Point-based rigid-body registration using an unscented Kalman filter

Anatomy-aware computed tomography-to-ultrasound spine registration

BACKGROUND

Ultrasound (US) has demonstrated to be an effective guidance technique for lumbar spine injections, enabling precise needle placement without exposing the surgeon or the patient to ionizing radiation. However, noise and acoustic shadowing artifacts make US data interpretation challenging. To mitigate these problems, many authors suggested using computed tomography (CT)-to-US registration to align the spine in pre-operative CT to intra-operative US data, thus providing localization of spinal landmarks.

PURPOSE

In this paper, we propose a deep learning (DL) pipeline for CT-to-US registration and address the problem of a need for annotated medical data for network training. Firstly, we design a data generation method to generate paired CT-US data where the spine is deformed in a physically consistent manner. Secondly, we train a point cloud (PC) registration network using anatomy-aware losses to enforce anatomically consistent predictions.

METHODS

Our proposed pipeline relies on training the network on realistic generated data. In our data generation method, we model the properties of the joints and disks between vertebrae based on biomechanical measurements in previous studies. We simulate the supine and prone position deformation by applying forces on the spine models. We choose the spine models from 35 patients in VerSe dataset. Each spine is deformed 10 times to create a noise-free data with ground-truth segmentation at hand. In our experiments, we use one-leave-out cross-validation strategy to measure the performance and the stability of the proposed method. For each experiment, we choose generated PCs from three spines as the test set. From the remaining, data from 3 spines act as the validation set and we use the rest of the data for training the algorithm. To train our network, we introduce anatomy-aware losses and constraints on the movement to match the physics of the spine, namely, rigidity loss and bio-mechanical loss. We define rigidity loss based on the fact that each vertebra can only transform rigidly while the disks and the surrounding tissue are deformable. Second, by using bio-mechanical loss we stop the network from inferring extreme movements by penalizing the force needed to get to a certain pose.

RESULTS

To validate the effectiveness of our fully automated data generation pipeline, we qualitatively assess the fidelity of the generated data. This assessment involves verifying the realism of the spinal deformation and subsequently confirming the plausibility of the simulated ultrasound images. Next, we demonstrate that the introduction of the anatomy-aware losses brings us closer to state-of-the-art (SOTA) and yields a reduction of 0.25 mm in terms of target registration error (TRE) compared to using only mean squared error (MSE) loss on the generated dataset. Furthermore, by using the proposed losses, the rigidity loss in inference decreases which shows that the inferred deformation respects the rigidity of the vertebrae and only introduces deformations in the soft tissue area to compensate the difference to the target PC. We also show that our results are close to the SOTA for the simulated US dataset with TRE of 3.89 mm and 3.63 mm for the proposed method and SOTA respectively. In addition, we show that our method is more robust against errors in the initialization in comparison to SOTA and significantly achieves better results (TRE of 4.88 mm compared to 5.66 mm) in this experiment.

CONCLUSIONS

In conclusion, we present a pipeline for spine CT-to-US registration and explore the potential benefits of utilizing anatomy-aware losses to enhance registration results. Additionally, we propose a fully automatic method to synthesize paired CT-US data with physically consistent deformations, which offers the opportunity to generate extensive datasets for network training. The generated dataset and the source code for data generation and registration pipeline can be accessed via https://github.com/mfazampour/medphys_ct_us_registration.

Effect of the number and distribution of fiducial markers on the accuracy of robot-guided implant surgery in edentulous mandibular arches: An in vitro study

OBJECTIVES

Robot-guided implant placement based on the screw marker-assisted registration technique has been applied in dentistry. This study aimed to identify the optimal number and distribution of fiducial markers for robot-guided implant placement in edentulous mandibular phantoms.

METHODS

Four implants were digitally planned and placed in edentulous mandibular phantoms under robotic guidance. Different numbers of fiducial markers (3, 4, 5, or 6) and distribution patterns (dispersed or localized) were used to register the robotic system. Platform, apex, and angular deviations were measured between the planned and actual implant positions using different numbers and distributions of fiducial markers.

