RKHS-BA: A Semantic Correspondence-Free Multi-View Registration Framework with Global Tracking

This work reports a novel Bundle Adjustment (BA) formulation using a Reproducing Kernel Hilbert Space (RKHS) representation called RKHS-BA. The proposed formulation is correspondence-free, enables the BA to use RGB-D/LiDAR and semantic labels in the optimization directly, and provides a generalization for the photometric loss function commonly used in direct methods. RKHS-BA can incorporate appearance and semantic labels within a continuous spatial-semantic functional representation that does not require optimization via image pyramids. We demonstrate its applications in sliding-window odometry and global LiDAR mapping, which show highly robust performance in extremely challenging scenes and the best trade-off of generalization and accuracy.

BDIS-SLAM: A lightweight CPU-based dense stereo SLAM for surgery

Purpose: Common dense stereo Simultaneous Localization and Mapping (SLAM) approaches in Minimally Invasive Surgery (MIS) require high-end parallel computational resources for real-time implementation. Yet, it is not always feasible since the computational resources should be allocated to other tasks like segmentation, detection, and tracking. To solve the problem of limited parallel computational power, this research aims at a lightweight dense stereo SLAM system that works on a single-core CPU and achieves real-time performance (more than 30 Hz in typical scenarios). Methods: A new dense stereo mapping module is integrated with the ORB-SLAM2 system and named BDIS-SLAM. Our new dense stereo mapping module includes stereo matching and 3D dense depth mosaic methods. Stereo matching is achieved with the recently proposed CPU-level real-time matching algorithm Bayesian Dense Inverse Searching (BDIS). A BDIS-based shape recovery and a depth mosaic strategy are integrated as a new thread and coupled with the backbone ORB-SLAM2 system for real-time stereo shape recovery. Results: Experiments on in-vivo data sets show that BDIS-SLAM runs at over 30 Hz speed on modern single-core CPU in typical endoscopy/colonoscopy scenarios. BDIS-SLAM only consumes around an additional 12% time compared with the backbone ORB-SLAM2. Although our lightweight BDIS-SLAM simplifies the process by ignoring deformation and fusion procedures, it can provide a usable dense mapping for modern MIS on computationally constrained devices. Conclusion: The proposed BDIS-SLAM is a lightweight stereo dense SLAM system for MIS. It achieves 30 Hz on a modern single-core CPU in typical endoscopy/colonoscopy scenarios (image size around 640*480). BDIS-SLAM provides a low-cost solution for dense mapping in MIS and has the potential to be applied in surgical robots and AR systems.

Iterative PnP and its application in 3D-2D vascular image registration for robot navigation

This paper reports on a new real-time robot-centered 3D-2D vascular image alignment algorithm, which is robust to outliers and can align nonrigid shapes. Few works have managed to achieve both real-time and accurate performance for vascular intervention robots. This work bridges high-accuracy 3D-2D registration techniques and computational efficiency requirements in intervention robot applications. We categorize centerline-based vascular 3D-2D image registration problems as an iterative Perspective-n-Point (PnP) problem and propose to use the Levenberg-Marquardt solver on the Lie manifold. Then, the recently developed Reproducing Kernel Hilbert Space (RKHS) algorithm is introduced to overcome the ``big-to-small'' problem in typical robotic scenarios. Finally, an iterative reweighted least squares is applied to solve RKHS-based formulation efficiently. Experiments indicate that the proposed algorithm processes registration over 50 Hz (rigid) and 20 Hz (nonrigid) and obtains competing registration accuracy similar to other works. Results indicate that our Iterative PnP is suitable for future vascular intervention robot applications.

