Real-time nonlinear shape interpolation

Real-time nonlinear shape interpolation

Von Tycowicz, C.
Schulz, C.
Seidel, H.P.
Hildebrandt, K.

Electrical Engineering, Mathematics and Computer Science

Intelligent Systems

2015-12-31

We introduce a scheme for real-time nonlinear interpolation of a set of shapes. The scheme exploits the structure of the shape interpolation problem, in particular, the fact that the set of all possible interpolated shapes is a low-dimensional object in a high-dimensional shape space. The interpolated shapes are defined as the minimizers of a nonlinear objective functional on the shape space. Our approach is to construct a reduced optimization problem that approximates its unreduced counterpart and can be solved in milliseconds. To achieve this, we restrict the optimization to a low-dimensional subspace that is specifically designed for the shape interpolation problem. The construction of the subspace is based on two components: a formula for the calculation of derivatives of the interpolated shapes and a Krylov-type sequence that combines the derivatives and the Hessian of the objective functional. To make the computational cost for solving the reduced optimization problem independent of the resolution of the example shapes, we combine the dimensional reduction with schemes for the efficient approximation of the reduced nonlinear objective functional and its gradient. In our experiments, we obtain rates of 20-100 interpolated shapes per second even for the largest examples which have 500k vertices per example shape.

http://resolver.tudelft.nl/uuid:671f2891-ecbd-4374-bad9-850466a36b5c

ACM

0730-0301

ACM Transactions on Graphics, 34 (3), 2015

Institutional Repository

journal article

(c) 2015 ACM. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution.