Multi-body Non-rigid Structure-from-Motion

Conventional structure-from-motion (SFM) research is primarily concerned with the 3D reconstruction of a single, rigidly moving object seen by a static camera, or a static and rigid scene observed by a moving camera --in both cases there are only one relative rigid motion involved. Recent progress have extended SFM to the areas of {multi-body SFM} (where there are {multiple rigid} relative motions in the scene), as well as {non-rigid SFM} (where there is a single non-rigid, deformable object or scene). Along this line of thinking, there is apparently a missing gap of "multi-body non-rigid SFM", in which the task would be to jointly reconstruct and segment multiple 3D structures of the multiple, non-rigid objects or deformable scenes from images. Such a multi-body non-rigid scenario is common in reality (e.g. two persons shaking hands, multi-person social event), and how to solve it represents a natural {next-step} in SFM research. By leveraging recent results of subspace clustering, this paper proposes, for the first time, an effective framework for multi-body NRSFM, which simultaneously reconstructs and segments each 3D trajectory into their respective low-dimensional subspace. Under our formulation, 3D trajectories for each non-rigid structure can be well approximated with a sparse affine combination of other 3D trajectories from the same structure (self-expressiveness). We solve the resultant optimization with the alternating direction method of multipliers (ADMM). We demonstrate the efficacy of the proposed framework through extensive experiments on both synthetic and real data sequences. Our method clearly outperforms other alternative methods, such as first clustering the 2D feature tracks to groups and then doing non-rigid reconstruction in each group or first conducting 3D reconstruction by using single subspace assumption and then clustering the 3D trajectories into groups.Comment: 21 pages, 16 figure

MHR-Net: Multiple-Hypothesis Reconstruction of Non-Rigid Shapes from 2D Views

We propose MHR-Net, a novel method for recovering Non-Rigid Shapes from Motion (NRSfM). MHR-Net aims to find a set of reasonable reconstructions for a 2D view, and it also selects the most likely reconstruction from the set. To deal with the challenging unsupervised generation of non-rigid shapes, we develop a new Deterministic Basis and Stochastic Deformation scheme in MHR-Net. The non-rigid shape is first expressed as the sum of a coarse shape basis and a flexible shape deformation, then multiple hypotheses are generated with uncertainty modeling of the deformation part. MHR-Net is optimized with reprojection loss on the basis and the best hypothesis. Furthermore, we design a new Procrustean Residual Loss, which reduces the rigid rotations between similar shapes and further improves the performance. Experiments show that MHR-Net achieves state-of-the-art reconstruction accuracy on Human3.6M, SURREAL and 300-VW datasets.Comment: Accepted to ECCV 202