RESULTS

Inserting six fiducial markers resulted in optimal implant position accuracy at the platform (0.53 ± 0.19 mm) and apex (0.59 ± 0.2 mm) deviations. However, the angular deviation did not differ significantly between different numbers of fiducial markers. Furthermore, the implant position accuracy did not differ significantly between the dispersed and localized distributions of fiducial markers.

CONCLUSION

In robot-guided implant placement for edentulous mandibular arches, the insertion of six fiducial markers significantly increases the implant placement accuracy.

CLINICAL SIGNIFICANCE

The findings of this in vitro study may serve as a reference for clinicians to determine the optimal placement of fiducial markers and to facilitate the clinical application of robot-guided systems for implant placement in edentulous patients. Further clinical studies are necessary to confirm these findings.

Open-source software for ultrasound-based guidance in spinal fusion surgery

Spinal instrumentation and surgical manipulations may cause loss of navigation accuracy requiring an efficient re-alignment of the patient anatomy with pre-operative images during surgery. While intra-operative ultrasound (iUS) guidance has shown clear potential to reduce surgery time, compared with clinical computed tomography (CT) guidance, rapid registration aiming to correct for patient misalignment has not been addressed. In this article, we present an open-source platform for pedicle screw navigation using iUS imaging. The alignment method is based on rigid registration of CT to iUS vertebral images and has been designed for fast and fully automatic patient re-alignment in the operating room. Two steps are involved: first, we use the iUS probe's trajectory to achieve an initial coarse registration; then, the registration transform is refined by simultaneously optimizing gradient orientation alignment and mean of iUS intensities passing through the CT-defined posterior surface of the vertebra. We evaluated our approach on a lumbosacral section of a porcine cadaver with seven vertebral levels. We achieved a median target registration error of 1.47 mm (100% success rate, defined by a target registration error <2 mm) when applying the probe's trajectory initial alignment. The approach exhibited high robustness to partial visibility of the vertebra with success rates of 89.86% and 88.57% when missing either the left or right part of the vertebra and robustness to initial misalignments with a success rate of 83.14% for random starts within ±20° rotation and ±20 mm translation. Our graphics processing unit implementation achieves an efficient registration time under 8 s, which makes the approach suitable for clinical application.

HFUS Imaging of the Cochlea: A Feasibility Study for Anatomical Identification by Registration with MicroCT

Cochlear implantation consists in electrically stimulating the auditory nerve by inserting an electrode array inside the cochlea, a bony structure of the inner ear. In the absence of any visual feedback, the insertion results in many cases of damages of the internal structures. This paper presents a feasibility study on intraoperative imaging and identification of cochlear structures with high-frequency ultrasound (HFUS). 6 ex-vivo guinea pig cochleae were subjected to both US and microcomputed tomography (µCT) we respectively referred as intraoperative and preoperative modalities. For each sample, registration based on simulating US from the scanner was performed to allow a precise matching between the visible structures. According to two otologists, the procedure led to a target registration error of 0.32 mm ± 0.05. Thanks to referring to a better preoperative anatomical representation, we were able to intraoperatively identify the modiolus, both scalae vestibuli and tympani and deduce the location of the basilar membrane, all of which is of great interest for cochlear implantation. Our main objective is to extend this procedure to the human case and thus provide a new tool for inner ear surgery.

Robust Point Set Registration Using Signature Quadratic Form Distance

Point set registration is a problem with a long history in many pattern recognition tasks. This paper presents a robust point set registration algorithm based on optimizing the distance between two probability distributions. A major problem in point to point algorithms is defining the correspondence between two point sets. This paper follows the idea of some probability-based point set registration methods by representing the point sets as Gaussian mixture models (GMMs). By optimizing the distance between the two GMMs, rigid transformations (rotation and translation) between two point sets can be obtained without having to find a correspondence. Previous studies have used L2, Kullback Leibler, etc. distance to measure similarity between two GMMs; however, these methods have problems with robustness to noise and outliers, especially when the covariance matrix is large, or a local minimum exists. Therefore, in this paper, the signature quadratic form distance is derived to measure the distribution similarity. The contribution of this paper lies in adopting the signature quadratic form distance for the point set registration algorithm. The experimental results show the precision and robustness of this algorithm and demonstrate that it outperforms other state-of-the-art point set registration algorithms regarding factors, such as noise, outliers, missing partial structures, and initial misalignment.

