Sparse Representation for 3D Shape Estimation: A Convex Relaxation Approach

By Xiaowei Zhou, Menglong Zhu, Spyridon Leonardos, Kostas Daniilidis. 2015

154 citations recorded by the source corpus.

We investigate the problem of estimating the 3D shape of an object defined by a set of 3D landmarks, given their 2D correspondences in a single image. A successful approach to alleviating the reconstruction ambiguity is the 3D deformable shape model and a sparse representation is often used to capture complex shape variability. But the model inference is still challenging due to the nonconvexity in the joint optimization of shape and viewpoint. In contrast to prior work that relies on an alternating scheme whose solution depends on initialization, we propose a convex approach to addressing this challenge and develop an efficient algorithm to solve the proposed convex program. We further propose a robust model to handle gross errors in the 2D correspondences. We demonstrate the exact recovery property of the proposed method, the advantage compared to several nonconvex baselines and the applicability to recover 3D human poses and car models from single images.

Subfields: Aerospace Engineering, Computational Mechanics, Computer Vision and Pattern Recognition

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Citations in the corpus

End-to-End Recovery of Human Shape and Pose (2017, methodology): “Two stage methods first predict 2D joint locations using 2D pose detectors [30, 49, 54] or ground truth 2D pose and then predict 3D joint locations from the 2D joints either by regression [26, 29] or model fitting, where a common approach exploits a learned dictionary of 3D skeletons [2, 34, 47, 37,”
MonoCap: Monocular Human Motion Capture using a CNN Coupled with a Geometric Prior (2017, unknown): “Next, the robust estimation algorithm from [58] is applied to initialize the parameters.”
License Plate Detection and Recognition in Unconstrained Scenarios (2018, methodology): “Although 3D pose estimation methods such as [32] might be used to determine the resize scale, this work presents a simple and fast procedure based on the aspect ratio of the vehicle BB.”
Graduated Non-Convexity for Robust Spatial Perception: From Non-Minimal Solvers to Global Outlier Rejection (2019, methodology): “While related techniques propose approximate relaxations [15], we provide a certifiably optimal solution using SOS relaxation.”
Monocular 3D Human Pose Estimation Using Transfer Learning and Improved CNN Supervision (2016, background): “This is computationally expensive, but allows incorporation of pose priors or inter-penetration constraints [11], sparsity assumptions [81, 88, 90], joint limits [55, 20, 2], and temporal constraints [56].”
3D Human Pose Estimation from a Single Image via Distance Matrix Regression (2016, methodology): “This is the same evaluation protocol used by the baselines we compare against [3, 6, 8, 10, 12, 21, 30, 31, 38, 39, 40, 45, 47, 50, 52, 55, 56].”
Unite the People: Closing the Loop Between 3D and 2D Human Representations (2017, background): “e estimator, we achieve an improvement of 5.4mm on average on the HumanEva dataset and an improvement of 1.6mm on average on the Human3.6M dataset (4th versus 5th row). HumanEva Human3.6M Zhou et al. [46] 110.0 106.7 DP from 91 landmarks 93.5 93.9 SMPLify on DeepCut CNN lms. [4] 79.9 82.3 SMPLify on”
HybrIK: A Hybrid Analytical-Neural Inverse Kinematics Solution for 3D Human Pose and Shape Estimation (2020, methodology): “Two-stage approaches first estimate 2D pose and then lift them to 3D joint locations by a learned dictionary of 3D skeleton [1, 53, 64, 56, 76, 77] or regression [46, 71, 40, 11, 32, 59].”
Sparseness Meets Deepness: 3D Human Pose Estimation from Monocular Video (2015, methodology): “Next, the robust estimation algorithm from [56] is applied to initialize the parameters.”
C3DPO: Canonical 3D Pose Networks for Non-Rigid Structure From Motion (2019, methodology): “Priors about the shape and the camera motion are employed to improve conditioning of the problem, including the use of low-rank subspaces in the spatial domain [3, 11, 9, 43], temporal domain, for example, fitting 2D keypoint trajectories to a set of predefined DCT basis functions [4, 5], spatio-tem”
Lifting from the Deep: Convolutional 3D Pose Estimation from a Single Image (2017, methodology): “Representing human 3D pose as a linear combination of a sparse set of 3D bases, pretrained using 3D mocap data, has also proved a popular approach for articulated human motion [28, 43, 49], while [49] propose a convex relaxation to jointly estimate the coefficients of the sparse representation and t”
A Simple Yet Effective Baseline for 3d Human Pose Estimation (2017, methodology): “2d/3d positions Our first design choice is to use 2d and 3d points as inputs and outputs, in contrast to recent work that has used raw images [11,13,24,32,33,45,46,54,56] or 2d probability distributions [33, 56] as inputs, and 3d probabilities [33], 3d motion parameters [54] or basis pose coefficien”
AI in Medical Imaging Informatics: Current Challenges and Future Directions (2020, unknown): “Active shapemodelscontaininformationonthestatisticalvariation oftheobjectinthepopulationandthecharacteristicoftheir images[91].”
Monocular 3D Human Pose Estimation in the Wild Using Improved CNN Supervision (2016, background): “3dhp-dataset of the projection of a 3D human model to the 2D predictions is computationally expensive and ambiguous, but the ambiguity can be addressed through pose priors and it further allows incorporation of various constraints such as inter-penetration constraints [7], sparsity assumptions [68, ”