확률적인 3차원 자세 복원과 행동인식

학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2016. 2. 오성회.These days, computer vision technology becomes popular and plays an important role in intelligent systems, such as augment reality, video and image analysis, and to name a few. Although cost effective depth cameras, like a Microsoft Kinect, have recently developed, most computer vision algorithms assume that observations are obtained from RGB cameras, which make 2D observations. If, somehow, we can estimate 3D information from 2D observations, it might give better solutions for many computer vision problems. In this dissertation, we focus on estimating 3D information from 2D observations, which is well known as non-rigid structure from motion (NRSfM). More formally, NRSfM finds the three dimensional structure of an object by analyzing image streams with the assumption that an object lies in a low-dimensional space. However, a human body for long periods of time can have complex shape variations and it makes a challenging problem for NRSfM due to its increased degree of freedom. In order to handle complex shape variations, we propose a Procrustean normal distribution mixture model (PNDMM) by extending a recently proposed Procrustean normal distribution (PND), which captures the distribution of non-rigid variations of an object by excluding the effects of rigid motion. Unlike existing methods which use a single model to solve an NRSfM problem, the proposed PNDMM decomposes complex shape variations into a collection of simpler ones, thereby model learning can be more tractable and accurate. We perform experiments showing that the proposed method outperforms existing methods on highly complex and long human motion sequences. In addition, we extend the PNDMM to a single view 3D human pose estimation problem. While recovering a 3D structure of a human body from an image is important, it is a highly ambiguous problem due to the deformation of an articulated human body. Moreover, before estimating a 3D human pose from a 2D human pose, it is important to obtain an accurate 2D human pose. In order to address inaccuracy of 2D pose estimation on a single image and 3D human pose ambiguities, we estimate multiple 2D and 3D human pose candidates and select the best one which can be explained by a 2D human pose detector and a 3D shape model. We also introduce a model transformation which is incorporated into the 3D shape prior model, such that the proposed method can be applied to a novel test image. Experimental results show that the proposed method can provide good 3D reconstruction results when tested on a novel test image, despite inaccuracies of 2D part detections and 3D shape ambiguities. Finally, we handle an action recognition problem from a video clip. Current studies show that high-level features obtained from estimated 2D human poses enable action recognition performance beyond current state-of-the-art methods using low- and mid-level features based on appearance and motion, despite inaccuracy of human pose estimation. Based on these findings, we propose an action recognition method using estimated 3D human pose information since the proposed PNDMM is able to reconstruct 3D shapes from 2D shapes. Experimental results show that 3D pose based descriptors are better than 2D pose based descriptors for action recognition, regardless of classification methods. Considering the fact that we use simple 3D pose descriptors based on a 3D shape model which is learned from 2D shapes, results reported in this dissertation are promising and obtaining accurate 3D information from 2D observations is still an important research issue for reliable computer vision systems.Chapter 1 Introduction 1 1.1 Motivation 1 1.2 Research Issues 4 1.3 Organization of the Dissertation 6 Chapter 2 Preliminary 9 2.1 Generalized Procrustes Analysis (GPA) 11 2.2 EM-GPA Algorithm 12 2.2.1 Objective function 12 2.2.2 E-step 15 2.2.3 M-step 16 2.3 Implementation Considerations for EM-GPA 18 2.3.1 Preprocessing stage 18 2.3.2 Small update rate for the covariance matrix 20 2.4 Experiments 21 2.4.1 Shape alignment with the missing information 23 2.4.2 3D shape modeling 24 2.4.3 2D+3D active appearance models 28 2.5 Chapter Summary and Discussion 32 Chapter 3 Procrustean Normal Distribution Mixture Model 33 3.1 Non-Rigid Structure from Motion 35 3.2 Procrustean Normal Distribution (PND) 38 3.3 PND Mixture Model 41 3.4 Learning a PNDMM 43 3.4.1 E-step 44 3.4.2 M-step 46 3.5 Learning an Adaptive PNDMM 48 3.6 Experiments 50 3.6.1 Experimental setup 50 3.6.2 CMU Mocap database 53 3.6.3 UMPM dataset 69 3.6.4 Simple and short motions 74 3.6.5 Real sequence - qualitative representation 77 3.7 Chapter Summary 78 Chapter 4 Recovering a 3D Human Pose from a Novel Image 83 4.1 Single View 3D Human Pose Estimation 85 4.2 Candidate Generation 87 4.2.1 Initial pose generation 87 4.2.2 Part recombination 88 4.3 3D Shape Prior Model 89 4.3.1 Procrustean mixture model learning 89 4.3.2 Procrustean mixture model fitting 91 4.4 Model Transformation 92 4.4.1 Model normalization 92 4.4.2 Model adaptation 95 4.5 Result Selection 96 4.6 Experiments 98 4.6.1 Implementation details 98 4.6.2 Evaluation of the joint 2D and 3D pose estimation 99 4.6.3 Evaluation of the 2D pose estimation 104 4.6.4 Evaluation of the 3D pose estimation 106 4.7 Chapter Summary 108 Chapter 5 Application to Action Recognition 109 5.1 Appearance and Motion Based Descriptors 112 5.2 2D Pose Based Descriptors 113 5.3 Bag-of-Features with a Multiple Kernel Method 114 5.4 Classification - Kernel Group Sparse Representation 115 5.4.1 Group sparse representation for classification 116 5.4.2 Kernel group sparse (KGS) representation for classification 118 5.5 Experiment on sub-JHMDB Dataset 120 5.5.1 Experimental setup 120 5.5.2 3D pose based descriptor 122 5.5.3 Experimental results 123 5.6 Chapter Summary 129 Chapter 6 Conclusion and Future Work 131 Appendices 135 A Proof of Propositions in Chapter 2 137 A.1 Proof of Proposition 1 137 A.2 Proof of Proposition 3 138 A.3 Proof of Proposition 4 139 B Calculation of p(XijDii) in Chapter 3 141 B.1 Without the Dirac-delta term 141 B.2 With the Dirac-delta term 142 C Procrustean Mixture Model Learning and Fitting in Chapter 4 145 C.1 Procrustean Mixture Model Learning 145 C.2 Procrustean Mixture Model Fitting 147 Bibliography 153 초 록 167Docto