A novel low-noise movement tracking system with real-time analog output for closed-loop experiments

BACKGROUND

Modern electrophysiological experiments are moving towards closing the loop, where the extrinsic (behavioral) and intrinsic (neuronal) variables automatically affect stimulation parameters. Rodent experiments targeting spatial behavior require animal 2D kinematics to be continuously monitored in a reliable and accurate manner. Cameras provide a robust, flexible, and simple way to track kinematics on the fly. Indeed, several available camera-based systems yield high spatiotemporal resolution. However, the acquired kinematic data cannot be accessed with sufficient temporal resolution for precise real-time feedback.

NEW METHOD

Here, we describe a novel software and hardware system for movement tracking based on color-markers with real-time low-noise output that works in both light and dark conditions. The analog outputs precisely represent 2D movement features including position, orientation, and their temporal derivatives, velocity and angular velocity.

RESULTS

Using adaptive windowing, contour extraction, and rigid-body Kalman filtering, a 640-by-360 pixel frame is processed in 28 ms with less than 4 ms jitter, for 100 frames per second. The system is robust to outliers, has low noise, and maintains a smooth, accurate output even when one or more markers are temporarily missing. Using freely-moving mice, we demonstrate novel applications such as replacing conventional sensors in a behavioral arena and inducing novel place fields via closed-loop optogenetic stimulation.

COMPARISON WITH EXISTING METHOD(S)

To the best of our knowledge, this is the first tracking system that yields analog output in real-time.

CONCLUSIONS

This modular system for closed-loop experiment tracking can be implemented by downloading an open-source software and assembling low-cost hardware circuity.

Registration with a small number of sparse measurements

This work introduces a method for performing robust registration given the geometric model of an object and a small number (less than 20) of sparse point and surface normal measurements of the object’s surface. Such a method is of critical importance in applications such as probing-based surgical registration, contact-based localization, manipulating objects devoid of visual features, etc. Our approach for sparse point and normal registration (SPNR) is iterative in nature. In each iteration, the current best pose estimate is perturbed to generate several candidate poses. Among the generated poses, one pose is selected as the best, by evaluating an inexpensive cost function. This pose is used as the initial condition to estimate the locally optimum registration. This process is repeated until the registration estimate converges within a tolerance bound. Two variants are developed: deterministic (dSPNR) and probabilistic (pSPNR). The dSPNR is faster than pSPNR in converging to the local optimum, but the pSPNR requires fewer parameters to be tuned. The pSPNR also provides pose-uncertainty information in addition to the registration estimate. Both approaches were evaluated in simulation using various standard datasets and then compared with results obtained using state-of-the-art methods. Upon comparison with other methods, both dSPNR and pSPNR were found to be robust to initial pose errors as well as noise in measurements. The effectiveness of the approaches are also demonstrated with robot experiments for the application of probing-based registration.

A Review of Point Set Registration: From Pairwise Registration to Groupwise Registration

This paper presents a comprehensive literature review on point set registration. The state-of-the-art modeling methods and algorithms for point set registration are discussed and summarized. Special attention is paid to methods for pairwise registration and groupwise registration. Some of the most prominent representative methods are selected to conduct qualitative and quantitative experiments. From the experiments we have conducted on 2D and 3D data, CPD-GL pairwise registration algorithm and JRMPC groupwise registration algorithm seem to outperform their rivals both in accuracy and computational complexity. Furthermore, future research directions and avenues in the area are identified.

