Learning NonRigid 3D Shape from 2D Motion（学习非刚性的三维形状的二维运动）.pdf

Learning Non-Rigid 3D Shape from 2D Motion Lorenzo Torresani Aaron Hertzmann Stanford University University of Toronto ltorresa@ hertzman@ Christoph Bregler New York University chris.bregler@ Abstract This paper presents an algorithm for learning the time-varying shape of a non-rigid 3D object from uncalibrated 2D tracking data. We model shape motion as a rigid component (rotation and translation) combined with a non-rigid deformation. Reconstruction is ill-posed if arbitrary deforma- tions are allowed. We constrain the problem by assuming that the object shape at each time instant is drawn from a Gaussian distribution. Based on this assumption, the algorithm simultaneously estimates 3D shape and motion for each time frame, learns the parameters of the Gaussian, and robustly fills-in missing data points. We then extend the algorithm to model temporal smoothness in object shape, thus allowing it to handle severe cases of missing data. 1 Introduction We can generally think of a non-rigid object’s motion as consisting of a rigid component plus a non-rigid deformation. For example, a person’s head can move rigidly (e.g. turning left or right) while deforming (due to changing facial expressions). If we view this non-rigid motion from a single camera view, the shape and motion are ambiguous: for any hypotheti- cal rigid motion, a corresponding 3D shape can be devised that fits the image observations. Even if camera calibration and rigid motion are known, a depth ambiguity remains. Despite this apparent ambiguity, humans interpret the shape and motion of non-rigid objects with relative