An Accelerated Procrustean Markov Process Model With Coherent Constraint for Non-Rigid Structure From Motion

Ying Zhang,Xia Chen,Zhan-Li Sun,Zhigang Zeng,Kin-Man Lam

doi:10.1109/access.2019.2945356

Abstract

Non-Rigid Structure from Motion (NRSfM) is the task of reconstructing the 3D point set of a non-rigid object from an ensemble of images with 2D correspondences, which has been a long-lasting challenging research topic. Compared to the state-of-the-art methods for NRSfM, the Procrustean Markov Process (PMP) model has obtained a relatively good performance. However, the estimation error and the convergence time of the PMP model will increase simultaneously when noise is present. To address this problem, in this paper, a coherent constraint is constructed to suppress the noise in the initialization step of the PMP algorithm. Moreover, an Accelerated Expectation Maximization (AEM) algorithm is devised to optimize the PMP estimation model. Experimental results on several widely used sequences demonstrate that our proposed algorithm achieves state-of-the-art performance, as well as its effectiveness and feasibility.

Highlights

Reconstructing the 3D object shapes from a set of 2D images has become a valuable approach to enhance the tasks in computer vision, such as virtual reality [1], object recognition [2], biometrics [3], human-computer interaction [4], [5], etc
In order to solve the uncertainty in Non-Rigid Structure from Motion (NRSfM), many different a priori information, assumptions and constraints have been utilized in reconstructing the 3D shapes
The proposed algorithm is composed of three main components: formulation of the Procrustean Markov Process (PMP) model [20], initialization of the PMP model with a coherent constraint, and the optimization of the PMP model using the proposed accelerated EM algorithm

Summary

INTRODUCTION

Reconstructing the 3D object shapes from a set of 2D images has become a valuable approach to enhance the tasks in computer vision, such as virtual reality [1], object recognition [2], biometrics [3], human-computer interaction [4], [5], etc. Inspired by the factorization technique for Structure from Motion (SfM) [6], a low-rank constraint was proposed in [7] to model the unknown time-varying deformable 3D shapes, represented as a linear combination of a small number of 3D shape bases. In [13] and [14], a better reconstruction of high-frequency deformation was achieved without relaxing the rank-3K constraint, by modeling a smoothly deforming 3D shape as a single point moving along a smooth timetrajectory within a linear shape space. A scalable, efficient, and accurate solution was proposed in [17] to solve the NRSfM problem, by combining the existing point-trajectory low-rank models with a probabilistic framework for matrix normal distributions.

METHODOLOGY

THE PMP MODEL OPTIMIZATION USING

Findings

CONCLUSION