Three-Dimensional Registration of Freehand-Tracked Ultrasound to CT Images of the Talocrural Joint

A rigid surface⁻volume registration scheme is presented in this study to register computed tomography (CT) and free-hand tracked ultrasound (US) images of the talocrural joint. Prior to registration, bone surfaces expected to be visible in US are extracted from the CT volume and bone contours in 2D US data are enhanced based on monogenic signal representation of 2D US images. A 3D monogenic signal data is reconstructed from the 2D data using the position of the US probe recorded with an optical tracking system. When registering the surface extracted from the CT scan to the monogenic signal feature volume, six transformation parameters are estimated so as to optimize the sum of monogenic signal features over the transformed surface. The robustness of the registration algorithm was tested on a dataset collected from 12 cadaveric ankles. The proposed method was used in a clinical case study to investigate the potential of US imaging for pre-operative planning of arthroscopic access to talar (osteo)chondral defects (OCDs). The results suggest that registrations with a registration error of 2 mm and less is achievable, and US has the potential to be used in assessment of an OCD' arthroscopic accessibility, given the fact that 51% of the talar surface could be visualized.

Probabilistic pose estimation using a Bingham distribution-based linear filter

Pose estimation is central to several robotics applications such as registration, hand–eye calibration, and simultaneous localization and mapping (SLAM). Online pose estimation methods typically use Gaussian distributions to describe the uncertainty in the pose parameters. Such a description can be inadequate when using parameters such as unit quaternions that are not unimodally distributed. A Bingham distribution can effectively model the uncertainty in unit quaternions, as it has antipodal symmetry, and is defined on a unit hypersphere. A combination of Gaussian and Bingham distributions is used to develop a truly linear filter that accurately estimates the distribution of the pose parameters. The linear filter, however, comes at the cost of state-dependent measurement uncertainty. Using results from stochastic theory, we show that the state-dependent measurement uncertainty can be evaluated exactly. To show the broad applicability of this approach, we derive linear measurement models for applications that use position, surface-normal, and pose measurements. Experiments assert that this approach is robust to initial estimation errors as well as sensor noise. Compared with state-of-the-art methods, our approach takes fewer iterations to converge onto the correct pose estimate. The efficacy of the formulation is illustrated with a number of examples on standard datasets as well as real-world experiments.

Multi-resolution simulation of focused ultrasound propagation through ovine skull from a single-element transducer

Transcranial focused ultrasound (tFUS) is emerging as a non-invasive brain stimulation modality. Complicated interactions between acoustic pressure waves and osseous tissue introduce many challenges in the accurate targeting of an acoustic focus through the cranium. Image-guidance accompanied by a numerical simulation is desired to predict the intracranial acoustic propagation through the skull; however, such simulations typically demand heavy computation, which warrants an expedited processing method to provide on-site feedback for the user in guiding the acoustic focus to a particular brain region. In this paper, we present a multi-resolution simulation method based on the finite-difference time-domain formulation to model the transcranial propagation of acoustic waves from a single-element transducer (250 kHz). The multi-resolution approach improved computational efficiency by providing the flexibility in adjusting the spatial resolution. The simulation was also accelerated by utilizing parallelized computation through the graphic processing unit. To evaluate the accuracy of the method, we measured the actual acoustic fields through ex vivo sheep skulls with different sonication incident angles. The measured acoustic fields were compared to the simulation results in terms of focal location, dimensions, and pressure levels. The computational efficiency of the presented method was also assessed by comparing simulation speeds at various combinations of resolution grid settings. The multi-resolution grids consisting of 0.5 and 1.0 mm resolutions gave acceptable accuracy (under 3 mm in terms of focal position and dimension, less than 5% difference in peak pressure ratio) with a speed compatible with semi real-time user feedback (within 30 s). The proposed multi-resolution approach may serve as a novel tool for simulation-based guidance for tFUS applications.

