Non-rigid structure from motion (NRSFM) is a difficult, underconstrained problem in computer vision. The stan dard approach in NRSFM constrains 3D shape deformation using a linear combination of K basis shapes; the solution is then obtained as the low-rank factorization of an input observation matrix. An important but overlooked problem with this approach is that non-linear deformations are often observed; these deformations lead to a weakened low-rank constraint due to the need to use additional basis shapes to linearly model points that move along curves. Here, we demonstrate how the kernel trick can be ap plied in standard NRSFM. As a result, we model com plex, deformable 3D shapes as the outputs of a non-linear mapping whose inputs are points within a low-dimensional shape space. This approach is flexible and can use diff erent kernels to build diff erent non-linear models. Using the ker nel trick, our model complements the low-rank constraint by capturing non-linear relationships in the shape coeffi cients of the linear model. The net e.ff ect can be seen as using non-linear dimensionality reduction to further com press the (shape) space of possible solutions.
Parallel to this work they proposed a solution that uses the kernel trick to also model nonlinear deformations REF which cannot be represented by a linear combination of basis shapes.
Kernel non-rigid structure from motion
2011 International Conference on Computer Vision
2011 International Conference on Computer Vision
Computer Science Medicine