DeepAI AI Chat
Log In Sign Up

Jumping Manifolds: Geometry Aware Dense Non-Rigid Structure from Motion

by   Suryansh Kumar, et al.
Australian National University

Given dense image feature correspondences of a non-rigidly moving object across multiple frames, this paper proposes an algorithm to estimate its 3D shape for each frame. To solve this problem accurately, the recent state-of-the-art algorithm reduces this task to set of local linear subspace reconstruction and clustering problem using Grassmann manifold representation kumar2018scalable. Unfortunately, their method missed on some of the critical issues associated with the modeling of surface deformations, for e.g., the dependence of a local surface deformation on its neighbors. Furthermore, their representation to group high dimensional data points inevitably introduce the drawbacks of categorizing samples on the high-dimensional Grassmann manifold huang2015projection, harandi2014manifold. Hence, to deal with such limitations with kumar2018scalable, we propose an algorithm that jointly exploits the benefit of high-dimensional Grassmann manifold to perform reconstruction, and its equivalent lower-dimensional representation to infer suitable clusters. To accomplish this, we project each Grassmannians onto a lower-dimensional Grassmann manifold which preserves and respects the deformation of the structure w.r.t its neighbors. These Grassmann points in the lower-dimension then act as a representative for the selection of high-dimensional Grassmann samples to perform each local reconstruction. In practice, our algorithm provides a geometrically efficient way to solve dense NRSfM by switching between manifolds based on its benefit and usage. Experimental results show that the proposed algorithm is very effective in handling noise with reconstruction accuracy as good as or better than the competing methods.


page 1

page 7


Dense Non-Rigid Structure from Motion: A Manifold Viewpoint

Non-Rigid Structure-from-Motion (NRSfM) problem aims to recover 3D geome...

Inferring Manifolds From Noisy Data Using Gaussian Processes

In analyzing complex datasets, it is often of interest to infer lower di...

Scalable Dense Non-rigid Structure-from-Motion: A Grassmannian Perspective

This paper addresses the task of dense non-rigid structure from motion (...

Hierarchic Neighbors Embedding

Manifold learning now plays a very important role in machine learning an...

Manifold Approximation by Moving Least-Squares Projection (MMLS)

In order to avoid the curse of dimensionality, frequently encountered in...

Efficient moving point handling for incremental 3D manifold reconstruction

As incremental Structure from Motion algorithms become effective, a good...

Using topological autoencoders as a filtering function for global and local topology

Choosing a suitable filtering function for the Mapper algorithm can be d...