Cubature Split Covariance Intersection Filter-based Point Set Registration

Point set registration is a basic but still open problem in numerous computer vision tasks. In general, there are more than one type of error sources for registration, for example, noise, outliers and false initialization may exist simultaneously. These errors could influence the registration independently and dependently. Previous works usually test performance under one of the two types of errors at one time, or they do not perform well under some extreme situations with both of the error sources. This work presents a robust point set registration algorithm under a filtering framework, which aims to be robust under various types of errors simultaneously. The point set registration problem can be cast into a non-linear state space model. We use a split covariance intersection filter (SCIF) to capture the correlation between the state transition and the observation (moving point set). The two above-mentioned types of errors can be represented as dependent and independent parts in the SCIF. The covariance of the two types of errors will be updated every iteration. Meanwhile, the non-linearity of the observation model is approximated by a cubature transformation. First, the recursive cubature split covariance intersection filter is derived based on the non-linear state space model. Then, we use this algorithm to solve the point set registration problem. This algorithm can approximate non-linearity by a third-order term and consider correlations between the process model and the observation model. Compared to other filtering-based methods, this algorithm is more robust and precise. Tests on both public datasets and experiments validate the precision and robustness of this algorithm to outliers and noise. Comparison experiments show that this algorithm outperforms state-of-the-art point set registration algorithms in certain respects.

Registration of 3D freehand ultrasound to a bone model for orthopedic procedures of the forearm

PURPOSE

For guidance of orthopedic surgery, the registration of preoperative images and corresponding surgical plans with the surgical setting can be of great value. Ultrasound (US) is an ideal modality for surgical guidance, as it is non-ionizing, real time, easy to use, and requires minimal (magnetic/radiation) safety limitations. By extracting bone surfaces from 3D freehand US and registering these to preoperative bone models, complementary information from these modalities can be fused and presented in the surgical realm.

METHODS

A partial bone surface is extracted from US using phase symmetry and a factor graph-based approach. This is registered to the detailed 3D bone model, conventionally generated for preoperative planning, based on a proposed multi-initialization and surface-based scheme robust to partial surfaces.

RESULTS

36 forearm US volumes acquired using a tracked US probe were independently registered to a 3D model of the radius, manually extracted from MRI. Given intraoperative time restrictions, a computationally efficient algorithm was determined based on a comparison of different approaches. For all 36 registrations, a mean (± SD) point-to-point surface distance of [Formula: see text] was obtained from manual gold standard US bone annotations (not used during the registration) to the 3D bone model.

CONCLUSIONS

A registration framework based on the bone surface extraction from 3D freehand US and a subsequent fast, automatic surface alignment robust to single-sided view and large false-positive rates from US was shown to achieve registration accuracy feasible for practical orthopedic scenarios and a qualitative outcome indicating good visual image alignment.

A Review on Medical Image Registration as an Optimization Problem

Objective:

In the course of clinical treatment, several medical media are required by a phy-sician in order to provide accurate and complete information about a patient. Medical image registra-tion techniques can provide a richer diagnosis and treatment information to doctors and to provide a comprehensive reference source for the researchers involved in image registration as an optimization problem.

Methods:

The essence of image registration is associating two or more different images spatial asso-ciation, and getting the translation of their spatial relationship. For medical image registration, its pro-cess is not absolute. Its core purpose is finding the conversion relationship between different images.

Result:

The major step of image registration includes the change of geometrical dimensions, and change of the image of the combination, image similarity measure, iterative optimization and interpo-lation process.

Conclusion:

The contribution of this review is sort of related image registration research methods, can provide a brief reference for researchers about image registration.

Fiducial-based registration with a touchable region model

PURPOSE

Image-guided surgery requires registration between an image coordinate system and an intraoperative coordinate system that is typically referenced to a tracking device. In fiducial-based registration methods, this is achieved by localizing points (fiducials) in each coordinate system. Often, both localizations are performed manually, first by picking a fiducial point in the image and then by using a hand-held tracked pointer to physically touch the corresponding fiducial on the patient. These manual procedures introduce localization error that is user-dependent and can significantly decrease registration accuracy. Thus, there is a need for a registration method that is tolerant of imprecise fiducial localization in the preoperative and intraoperative phases.

METHODS

We propose the iterative closest touchable point (ICTP) registration framework, which uses model-based localization and a touchable region model. This method consists of three stages: (1) fiducial marker localization in image space, using a fiducial marker model, (2) initial registration with paired-point registration, and (3) fine registration based on the iterative closest point method.