Lifting from the Deep: Convolutional 3D Pose Estimation from a Single Image

We propose a unified formulation for the problem of 3D human pose estimation from a single raw RGB image that reasons jointly about 2D joint estimation and 3D pose reconstruction to improve both tasks. We take an integrated approach that fuses probabilistic knowledge of 3D human pose with a multi-stage CNN architecture and uses the knowledge of plausible 3D landmark locations to refine the search for better 2D locations. The entire process is trained end-to-end, is extremely efficient and obtains state- of-the-art results on Human3.6M outperforming previous approaches both on 2D and 3D errors.Comment: Paper presented at CVPR 1

3차원 사람 자세 추정을 위한 3차원 복원, 약지도학습, 지도학습 방법

학위논문 (박사)-- 서울대학교 대학원 : 융합과학기술대학원 융합과학부(지능형융합시스템전공), 2019. 2. 곽노준.Estimating human poses from images is one of the fundamental tasks in computer vision, which leads to lots of applications such as action recognition, human-computer interaction, and virtual reality. Especially, estimating 3D human poses from 2D inputs is a challenging problem since it is inherently under-constrained. In addition, obtaining 3D ground truth data for human poses is only possible under the limited and restricted environments. In this dissertation, 3D human pose estimation is studied in different aspects focusing on various types of the availability of the data. To this end, three different methods to retrieve 3D human poses from 2D observations or from RGB images---algorithms of 3D reconstruction, weakly-supervised learning, and supervised learning---are proposed. First, a non-rigid structure from motion (NRSfM) algorithm that reconstructs 3D structures of non-rigid objects such as human bodies from 2D observations is proposed. In the proposed framework which is named as Procrustean Regression, the 3D shapes are regularized based on their aligned shapes. We show that the cost function of the Procrustean Regression can be casted into an unconstrained problem or a problem with simple bound constraints, which can be efficiently solved by existing gradient descent solvers. This framework can be easily integrated with numerous existing models and assumptions, which makes it more practical for various real situations. The experimental results show that the proposed method gives competitive result to the state-of-the-art methods for orthographic projection with much less time complexity and memory requirement, and outperforms the existing methods for perspective projection. Second, a weakly-supervised learning method that is capable of learning 3D structures when only 2D ground truth data is available as a training set is presented. Extending the Procrustean Regression framework, we suggest Procrustean Regression Network, a learning method that trains neural networks to learn 3D structures using training data with 2D ground truths. This is the first attempt that directly integrates an NRSfM algorithm into neural network training. The cost function that contains a low-rank function is also firstly used as a cost function of neural networks that reconstructs 3D shapes. During the test phase, 3D structures of human bodies can be obtained via a feed-forward operation, which enables the framework to have much faster inference time compared to the 3D reconstruction algorithms. Third, a supervised learning method that infers 3D poses from 2D inputs using neural networks is suggested. The method exploits a relational unit which captures the relations between different body parts. In the method, each pair of different body parts generates relational features, and the average of the features from all the pairs are used for 3D pose estimation. We also suggest a dropout method called relational dropout, which can be used in relational modules to impose robustness to the occlusions. The experimental results validate that the performance of the proposed algorithm does not degrade much when missing points exist while maintaining state-of-the-art performance when every point is visible.RGB 영상에서의 사람 자세 추정 방법은 컴퓨터 비전 분야에서 중요하며 여러 어플리케이션의 기본이 되는 기술이다. 사람 자세 추정은 동작 인식, 인간-컴퓨터 상호작용, 가상 현실, 증강 현실 등 광범위한 분야에서 기반 기술로 사용될 수 있다. 특히, 2차원 입력으로부터 3차원 사람 자세를 추정하는 문제는 무수히 많은 해를 가질 수 있는 문제이기 때문에 풀기 어려운 문제로 알려져 있다. 