A closed-form solution to estimate uncertainty in non-rigid structure from motion

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.

Combining Deep Learning with Geometric Features for Image based Localization in the Gastrointestinal Tract

Tracking monocular colonoscope in the Gastrointestinal tract (GI) is a challenging problem as the images suffer from deformation, blurred textures, significant changes in appearance. They greatly restrict the tracking ability of conventional geometry based methods. Even though Deep Learning (DL) can overcome these issues, limited labeling data is a roadblock to state-of-art DL method. Considering these, we propose a novel approach to combine DL method with traditional feature based approach to achieve better localization with small training data. Our method fully exploits the best of both worlds by introducing a Siamese network structure to perform few-shot classification to the closest zone in the segmented training image set. The classified label is further adopted to initialize the pose of scope. To fully use the training dataset, a pre-generated triangulated map points within the zone in the training set are registered with observation and contribute to estimating the optimal pose of the test image. The proposed hybrid method is extensively tested and compared with existing methods, and the result shows significant improvement over traditional geometric based or DL based localization. The accuracy is improved by 28.94% (Position) and 10.97% (Orientation) with respect to state-of-art method.

Uncertainty Quantification for Hyperspectral Image Denoising Frameworks based on Low-rank Matrix Approximation

Low-rank matrix approximation (LRMA) is a technique widely applied in hyperspectral images (HSI) denoising or completion. The uncertainty quantification of the estimated restored HSI, however, has not been addressed in previous researches. The lack of uncertainty of the product significantly limits the applications like multi-source or multi-scale data fusion, data assimilation and product confidence quantification, since these applications require an accurate way to describe the statistical distributions of the source data. To address this issue, we propose a prior-free closed-form element-wise uncertainty quantification method for the LRMA based HSI restoration. The proposed approach only requires the uncertainty of the observed HSI and can yield uncertainty in a limited amount of time and with similar time complexity comparing to the LRMA technique. We conduct extensive experiments to validate that the closed-form uncertainty describes the estimation accurately, is robust to at least 10\% ratio of random impulse noises and takes only around 10-20% amount of time of LRMA. All the experiments indicate that the proposed closed-form uncertainty quantification method is more applicable to be deployed to real-world applications than the baseline Monte-Carlo tests.

Dynamic Reconstruction of Deformable Soft-tissue with Stereo Scope in Minimal Invasive Surgery

In minimal invasive surgery, it is important to rebuild and visualize the latest deformed shape of soft-tissue surfaces to mitigate tissue damages. This paper proposes an innovative Simultaneous Localization and Mapping (SLAM) algorithm for deformable dense reconstruction of surfaces using a sequence of images from a stereoscope. We introduce a warping field based on the Embedded Deformation (ED) nodes with 3D shapes recovered from consecutive pairs of stereo images. The warping field is estimated by deforming the last updated model to the current live model. Our SLAM system can: (1) Incrementally build a live model by progressively fusing new observations with vivid accurate texture. (2) Estimate the deformed shape of unobserved region with the principle As-Rigid-As-Possible. (3) Show the consecutive shape of models. (4) Estimate the current relative pose between the soft-tissue and the scope. In-vivo experiments with publicly available datasets demonstrate that the 3D models can be incrementally built for different soft-tissues with different deformations from sequences of stereo images obtained by laparoscopes. Results show the potential clinical application of our SLAM system for providing surgeon useful shape and texture information in minimal invasive surgery.

Curved Buildings Reconstruction from Airborne LiDAR Data by Matching and Deforming Geometric Primitives

Airborne LiDAR (Light Detection and Ranging) data is widely applied in building reconstruction, with studies reporting success in typical buildings. However, the reconstruction of curved buildings remains an open research problem. To this end, we propose a new framework for curved building reconstruction via assembling and deforming geometric primitives. The input LiDAR point cloud are first converted into contours where individual buildings are identified. After recognizing geometric units (primitives) from building contours, we get initial models by matching basic geometric primitives to these primitives. To polish assembly models, we employ a warping field for model refinements. Specifically, an embedded deformation (ED) graph is constructed via downsampling the initial model. Then, the point-to-model displacements are minimized by adjusting node parameters in the ED graph based on our objective function. The presented framework is validated on several highly curved buildings collected by various LiDAR in different cities. The experimental results, as well as accuracy comparison, demonstrate the advantage and effectiveness of our method. {The new insight attributes to an efficient reconstruction manner.} Moreover, we prove that the primitive-based framework significantly reduces the data storage to 10-20 percent of classical mesh models.