RESULTS

We perform phantom experiments with a fiducial marker design that is commonly used in neurosurgery. The results demonstrate that ICTP can provide accuracy improvements compared to the standard paired-point registration method that is widely used for surgical navigation and surgical robot systems, especially in cases where the surgeon introduces large localization errors.

CONCLUSIONS

The results demonstrate that the proposed method can reduce the effect of the surgeon's localization performance on the accuracy of registration, thereby producing more consistent and less user-dependent registration outcomes.

Generalized iterative most likely oriented-point (G-IMLOP) registration

PURPOSE

The need to align multiple representations of anatomy is a problem frequently encountered in clinical applications. A new algorithm for feature-based registration is presented that solves this problem by aligning both position and orientation information of the shapes being registered.

METHODS

The iterative most likely oriented-point (IMLOP) algorithm and its generalization (G-IMLOP) to the anisotropic noise case are described. These algorithms may be understood as probabilistic variants of the popular iterative closest point (ICP) algorithm. A probabilistic model provides the framework, wherein both position information and orientation information are simultaneously optimized. Like ICP, the proposed algorithms iterate between correspondence and registration subphases. Efficient and optimal solutions are presented for implementing each subphase of the proposed methods.

RESULTS

Experiments based on human femur data demonstrate that the IMLOP and G-IMLOP algorithms provide a strong accuracy advantage over ICP, with G-IMLOP providing additional accuracy improvement over IMLOP for registering data characterized by anisotropic noise. Furthermore, the proposed algorithms have increased ability to robustly identify an accurate versus inaccurate registration result.

CONCLUSION

The IMLOP and G-IMLOP algorithms provide a cohesive framework for incorporating orientation data into the registration problem, thereby enabling improvement in accuracy as well as increased confidence in the quality of registration outcomes. For shape data having anisotropic uncertainty in position and/or orientation, the anisotropic noise model of G-IMLOP enables further gains in registration accuracy to be achieved.

Global registration of subway tunnel point clouds using an augmented extended Kalman filter and central-axis constraint

Because tunnels generally have tubular shapes, the distribution of tie points between adjacent scans is usually limited to a narrow region, which makes the problem of registration error accumulation inevitable. In this paper, a global registration method is proposed based on an augmented extended Kalman filter and a central-axis constraint. The point cloud registration is regarded as a stochastic system, and the global registration is considered to be a process that recursively estimates the rigid transformation parameters between each pair of adjacent scans. Therefore, the augmented extended Kalman filter (AEKF) is used to accurately estimate the rigid transformation parameters by eliminating the error accumulation caused by the pair-wise registration. Moreover, because the scanning range of a terrestrial laser scanner can reach hundreds of meters, a single scan can cover a tunnel segment with a length of more than one hundred meters, which means that the central axis extracted from the scan can be employed to control the registration of multiple scans. Therefore, the central axis of the subway tunnel is first determined through the 2D projection of the tunnel point cloud and curve fitting using the RANSAC (RANdom SAmple Consensus) algorithm. Because the extraction of the central axis by quadratic curve fitting may suffer from noise in the tunnel points and from variations in the tunnel, we present a global extraction algorithm that is based on segment-wise quadratic curve fitting. We then derive the central-axis constraint as an additional observation model of AEKF to optimize the registration parameters between each pair of adjacent scans. The proposed approach is tested on terrestrial point clouds that were acquired in a subway tunnel. The results show that the proposed algorithm is capable of improving the accuracy of aligning multiple scans by 48%.

A Kalman Filtering Perspective for Multiatlas Segmentation

In multiatlas segmentation, one typically registers several atlases to the novel image, and their respective segmented label images are transformed and fused to form the final segmentation. In this work, we provide a new dynamical system perspective for multiatlas segmentation, inspired by the following fact: The transformation that aligns the current atlas to the novel image can be not only computed by direct registration but also inferred from the transformation that aligns the previous atlas to the image together with the transformation between the two atlases. This process is similar to the global positioning system on a vehicle, which gets position by inquiring from the satellite and by employing the previous location and velocity-neither answer in isolation being perfect. To solve this problem, a dynamical system scheme is crucial to combine the two pieces of information; for example, a Kalman filtering scheme is used. Accordingly, in this work, a Kalman multiatlas segmentation is proposed to stabilize the global/affine registration step. The contributions of this work are twofold. First, it provides a new dynamical systematic perspective for standard independent multiatlas registrations, and it is solved by Kalman filtering. Second, with very little extra computation, it can be combined with most existing multiatlas segmentation schemes for better registration/segmentation accuracy.

