Eigenvalue problems are ubiquitous in computer vision, covering a very broad spectrum of applications ranging from estimation problems in multi-view geometry to image segmentation. Few other linear algebra problems have a more mature set of numerical routines available and many computer vision libraries leverage such tools extensively. However, the ability to call the underlying solver only as a "black box" can often become restrictive. Many 'human in the loop' settings in vision frequently exploit supervision from an expert, to the extent that the user can be considered a subroutine in the overall system. In other cases, there is additional domain knowledge, side or even partial information that one may want to incorporate within the formulation. In general, regularizing a (generalized) eigenvalue problem with such side information remains difficult. Motivated by these needs, this paper presents an optimization scheme to solve generalized eigenvalue problems (GEP) involving a (nonsmooth) regularizer. We start from an alternative formulation of GEP where the feasibility set of the model involves the Stiefel manifold. The core of this paper presents an end to end stochastic optimization scheme for the resultant problem. We show how this general algorithm enables improved statistical analysis of brain imaging data where the regularizer is derived from other 'views' of the disease pathology, involving clinical measurements and other image-derived representations.
|Title of host publication||2015 International Conference on Computer Vision, ICCV 2015|
|Publisher||Institute of Electrical and Electronics Engineers Inc.|
|Number of pages||9|
|Publication status||Published - 2015 Feb 17|
|Event||15th IEEE International Conference on Computer Vision, ICCV 2015 - Santiago, Chile|
Duration: 2015 Dec 11 → 2015 Dec 18
|Name||Proceedings of the IEEE International Conference on Computer Vision|
|Volume||2015 International Conference on Computer Vision, ICCV 2015|
|Other||15th IEEE International Conference on Computer Vision, ICCV 2015|
|Period||15/12/11 → 15/12/18|
Bibliographical notePublisher Copyright:
© 2015 IEEE.
All Science Journal Classification (ASJC) codes
- Computer Vision and Pattern Recognition