Abstract

In the field of computer animation, character animation using keyframes remains a popular technique. In this, the animation sequence is represented compactly by just the more important character poses, termed as keyframes and the rest of the frames, known as in-betweens are generated when needed, say during playing the animation, using the keyframes. The animator specifies (creates) the keyframes while the in-between frames are computed using a suitable interpolation scheme. Interpolation parameters are usually under the control of the animator. Most animation software today will include support for keyframe animation. However, specifying the parameters so that the generated animation sequence fulfils the animator expectations and other motion requirements, say like preserving area or volume, or satisfying a physical constraint, can be quite difficult. The number of degrees of freedom is very high for skeleton-based animation and much higher for mesh-based animation. Physically-based animation techniques have been proposed for character poses to satisfy physics constraints. But animators find it difficult and non-intuitive to specify physics parameters, like body mass, forces. etc. and seem to very much dislike the fact that they lose control over the final animation. Trial and error using the keyframe technique is presently the most popularly adopted solution by animators.

Our main thesis is that for a character action, given just the keyframe representation or the entire animation sequence, we can recover a characterizing motion representation in lower dimension space using manifold learning. This characterizing motion recovers distinguishing information hidden in the huge amount of correlated and coherent character animation data in high dimensional space. Then we can use it to enhance keyframe animation techniques, which can considerably reduce animator effort required for specifying the keyframes for desired quality of animation. Further, these new techniques are equally applicable to 3D skeleton and mesh animation.

In our first major contribution, we present a formulation to adopt the technique of locally linear embedding (LLE) to project the given character animation data into a much lower dimension embedding space. We show that animations depicting distinguishable activities, say walking, running, jumping, etc. take distinct characteristic shapes in lower dimensional embedding space. Based on this embedding, we present a new framework consisting of a reconstruction matrix combined with motion represented in the low dimension embedding space. This framework enables us to generate complete animation sequences in the original high dimensional space while maintaining desirable physical properties in a deformable shape. The latter is done by introducing the concept of a property map in the embedding space of values for the different physical properties of the mesh, for example area, volume, etc. A probability distribution function in embedding space then helps us rapidly choose the required number of in-between poses with desired physical properties. The reconstruction of the animation sequence is achieved by using the whole set of keyframes during interpolation for generating each in-between. This framework has many other applications and we demonstrate this by introducing two other new techniques which further enhance key frame animation.

In another contribution of this research, we present a non-physically based method for incorporating perceivable variations in repetitive motion of an autonomous virtual character while retaining its principal characteristics. Usually, this is rather difficult to achieve using standard keyframe animation techniques, since even small changes in keyframes can result in less predictable changes in the final interpolated animation. The basis for our method is provided by asymmetric bilinear factorization of a given animation derived using the above framework. Keeping the action unchanged (that is the characterizing motion extracted as the embedding in the low dimensional space), we define a method to incorporate controlled perturbations into the reconstruction matrix so as to yield variations of the same motion. Further, to join the varied motion segments into a longer animation sequence, we present an embedding space method, which again makes use of the property map to maintain the desired physical properties.

We also present an effective method for optimized keyframe selection from complete animations or motion capture sequences. Given the fact that most animators are very comfortable with the keyframe animation technique, this will enable animators to work easily with previously created animations or motion capture data. Our solution uses animation saliency and combines it with the embedding. For this, we use the representation of the animation in the form of matrix multiplication of reconstruction matrix with combination weights and then cast the keyframe selection problem into a constrained matrix factorization problem. The error metric that is minimized however uses animation saliency computed in the original high dimensional space. This way, the time consuming optimal search required by the matrix factorization problem in high dimensional space is simplified to a much more efficient method in low dimensional space.

These enhancements to the character keyframe animation technique are possible because of capability of the manifold learning technique like LLE to effectively capture in low dimensional space the characterizing motion information that is present in a given character animation. Together these form the most significant contributions of this thesis.