Visual Comput (2007) 23: 753–761 DOI 10.1007/s00371-007-0141-8 ORIGINAL ARTICLE Chao Jin Thomas Fevens Shuo Li Sudhir Mudur Motion learning-based framework for unarticulated shape animation ∗ Published online: 30 June 2007  Springer-Verlag 2007 C. Jin (✉) · T. Fevens · S. Mudur Department of Computer Science and Software Engineering, Concordia University, Montreal, Canada {chao jin, fevens, mudur} @cse.concordia.ca S. Li GE Healthcare, Canada shuo.li@ge.com Abstract This paper presents a framework for generating ani- mation sequences while maintaining desirable physical properties in a deformable shape. The framework consists of three important processes. Firstly, considering the given key pose configurations in the form of unarticulated meshes in high dimensional space, we cast our motion in low dimensional space using the unsupervised learning method of locally linear embedding (LLE). Corresponding to each point in LLE space, we can reconstruct the in-between pose using generalized radial basis functions. Next we create a map in the LLE space of the values for the different physical properties of the mesh, for example area, volume, etc. Finally, a probability distribution function in LLE space helps us rapidly choose the required number of in-between poses with desired physical properties. A significant advantage of this framework is that it relieves the animator the tedium of having to carefully provide key poses to suit the interpolant. Keywords Computer animation · Keyframe · Mesh deformation · Motion learning 1 Introduction Generating animation sequences by specifying key poses of the desired motion is among the most popular tech- niques in use today. Given the key poses in the form of unarticulated 3D meshes, the dominant method of prod- ucing the deformation for the in-between meshes is to use a suitable interpolant, such as linear or spline. Given the high sensitivity of these interpolants to the supplied sample data, this results in a significant burden on the ani- mator to carefully provide the number and spacing of the key poses to suit the interpolant so that the generated in- between meshes satisfy the required physical properties of ∗ This research was supported in part by Discovery Grants from NSERC, Canada. the desired motion, such as mesh surface area or volume, or any other such computable mesh metric. The inter- polants in use today are generally driven by issues such as computational efficiency and geometric continuity of individual vertices of the mesh. They do not take into con- sideration the high correlation amongst mesh vertices or desirable constraints on physical properties of the meshes. Related to such constraints, recently in [7, 26], the con- ventional inverse kinematics method for limbed structures has been extended to meshes. Similarly, physics-based methods such as forward and inverse dynamics methods, which are also used in bio-mechanics rely on physical properties like joint torques for limbed structures [28]. In order to provide the right perspective for our frame- work, let us look at the following example. Consider the goal of producing an animation sequence showing a gal-