This article presents a new method to animate photos of 2D characters using 3D motion capture data. Given a single image of a person or essentially human-like subject, our method transfers the motion of a 3D skeleton onto the subject’s 2D shape in image space, generating the impression of a realistic movement. We present robust solutions to reconstruct a projective camera model and a 3D model pose which matches best to the given 2D image. Depending on the reconstructed view, a 2D shape template is selected, which enables the proper handling of occlusions. After fitting the template to the character in the input image, it is deformed as-rigid-as-possible by taking the projected 3D motion data into account. Unlike previous work, our method thereby correctly handles projective shape distortion. It works for images from arbitrary views and requires only a small amount of user interaction. We present animations of a diverse set of human (and non-human) characters with different types of motions, such as walking, jumping, or dancing.

Article originally published as: Hornung, A. et al, Character Animation from 2D Pictures and 3D Motion Data, ‘ACM Transactions on Graphics (TOG)’, V. 26 (2007), n.1, ©2007 Association for Computing Machinery, Inc.  //doi.acm.org/10.1145/1189762.1189763

Reprinted with permission.