Joint Rigid Registration of Multiple Generalized Point Sets With Anisotropic Positional Uncertainties in Image-Guided Surgery

In medical image analysis (MIA) and computer-assisted surgery (CAS), aligning two multiple point sets (PSs) together is an essential but also a challenging problem. For example, rigidly aligning multiple point sets into one common coordinate frame is a prerequisite for statistical shape modelling (SSM). Accurately aligning the pre-operative space with the intra-operative space in CAS is very crucial to successful interventions. In this article, we formally formulate the multiple generalized point set registration problem (MGPSR) in a probabilistic manner, where both the positional and the normal vectors are used. The six-dimensional vectors consisting of both positional and normal vectors are called as generalized points. In the formulated model, all the generalized PSs to be registered are considered to be the realizations of underlying unknown hybrid mixture models (HMMs). By assuming the independence of the positional and orientational vectors (i.e., the normal vectors), the probability density function (PDF) of an observed generalized point is computed as the product of Gaussian and Fisher distributions. Furthermore, to consider the anisotropic noise in surgical navigation, the positional error is assumed to obey a multi-variate Gaussian distribution. Finally, registering PSs is formulated as a maximum likelihood (ML) problem, and solved under the expectation maximization (EM) technique. By using more enriched information (i.e., the normal vectors), our algorithm is more robust to outliers. By treating all PSs equally, our algorithm does not bias towards any PS. To validate the proposed approach, extensive experiments have been conducted on surface points extracted from CT images of (i) a human femur bone model; (ii) a human pelvis bone model. Results demonstrate our algorithm's high accuracy, robustness to noise and outliers

Generalized Point Set Registration with the Kent Distribution

Point set registration (PSR) is an essential problem in communities of computer vision, medical robotics and biomedical engineering. This paper is motivated by considering the anisotropic characteristics of the error values in estimating both the positional and orientational vectors from the PSs to be registered. To do this, the multi-variate Gaussian and Kent distributions are utilized to model the positional and orientational uncertainties, respectively. Our contributions of this paper are three-folds: (i) the PSR problem using normal vectors is formulated as a maximum likelihood estimation (MLE) problem, where the anisotropic characteristics in both positional and normal vectors are considered; (ii) the matrix forms of the objective function and its associated gradients with respect to the desired parameters are provided, which can facilitate the computational process; (iii) two approaches of computing the normalizing constant in the Kent distribution are compared. We verify our proposed registration method on various PSs (representing pelvis and femur bones) in computer-assisted orthopedic surgery (CAOS). Extensive experimental results demonstrate that our method outperforms the state-of-the-art methods in terms of the registration accuracy and the robustness

Aligning 3D Curve with Surface Using Tangent and Normal Vectors for Computer-Assisted Orthopedic Surgery

Registration that aligns different views of one interested organ together is an essential technique and outstanding problem in medical robotics and image-guided surgery (IGS). This work introduces a novel rigid point set registration (PSR) approach that aims to accurately map the pre-operative space with the intra-operative space to enable successful image guidance for computer-assisted orthopaedic surgery (CAOS). The normal vectors and tangent vectors are first extracted from the pre-operative and intra-operative point sets (PSs) respectively, and are further utilized to enhance the registration accuracy and robustness. The contributions of this article are three-folds. First, we propose and formulate a novel distribution that describes the error between one normal vector and the corresponding tangent vector based on the von-Mises Fisher (vMF) distribution. Second, by modelling the anisotropic position localization error with the multi-variate Gaussian distribution, we formulate the PSR considering anisotropic localization error as a maximum likelihood estimation (MLE) problem and then solve it under the expectation maximization (EM) framework. Third, to facilitate the optimization process, the gradients of the objective function with respect to the desired parameters are computed and presented. Extensive experimental results on the human femur and pelvis models verify that the proposed approach outperforms the state-of-the-art methods, and demonstrate potential clinical values for relevant surgical navigation applications

Generalized Coherent Point Drift With Multi-Variate Gaussian Distribution and Watson Distribution

This letter introduces a novel rigid point set registration (PSR) approach that accurately aligns the pre-operative space and the intra-operative space together in the scenario of computer-Assisted orthopedic surgery (CAOS). Motivated by considering anisotropic positional localization noise and utilizing undirected normal vectors in the point sets (PSs), the multi-variate Gaussian distribution and the Watson distribution are utilized to model positional and normal vectors' error distributions respectively. In the proposed approach, with the above probability distributions, the PSR problem is then formulated as a maximum likelihood estimation (MLE) problem and solved under the expectation maximization (EM) framework. Our contributions are three folds. First, the rigid registration problem of aligning generalized points with undirected normal vectors is formally formulated in a probabilistic manner. Second, the MLE problem is solved under the EM framework. Third, the gradients of associated objective functions with respect to desired parameters are computed and provided. Experimental results on both the human pelvis and femur models demonstrate the potential clinical values and that the proposed approach owns significantly improved performances compared with existing methods

