Semi-Definite Programming (SDP) with low-rank prior has been widely applied in Non-Rigid Structure from Motion (NRSfM). Based on a low-rank constraint, it avoids the inherent ambiguity of basis number selection in conventional base-shape or base-trajectory methods. Despite the efficiency in deformable shape reconstruction, it remains unclear how to assess the uncertainty of the recovered shape from the SDP process. In this paper, we present a statistical inference on the element-wise uncertainty quantification of the estimated deforming 3D shape points in the case of the exact low-rank SDP problem. A closed-form uncertainty quantification method is proposed and tested. Moreover, we extend the exact low-rank uncertainty quantification to the approximate low-rank scenario with a numerical optimal rank selection method, which enables solving practical application in SDP based NRSfM scenario. The proposed method provides an independent module to the SDP method and only requires the statistic information of the input 2D tracked points. Extensive experiments prove that the output 3D points have identical normal distribution to the 2D trackings, the proposed method and quantify the uncertainty accurately, and supports that it has desirable effects on routinely SDP low-rank based NRSfM solver.
Imperial College London（帝国理工学院）；Technische Universität München（慕尼黑工业大学）；Sharif University of Technology（谢里夫理工大学）；Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡大学）
We develop a new Bayesian model for non-rigid registration of three-dimensional medical images, with a focus on uncertainty quantification. Probabilistic registration of large images with calibrated uncertainty estimates is difficult for both computational and modelling reasons. To address the computational issues, we explore connections between the Markov chain Monte Carlo by backpropagation and the variational inference by backpropagation frameworks, in order to efficiently draw samples from the posterior distribution of transformation parameters. To address the modelling issues, we formulat…
NICTA（澳大利亚国家信息与通信技术研究院）；Australian National University（澳大利亚国立大学）
A recent paper \cite{CaeCaeSchBar06} proposed a provably optimal, polynomial time method for performing near-isometric point pattern matching by means of exact probabilistic inference in a chordal graphical model. Their fundamental result is that the chordal graph in question is shown to be globally rigid, implying that exact inference provides the same matching solution as exact inference in a complete graphical model. This implies that the algorithm is optimal when there is no noise in the point patterns. In this paper, we present a new graph which is also globally rigid but has an advantage…
Brigham and Women’s Hospital（布莱根妇女医院）；Harvard Medical School（哈佛医学院）；Graduate School of Frontier Sciences, The University of Tokyo（东京大学前沿科学研究生院）；Department of Automation, Tsinghua University（清华大学自动化系）；Center for Advanced Intelligence Project, RIKEN（理化学研究所先进智能项目中心）
In image-guided neurosurgery, current commercial systems usually provide only rigid registration, partly because it is harder to predict, validate and understand non-rigid registration error. For instance, when surgeons see a discrepancy in aligned image features, they may not be able to distinguish between registration error and actual tissue deformation caused by tumor resection. In this case, the spatial distribution of registration error could help them make more informed decisions, e.g., ignoring the registration where the estimated error is high. However, error estimates are difficult to…
Uncertainty Propagation for Echocardiography Clinical Metric Estimation via Contour Sampling
University of Sherbrooke（谢布鲁克大学）；INSA（国立应用科学学院）；Universite Claude Bernard Lyon 1（里昂第一大学（克洛德·贝尔纳））；CNRS（法国国家科学研究中心）；Inserm（法国国家健康与医学研究院）；CREATIS（CREATIS研究机构）；Ultromics Ltd.（Ultromics有限公司）；King’s College London（伦敦国王学院）
Institute of Intelligent Vehicles, School of Automotive Studies, Tongji University（同济大学汽车学院智能车辆研究所）
Object localization in 3D space is a challenging aspect in monocular 3D object detection. Recent advances in 6DoF pose estimation have shown that predicting dense 2D-3D correspondence maps between image and object 3D model and then estimating object pose via Perspective-n-Point (PnP) algorithm can achieve remarkable localization accuracy. Yet these methods rely on training with ground truth of object geometry, which is difficult to acquire in real outdoor scenes. To address this issue, we propose MonoRUn, a novel detection framework that learns dense correspondences and geometry in a self-supe…
The two-stage object pose estimation paradigm first detects semantic keypoints on the image and then estimates the 6D pose by minimizing reprojection errors. Despite performing well on standard benchmarks, existing techniques offer no provable guarantees on the quality and uncertainty of the estimation. In this paper, we inject two fundamental changes, namely conformal keypoint detection and geometric uncertainty propagation, into the two-stage paradigm and propose the first pose estimator that endows an estimation with provable and computable worst-case error bounds. On one hand, conformal ke…
Propagation and Attribution of Uncertainty in Medical Imaging Pipelines
Technical University of Munich（慕尼黑工业大学）；Imperial College London（帝国理工学院）；German Cancer Consortium DKTK（德国癌症研究联盟（DKTK））；Helmholtz-Zentrum Munich（慕尼黑亥姆霍兹中心）
The inputs of deep neural network (DNN) from real-world data usually come with uncertainties. Yet, it is challenging to propagate the uncertainty in the input features to the DNN predictions at a low computational cost. This work employs a gradient-based subspace method and response surface technique to accelerate the uncertainty propagation in DNN. Specifically, the active subspace method is employed to identify the most important subspace in the input features using the gradient of the DNN output to the inputs. Then the response surface within that low-dimensional subspace can be efficiently…
GUPNet++: Geometry Uncertainty Propagation Network for Monocular 3D Object Detection
School of Electrical and Information Engineering, University of Sydney（悉尼大学电气与信息工程学院）；Shanghai AI Laboratory（上海人工智能实验室）；SenseTime Group Limited（商汤科技集团有限公司）；University of Science and Technology of China（中国科学技术大学）
From Propagation to Prediction: Point-level Uncertainty Evaluation of MLS Point Clouds under Limited Ground Truth
Chair of Engineering Geodesy, TUM School of Engineering and Design, Technical University of Munich（工程测绘学系，技术大学慕尼黑工程与设计学院）；TUM Leonhard Obermeyer Center, Technical University of Munich（技术大学慕尼黑Leonhard Obermeyer中心）；CV4DT, University of Cambridge（剑桥大学CV4DT）
University of Bath（巴斯大学）；University of Bristol（布里斯托大学）
The shape of an object is an important characteristic for many vision problems such as segmentation, detection and tracking. Being independent of appearance, it is possible to generalize to a large range of objects from only small amounts of data. However, shapes represented as silhouette images are challenging to model due to complicated likelihood functions leading to intractable posteriors. In this paper we present a generative model of shapes which provides a low dimensional latent encoding which importantly resides on a smooth manifold with respect to the silhouette images. The proposed m…
We propose a feed-forward inference method applicable to belief and neural networks. In a belief network, the method estimates an approximate factorized posterior of all hidden units given the input. In neural networks the method propagates uncertainty of the input through all the layers. In neural networks with injected noise, the method analytically takes into account uncertainties resulting from this noise. Such feed-forward analytic propagation is differentiable in parameters and can be trained end-to-end. Compared to standard NN, which can be viewed as propagating only the means, we propa…