또한, 3차원 실제 데이터의 습득은 모션캡처 스튜디오 등 제한된 환경하에서만 가능하기 때문에 얻을 수 있는 데이터의 양이 한정적이다. 본 논문에서는, 얻을 수 있는 학습 데이터의 종류에 따라 여러 방면으로 3차원 사람 자세를 추정하는 방법을 연구하였다. 구체적으로, 2차원 관측값 또는 RGB 영상을 바탕으로 3차원 사람 자세를 추정, 복원하는 세 가지 방법--3차원 복원, 약지도학습, 지도학습--을 제시하였다. 첫 번째로, 사람의 신체와 같이 비정형 객체의 2차원 관측값으로부터 3차원 구조를 복원하는 비정형 움직임 기반 구조 (Non-rigid structure from motion) 알고리즘을 제안하였다. 프로크루스테스 회귀 (Procrustean regression)으로 명명한 제안된 프레임워크에서, 3차원 형태들은 그들의 정렬된 형태에 대한 함수로 정규화된다. 제안된 프로크루스테스 회귀의 비용 함수는 3차원 형태 정렬과 관련된 제약을 비용 함수에 포함시켜 경사 하강법을 이용한 최적화가 가능하다. 제안된 방법은 다양한 모델과 가정을 포함시킬 수 있어 실용적이고 유연한 프레임워크이다. 다양한 실험을 통해 제안된 방법은 세계 최고 수준의 방법들과 비교해 유사한 성능을 보이면서, 동시에 시간, 공간 복잡도 면에서 기존 방법에 비해 우수함을 보였다. 두 번째로 제안된 방법은, 2차원 학습 데이터만 주어졌을 때 2차원 입력에서 3차원 구조를 복원하는 약지도학습 방법이다. 프로크루스테스 회귀 신경망 (Procrustean regression network)로 명명한 제안된 학습 방법은 신경망 또는 컨볼루션 신경망을 통해 사람의 2차원 자세로부터 3차원 자세를 추정하는 방법을 학습한다. 프로크루스테스 회귀에 사용된 비용 함수를 수정하여 신경망을 학습시키는 본 방법은, 비정형 움직임 기반 구조에 사용된 비용 함수를 신경망 학습에 적용한 최초의 시도이다. 또한 비용함수에 사용된 저계수 함수 (low-rank function)를 신경망 학습에 처음으로 사용하였다. 테스트 데이터에 대해서 3차원 사람 자세는 신경망의 전방전달(feed forward)연산에 의해 얻어지므로, 3차원 복원 방법에 비해 훨씬 빠른 3차원 자세 추정이 가능하다. 마지막으로, 신경망을 이용해 2차원 입력으로부터 3차원 사람 자세를 추정하는 지도학습 방법을 제시하였다. 본 방법은 관계 신경망 모듈(relational modules)을 활용해 신체의 다른 부위간의 관계를 학습한다. 서로 다른 부위의 쌍마다 관계 특징을 추출해 모든 관계 특징의 평균을 최종 3차원 자세 추정에 사용한다. 또한 관계형 드랍아웃(relational dropout)이라는 새로운 학습 방법을 제시해 가려짐에 의해 나타나지 않은 2차원 관측값이 있는 상황에서, 강인하게 동작할 수 있는 3차원 자세 추정 방법을 제시하였다. 실험을 통해 해당 방법이 2차원 관측값이 일부만 주어진 상황에서도 큰 성능 하락이 없이 효과적으로 3차원 자세를 추정함을 증명하였다.Abstract i Contents iii List of Tables vi List of Figures viii 1 Introduction 1 1.1 Problem Definition . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.4.1 3D Reconstruction of Human Bodies . . . . . . . . . . 9 1.4.2 Weakly-Supervised Learning for 3D HPE . . . . . . . . 11 1.4.3 Supervised Learning for 3D HPE . . . . . . . . . . . . 11 1.5 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2 Related Works 14 2.1 2D Human Pose Estimation . . . . . . . . . . . . . . . . . . . . 14 2.2 3D Human Pose Estimation . . . . . . . . . . . . . . . . . . . . 16 2.3 Non-rigid Structure from Motion . . . . . . . . . . . . . . . . . 18 2.4 Learning to Reconstruct 3D Structures via Neural Networks . . 23 3 3D Reconstruction of Human Bodies via Procrustean Regression 25 3.1 Formalization of NRSfM . . . . . . . . . . . . . . . . . . . . . 27 3.2 Procrustean Regression . . . . . . . . . . . . . . . . . . . . . . 28 3.2.1 The Cost Function of Procrustean Regression . . . . . . 29 3.2.2 Derivatives of the Cost Function . . . . . . . . . . . . . 32 3.2.3 Example Functions for f and g . . . . . . . . . . . . . . 38 3.2.4 Handling Missing Points . . . . . . . . . . . . . . . . . 43 3.2.5 Optimization . . . . . . . . . . . . . . . . . . . . . . . 44 3.2.6 Initialization . . . . . . . . . . . . . . . . . . . . . . . 44 3.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . 45 3.3.1 Orthographic Projection . . . . . . . . . . . . . . . . . 46 3.3.2 Perspective Projection . . . . . . . . . . . . . . . . . . 56 3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4 Weakly-Supervised Learning of 3D Human Pose via Procrustean Regression Networks 69 4.1 The Cost Function for Procrustean Regression Network . . . . . 70 4.2 Choosing f and g for Procrustean Regression Network . . . . . 74 4.3 Implementation Details . . . . . . . . . . . . . . . . . . . . . . 75 4.4 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . 77 4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 5 Supervised Learning of 3D Human Pose via Relational Networks 86 5.1 Relational Networks . . . . . . . . . . . . . . . . . . . . . . . 88 5.2 Relational Networks for 3D HPE . . . . . . . . . . . . . . . . . 88 5.3 Extensions to Multi-Frame Inputs . . . . . . . . . . . . . . . . 91 5.4 Relational Dropout . . . . . . . . . . . . . . . . . . . . . . . . 93 5.5 Implementation Details . . . . . . . . . . . . . . . . . . . . . . 94 5.6 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . 95 5.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 6 Concluding Remarks 105 6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 6.2 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 6.3 Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . 108 Abstract (In Korean) 128Docto