Generalized Point Set Registration with Fuzzy Correspondences Based on Variational Bayesian Inference

Point set registration (PSR) is an essential problem in surgical navigation and computer-assisted surgery (CAS). In CAS, PSR can be used to map the intra-operative surgical space with the pre-operative volumetric image space. The performances of PSR in real-world surgical scenarios are sensitive to noise and outliers. This paper proposes a novel point set registration approach where the additional features (i.e., the normal vectors) extracted from the point sets are utilized, and the convergence of the algorithm is guaranteed from the theoretical perspective. More specifically, we formulate the PSR with normal vectors by generalizing the Bayesian coherent point drift (BCPD) into the six-dimensional scenario. The proposed algorithm is more accurate and robust to noise and outliers, and the theoretical convergence of the proposed approach is guaranteed. Our contributions of this paper are summarized as follows. (1) The PSR problem with normal vectors is formally formulated through generalizing the BCPD approach; (2) The formulas for updating the parameters during the algorithm's iterations are given in closed forms; (3) Extensive experiments have been done to verify the proposed approach and specifically its significant improvements over the BCPD has been validated

Robust Moving Objects Detection in Lidar Data Exploiting Visual Cues

Detecting moving objects in dynamic scenes from sequences of lidar scans is an important task in object tracking, mapping, localization, and navigation. Many works focus on changes detection in previously observed scenes, while a very limited amount of literature addresses moving objects detection. The state-of-the-art method exploits Dempster-Shafer Theory to evaluate the occupancy of a lidar scan and to discriminate points belonging to the static scene from moving ones. In this paper we improve both speed and accuracy of this method by discretizing the occupancy representation, and by removing false positives through visual cues. Many false positives lying on the ground plane are also removed thanks to a novel ground plane removal algorithm. Efficiency is improved through an octree indexing strategy. Experimental evaluation against the KITTI public dataset shows the effectiveness of our approach, both qualitatively and quantitatively with respect to the state- of-the-art

Robust Localization in 3D Prior Maps for Autonomous Driving.

In order to navigate autonomously, many self-driving vehicles require precise localization within an a priori known map that is annotated with exact lane locations, traffic signs, and additional metadata that govern the rules of the road. This approach transforms the extremely difficult and unpredictable task of online perception into a more structured localization problem—where exact localization in these maps provides the autonomous agent a wealth of knowledge for safe navigation. This thesis presents several novel localization algorithms that leverage a high-fidelity three-dimensional (3D) prior map that together provide a robust and reliable framework for vehicle localization. First, we present a generic probabilistic method for localizing an autonomous vehicle equipped with a 3D light detection and ranging (LIDAR) scanner. This proposed algorithm models the world as a mixture of several Gaussians, characterizing the z-height and reflectivity distribution of the environment—which we rasterize to facilitate fast and exact multiresolution inference. Second, we propose a visual localization strategy that replaces the expensive 3D LIDAR scanners with significantly cheaper, commodity cameras. In doing so, we exploit a graphics processing unit to generate synthetic views of our belief environment, resulting in a localization solution that achieves a similar order of magnitude error rate with a sensor that is several orders of magnitude cheaper. Finally, we propose a visual obstacle detection algorithm that leverages knowledge of our high-fidelity prior maps in its obstacle prediction model. This not only provides obstacle awareness at high rates for vehicle navigation, but also improves our visual localization quality as we are cognizant of static and non-static regions of the environment. All of these proposed algorithms are demonstrated to be real-time solutions for our self-driving car.PhDComputer Science and EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133410/1/rwolcott_1.pd

Robust and Accurate Point Set Registration with Generalized Bayesian Coherent Point Drift

Point set registration (PSR) is an essential problem in surgical navigation and image-guided surgery (IGS). It can help align the pre-operative volumetric images with the intra-operative surgical space. The performances of PSR are susceptible to noise and outliers, which are the cases in real-world surgical scenarios. In this paper, we provide a novel point set registration method that utilizes the features extracted from the PSs and can guarantee the convergence of the algorithm simultaneously. More specifically, we formulate the PSR with normal vectors by generalizing the bayesian coherent point drift (BCPD) into the six-dimension scenario. Our contributions can be summarized as follows. (1) The PSR problem with normal vectors is formulated by generalizing the Bayesian coherent point drift (BCPD) approach; (2) The updated parameters during the algorithm's iterations are given in closed-forms; (3) Extensive experiments have been done to verify the proposed approach and its significant improvements over the BCPD has been validated. We have validated our proposed registration approach on both the human femur model. Results demonstrate that our proposed method outperforms the state-of-the-art registration methods and the convergence is guaranteed at the same time