Minimally invasive registration for computer-assisted orthopedic surgery: combining tracked ultrasound and bone surface points via the P-IMLOP algorithm

PURPOSE

We present a registration method for computer-assisted total hip replacement (THR) surgery, which we demonstrate to improve the state of the art by both reducing the invasiveness of current methods and increasing registration accuracy. A critical element of computer-guided procedures is the determination of the spatial correspondence between the patient and a computational model of patient anatomy. The current method for establishing this correspondence in robot-assisted THR is to register points intraoperatively sampled by a tracked pointer from the exposed proximal femur and, via auxiliary incisions, from the distal femur.

METHODS

In this paper, we demonstrate a noninvasive technique for sampling points on the distal femur using tracked B-mode ultrasound imaging and present a new algorithm for registering these data called Projected Iterative Most-Likely Oriented Point (P-IMLOP). Points and normal orientations of the distal bone surface are segmented from ultrasound images and registered to the patient model along with points sampled from the exposed proximal femur via a tracked pointer.

RESULTS

The proposed approach is evaluated using a bone- and tissue-mimicking leg phantom constructed to enable accurate assessment of experimental registration accuracy with respect to a CT-image-based model of the phantom. These experiments demonstrate that localization of the femur shaft is greatly improved by tracked ultrasound. The experiments further demonstrate that, for ultrasound-based data, the P-IMLOP algorithm significantly improves registration accuracy compared to the standard ICP algorithm.

CONCLUSION

Registration via tracked ultrasound and the P-IMLOP algorithm has high potential to reduce the invasiveness and improve the registration accuracy of computer-assisted orthopedic procedures.

Iterative most-likely point registration (IMLP): a robust algorithm for computing optimal shape alignment

We present a probabilistic registration algorithm that robustly solves the problem of rigid-body alignment between two shapes with high accuracy, by aptly modeling measurement noise in each shape, whether isotropic or anisotropic. For point-cloud shapes, the probabilistic framework additionally enables modeling locally-linear surface regions in the vicinity of each point to further improve registration accuracy. The proposed Iterative Most-Likely Point (IMLP) algorithm is formed as a variant of the popular Iterative Closest Point (ICP) algorithm, which iterates between point-correspondence and point-registration steps. IMLP’s probabilistic framework is used to incorporate a generalized noise model into both the correspondence and the registration phases of the algorithm, hence its name as a most-likely point method rather than a closest-point method. To efficiently compute the most-likely correspondences, we devise a novel search strategy based on a principal direction (PD)-tree search. We also propose a new approach to solve the generalized total-least-squares (GTLS) sub-problem of the registration phase, wherein the point correspondences are registered under a generalized noise model. Our GTLS approach has improved accuracy, efficiency, and stability compared to prior methods presented for this problem and offers a straightforward implementation using standard least squares. We evaluate the performance of IMLP relative to a large number of prior algorithms including ICP, a robust variant on ICP, Generalized ICP (GICP), and Coherent Point Drift (CPD), as well as drawing close comparison with the prior anisotropic registration methods of GTLS-ICP and A-ICP. The performance of IMLP is shown to be superior with respect to these algorithms over a wide range of noise conditions, outliers, and misalignments using both mesh and point-cloud representations of various shapes.