Are We Ready for Service Robots? The OpenLORIS-Scene Datasets for Lifelong SLAM

Service robots should be able to operate autonomously in dynamic and daily changing environments over an extended period of time. While Simultaneous Localization And Mapping (SLAM) is one of the most fundamental problems for robotic autonomy, most existing SLAM works are evaluated with data sequences that are recorded in a short period of time. In real-world deployment, there can be out-of-sight scene changes caused by both natural factors and human activities. For example, in home scenarios, most objects may be movable, replaceable or deformable, and the visual features of the same place may be significantly different in some successive days. Such out-of-sight dynamics pose great challenges to the robustness of pose estimation, and hence a robot's long-term deployment and operation. To differentiate the forementioned problem from the conventional works which are usually evaluated in a static setting in a single run, the term lifelong SLAM is used here to address SLAM problems in an ever-changing environment over a long period of time. To accelerate lifelong SLAM research, we release the OpenLORIS-Scene datasets. The data are collected in real-world indoor scenes, for multiple times in each place to include scene changes in real life. We also design benchmarking metrics for lifelong SLAM, with which the robustness and accuracy of pose estimation are evaluated separately. The datasets and benchmark are available online at https://lifelong-robotic-vision.github.io/dataset/scene.

An observable time series based SLAM algorithm for deforming environment

In this paper, we study the back-end of simultaneous localization and mapping (SLAM) problem in deforming environment, where robot localizes itself and tracks multiple non-rigid soft surface using its onboard sensor measurements. An elaborate analysis is conducted on conventional deformation modelling method, Embedded Deformation (ED) graph. We demonstrate and prove that the ED graph widely used in such scenarios is unobservable and leads to multiple solutions unless suitable priors are provided. Example as well as theoretical prove are provided to show the ambiguity of ED graph and camera pose. In modelling non-rigid scenario with ED graph, motion priors of the deforming environment is essential to separate robot pose and deforming environment. The conclusion can be extrapolated to any free form deformation formulation. In solving the observability, this research proposes a preliminary deformable SLAM approach to estimate robot pose in complex environments that exhibits regular motion. A strategy that approximates deformed shape using a linear combination of several previous shapes is proposed to avoid the ambiguity in robot movement and rigid and non-rigid motions of the environment. Fisher information matrix rank analysis with a base case is discussed to prove the effectiveness. Moreover, the proposed algorithm is validated extensively on Monte Carlo simulations and real experiments. It is demonstrated that the new algorithm significantly outperforms conventional rigid SLAM and ED based SLAM especially in scenarios where there is large deformation.

Efficient two step optimization for large embedded deformation graph based SLAM

Embedded deformation nodes based formulation has been widely applied in deformable geometry and graphical problems. Though being promising in stereo (or RGBD) sensor based SLAM applications, it remains challenging to keep constant speed in deformation nodes parameter estimation when model grows larger. In practice, the processing time grows rapidly in accordance with the expansion of maps. In this paper, we propose an approach to decouple nodes of deformation graph in large scale dense deformable SLAM and keep the estimation time to be constant. We observe that only partial deformable nodes in the graph are connected to visible points. Based on this fact, sparsity of original Hessian matrix is utilized to split parameter estimation in two independent steps. With this new technique, we achieve faster parameter estimation with amortized computation complexity reduced from O(n^2) to closing O(1). As a result, the computation cost barely increases as the map keeps growing. Based on our strategy, computational bottleneck in large scale embedded deformation graph based applications will be greatly mitigated. The effectiveness is validated by experiments, featuring large scale deformation scenarios.

MIS-SLAM: Real-time Large Scale Dense Deformable SLAM System in Minimal Invasive Surgery Based on Heterogeneous Computing

Real-time simultaneously localization and dense mapping is very helpful for providing Virtual Reality and Augmented Reality for surgeons or even surgical robots. In this paper, we propose MIS-SLAM: a complete real-time large scale dense deformable SLAM system with stereoscope in Minimal Invasive Surgery based on heterogeneous computing by making full use of CPU and GPU. Idled CPU is used to perform ORB- SLAM for providing robust global pose. Strategies are taken to integrate modules from CPU and GPU. We solved the key problem raised in previous work, that is, fast movement of scope and blurry images make the scope tracking fail. Benefiting from improved localization, MIS-SLAM can achieve large scale scope localizing and dense mapping in real-time. It transforms and deforms current model and incrementally fuses new observation while keeping vivid texture. In-vivo experiments conducted on publicly available datasets presented in the form of videos demonstrate the feasibility and practicality of MIS-SLAM for potential clinical purpose.

Convergence and Consistency Analysis for A 3D Invariant-EKF SLAM

In this paper, we investigate the convergence and consistency properties of an Invariant-Extended Kalman Filter (RI-EKF) based Simultaneous Localization and Mapping (SLAM) algorithm. Basic convergence properties of this algorithm are proven. These proofs do not require the restrictive assumption that the Jacobians of the motion and observation models need to be evaluated at the ground truth. It is also shown that the output of RI-EKF is invariant under any stochastic rigid body transformation in contrast to $\mathbb{SO}(3)$ based EKF SLAM algorithm ($\mathbb{SO}(3)$-EKF) that is only invariant under deterministic rigid body transformation. Implications of these invariance properties on the consistency of the estimator are also discussed. Monte Carlo simulation results demonstrate that RI-EKF outperforms $\mathbb{SO}(3)$-EKF, Robocentric-EKF and the "First Estimates Jacobian" EKF, for 3D point feature based SLAM.