Optical flow-based vascular respiratory motion compensation

This paper develops a new vascular respiratory motion compensation algorithm, Motion-Related Compensation (MRC), to conduct vascular respiratory motion compensation by extrapolating the correlation between invisible vascular and visible non-vascular. Robot-assisted vascular intervention can significantly reduce the radiation exposure of surgeons. In robot-assisted image-guided intervention, blood vessels are constantly moving/deforming due to respiration, and they are invisible in the X-ray images unless contrast agents are injected. The vascular respiratory motion compensation technique predicts 2D vascular roadmaps in live X-ray images. When blood vessels are visible after contrast agents injection, vascular respiratory motion compensation is conducted based on the sparse Lucas-Kanade feature tracker. An MRC model is trained to learn the correlation between vascular and non-vascular motions. During the intervention, the invisible blood vessels are predicted with visible tissues and the trained MRC model. Moreover, a Gaussian-based outlier filter is adopted for refinement. Experiments on in-vivo data sets show that the proposed method can yield vascular respiratory motion compensation in 0.032 sec, with an average error 1.086 mm. Our real-time and accurate vascular respiratory motion compensation approach contributes to modern vascular intervention and surgical robots.

BDIS: Bayesian Dense Inverse Searching Method for Real-Time Stereo Surgical Image Matching

In stereoscope-based Minimally Invasive Surgeries (MIS), dense stereo matching plays an indispensable role in 3D shape recovery, AR, VR, and navigation tasks. Although numerous Deep Neural Network (DNN) approaches are proposed, the conventional prior-free approaches are still popular in the industry because of the lack of open-source annotated data set and the limitation of the task-specific pre-trained DNNs. Among the prior-free stereo matching algorithms, there is no successful real-time algorithm in none GPU environment for MIS. This paper proposes the first CPU-level real-time prior-free stereo matching algorithm for general MIS tasks. We achieve an average 17 Hz on 640*480 images with a single-core CPU (i5-9400) for surgical images. Meanwhile, it achieves slightly better accuracy than the popular ELAS. The patch-based fast disparity searching algorithm is adopted for the rectified stereo images. A coarse-to-fine Bayesian probability and a spatial Gaussian mixed model were proposed to evaluate the patch probability at different scales. An optional probability density function estimation algorithm was adopted to quantify the prediction variance. Extensive experiments demonstrated the proposed method's capability to handle ambiguities introduced by the textureless surfaces and the photometric inconsistency from the non-Lambertian reflectance and dark illumination. The estimated probability managed to balance the confidences of the patches for stereo images at different scales. It has similar or higher accuracy and fewer outliers than the baseline ELAS in MIS, while it is 4-5 times faster. The code and the synthetic data sets are available at https://github.com/JingweiSong/BDIS-v2.

Fusing Convolutional Neural Network and Geometric Constraint for Image-based Indoor Localization

This paper proposes a new image-based localization framework that explicitly localizes the camera/robot by fusing Convolutional Neural Network (CNN) and sequential images' geometric constraints. The camera is localized using a single or few observed images and training images with 6-degree-of-freedom pose labels. A Siamese network structure is adopted to train an image descriptor network, and the visually similar candidate image in the training set is retrieved to localize the testing image geometrically. Meanwhile, a probabilistic motion model predicts the pose based on a constant velocity assumption. The two estimated poses are finally fused using their uncertainties to yield an accurate pose prediction. This method leverages the geometric uncertainty and is applicable in indoor scenarios predominated by diffuse illumination. Experiments on simulation and real data sets demonstrate the efficiency of our proposed method. The results further show that combining the CNN-based framework with geometric constraint achieves better accuracy when compared with CNN-only methods, especially when the training data size is small.

Bayesian dense inverse searching algorithm for real-time stereo matching in minimally invasive surgery

This paper reports a CPU-level real-time stereo matching method for surgical images (10 Hz on 640 * 480 image with a single core of i5-9400). The proposed method is built on the fast ''dense inverse searching'' algorithm, which estimates the disparity of the stereo images. The overlapping image patches (arbitrary squared image segment) from the images at different scales are aligned based on the photometric consistency presumption. We propose a Bayesian framework to evaluate the probability of the optimized patch disparity at different scales. Moreover, we introduce a spatial Gaussian mixed probability distribution to address the pixel-wise probability within the patch. In-vivo and synthetic experiments show that our method can handle ambiguities resulted from the textureless surfaces and the photometric inconsistency caused by the Lambertian reflectance. Our Bayesian method correctly balances the probability of the patch for stereo images at different scales. Experiments indicate that the estimated depth has higher accuracy and fewer outliers than the baseline methods in the surgical scenario.

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.