Learning On Manifolds A Computer Vision Viewpoint
Many computer vision problems can be formulated on analytic manifolds using Riemannian geometry including feature selection, dimensionality reduction, object detection, appearance tracking, and event classification. Unlike Euclidean spaces, analytic manifolds exhibit local homeomorphism, thus, differential geometry is applicable only within local tangent spaces. This prevents direct application of conventional learning methods that require vector norms.
Recently we introduced a region covariance descriptor that exhibits a Riemannian manifold structure on positive definite matrices, and developed inference techniques that do not require flattening of the manifold or discovering its underlying topology. For instance, to detect humans, we impose weak classifiers on tangent spaces and establish weighted sums via Karcher mean to bootstrap an ensemble of boosted classifiers with logistic loss functions.
In this talk I will present a number of exciting results of inference algorithms on analytic manifolds from image query search to target detection to pose estimation to affine tracking.