A Benchmark and Evaluation of Non-Rigid Structure from Motion

Non-Rigid structure from motion (NRSfM), is a long standing and central problem in computer vision, allowing us to obtain 3D information from multiple images when the scene is dynamic. A main issue regarding the further development of this important computer vision topic, is the lack of high quality data sets. We here address this issue by presenting of data set compiled for this purpose, which is made publicly available, and considerably larger than previous state of the art. To validate the applicability of this data set, and provide and investigation into the state of the art of NRSfM, including potential directions forward, we here present a benchmark and a scrupulous evaluation using this data set. This benchmark evaluates 16 different methods with available code, which we argue reasonably spans the state of the art in NRSfM. We also hope, that the presented and public data set and evaluation, will provide benchmark tools for further development in this field

Simultaneous Correspondences Estimation and Non-Rigid Structure Reconstruction

Given multi-view correspondences, it has been shown that 3D non-rigid structure can be recovered through factorization based techniques. However, establishing reliable correspondences across multi-view images of non-rigid structure is not an easy task. Existing methods solve multi-view correspondences and 3D non-rigid structure in sequel, which cannot exploit the crossover constraints in each sub-problem (i.e., constraints in non-rigid structure has not been enforced in establishing multi-view correspondences and verse vise). In this paper, we present a unified framework to simultaneously solve for multi-view correspondences and non-rigid structure. We formulate the problem by using the Partial Permutation Matrices (PPMs) and aim at establishing multi-view correspondences while simultaneously enforcing the low-rank constraint in non-rigid structure deformation. Additionally, our method can handle outliers and missing data elegantly under the same framework. We solve the simultaneous non-rigid structure and correspondences recovery problem via the Alternating Direction Method of Multipliers (ADMM). Experimental results on both synthetic and real images show that the proposed method achieves state-of-the-art performance on both sparse and dense non-rigid reconstruction problems.This work was supported in part by Australian Research Council (ARC) grants (DE140100180, DP120103896, LP100100588, and CE140100016) and Natural Science Foundation of China (61420106007)

Real-time 3D reconstruction of non-rigid shapes with a single moving camera

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/This paper describes a real-time sequential method to simultaneously recover the camera motion and the 3D shape of deformable objects from a calibrated monocular video. For this purpose, we consider the Navier-Cauchy equations used in 3D linear elasticity and solved by finite elements, to model the time-varying shape per frame. These equations are embedded in an extended Kalman filter, resulting in sequential Bayesian estimation approach. We represent the shape, with unknown material properties, as a combination of elastic elements whose nodal points correspond to salient points in the image. The global rigidity of the shape is encoded by a stiffness matrix, computed after assembling each of these elements. With this piecewise model, we can linearly relate the 3D displacements with the 3D acting forces that cause the object deformation, assumed to be normally distributed. While standard finite-element-method techniques require imposing boundary conditions to solve the resulting linear system, in this work we eliminate this requirement by modeling the compliance matrix with a generalized pseudoinverse that enforces a pre-fixed rank. Our framework also ensures surface continuity without the need for a post-processing step to stitch all the piecewise reconstructions into a global smooth shape. We present experimental results using both synthetic and real videos for different scenarios ranging from isometric to elastic deformations. We also show the consistency of the estimation with respect to 3D ground truth data, include several experiments assessing robustness against artifacts and finally, provide an experimental validation of our performance in real time at frame rate for small mapsPeer ReviewedPostprint (author's final draft