Homeomorphic Manifold Analysis (HMA): Generalized separation of style and content on manifolds

Abstract

The problem of separation of style and content is an essential element of visual perception, and is a fundamental mystery of perception. This problem appears extensively in different computer vision applications. The problem we address in this paper is the separation of style and content when the content lies on a low dimensional nonlinear manifold representing a dynamic object. We show that such a setting appears in many human motion analysis problems. We introduce a framework for learning parameterization of style and content in such settings. Given a set of topologically equivalent manifolds, the Homeomorphic Manifold Analysis (HMA) framework models the variation in their geometries in the space of functions that maps between a topologically-equivalent common representation and each of them. The framework is based on decomposing the style parameters in the space of nonlinear functions that map between a unified embedded representation of the content manifold and style-dependent visual observations. We show the application of the framework in synthesis, recognition, and tracking of certain human motions that follow this setting, such as gait and facial expressions.

Cross-Speed Gait Recognition Using Speed-Invariant Gait Templates and Globality–Locality Preserving Projections

“…2) Manifold Fitting Using TPS Based Interpolation: Several recent studies indicate the gait manifold is topologically equivalent to a unit circle [19]- [21]. However, subject-specific factors such as walking style, walking speed and body shape transform and deform the circle to a general one-dimensional closed manifold in the input space (denoted as gait manifold).…”

“…Recent studies indicated that walking actions reside on manifolds [17], [18], and the manifold of walking action is topologically equivalent to a unit circle [19]- [21]. By using this strong prior, we model the problem of walking action as a problem of gait manifold fitting.…”

Manifolds for pose tracking from monocular video

“…8,[22][23][24][25][26][27] We denote these approaches as learning of the input-output space. 8,[22][23][24][25][26][27] We denote these approaches as learning of the input-output space.…”

“…8,[16][17][18][22][23][24][25][26][27]31,[34][35][36] Any unknown image is mapped to its corresponding pose by inverting the learned mathematical map. The domain of motion of the human is sampled into a database of stored images and a mathematical map is built to associate the sampled database images to their known poses.…”

“…23 25,26,27 is to fit a nonlinear interpolating function between the individual pixels of the high-dimensional images (or image features) and a locally linear embedding 37 of the high-dimensional images into a low-dimensional "parameter" space in a least squares sense. 23 25,26,27 is to fit a nonlinear interpolating function between the individual pixels of the high-dimensional images (or image features) and a locally linear embedding 37 of the high-dimensional images into a low-dimensional "parameter" space in a least squares sense.…”