Automatic registration of pre- and intraoperative data for long bones in minimally invasive surgery

The Minimally Invasive Procedures (MIP) in orthopedics have grown rapidly worldwide, as clinical results indicate that patients who undergo MIP typically experience minimized blood loss, smaller incision and shorter hospital stays. For most MIP, a preoperative 3D model of the patient anatomy is usually generated in order to plan the surgery. The challenge in MIP consists in finding the correspondence between the preoperative model and the actual position of the patient in the operating room, also known as image-to-patient registration. This paper proposes a real-time solution based on ultrasound (US) images: the patient anatomy is scanned by an US probe. Then, the segmentation and the extraction of bone contours from US images result in a 3D point cloud. The Poisson surface reconstruction method provides a 3D surface from 2D US data which will be registered with the preoperative model (CT volume) using the principal axes of inertia and the Iterative Closest Point robust (ICPr) algorithm. We present quantitative and qualitative results on both phantom and clinical data and show a mean registration accuracy of 0.66 mm for clinical radius scan. The promising registration results show the possible use of the proposed registration algorithm in clinical procedures.

Elastic registration of prostate MR images based on estimation of deformation states

Magnetic resonance imaging (MRI) is being used increasingly for image-guided targeted biopsy and focal therapy of prostate cancer. In this paper, a combined rigid and deformable registration technique is proposed to register pre-treatment diagnostic 3T magnetic resonance (MR) images of the prostate, with the identified target tumor(s), to intra-treatment 1.5T MR images. The pre-treatment T2-weighted MR images were acquired with patients in a supine position using an endorectal coil in a 3T scanner, while the intra-treatment T2-weighted MR images were acquired in a 1.5T scanner before insertion of the needle with patients in the semi-lithotomy position. Both the rigid and deformable registration algorithms employ an intensity-based distance metric defined based on the modality independent neighborhood descriptors (MIND) between images. The optimization routine for estimating the rigid transformation parameters is initialized using four pairs of manually selected approximate corresponding points on the boundaries of the prostate. In this paper, the problem of deformable image registration is approached from the perspective of state estimation for dynamical systems. The registration algorithm employs a rather generic dynamic linear elastic model of the tissue deformation discretized by the finite element method (FEM). We use the model in a classical state estimation framework to estimate the deformation of the prostate based on the distance metric between pre- and intra-treatment images. Our deformable registration results using 17 sets of prostate MR images showed that the proposed method yielded a target registration error (TRE) of 1.87 ± 0.94 mm,2.03 ± 0.94 mm, and 1.70 ± 0.93 mm for the whole gland (WG), central gland (CG), and peripheral zone (PZ), respectively, using 76 manually-identified fiducial points. This was an improvement over the 2.67 ± 1.31 mm, 2.95 ± 1.43 mm, and 2.34 ± 1.11 mm, respectively for the WG, CG, and PZ after rigid registration alone. Dice similarity coefficients (DSC) in the WG, CG and PZ were 88.2 ± 5.3, 85.6 ± 7.6 and 68.7 ± 6.9 percent, respectively. Furthermore, the mean absolute distances (MAD) between surfaces was 1.26 ± 0.56 mm and 1.27 ± 0.55 mm in the WG and CG, after deformable registration. These results indicate that the proposed registration technique has sufficient accuracy for localizing prostate tumors in MRI-guided targeted biopsy or focal therapy of clinically localized prostate cancer.

Local phase tensor features for 3-D ultrasound to statistical shape+pose spine model registration

Most conventional spine interventions are performed under X-ray fluoroscopy guidance. In recent years, there has been a growing interest to develop nonionizing imaging alternatives to guide these procedures. Ultrasound guidance has emerged as a leading alternative. However, a challenging problem is automatic identification of the spinal anatomy in ultrasound data. In this paper, we propose a local phase-based bone feature enhancement technique that can robustly identify the spine surface in ultrasound images. The local phase information is obtained using a gradient energy tensor filter. This information is used to construct local phase tensors in ultrasound images, which highlight the spine surface. We show that our proposed approach results in a more distinct enhancement of the bone surfaces compared to recently proposed techniques based on monogenic scale-space filters and logarithmic Gabor filters. We also demonstrate that registration accuracy of a statistical shape+pose model of the spine to 3-D ultrasound images can be significantly improved, using the proposed method, compared to those obtained using monogenic scale-space filters and logarithmic Gabor filters.

Registration of whole-mount histology and volumetric imaging of the prostate using particle filtering

Registration of histological slices to volumetric imaging of the prostate is an important task that can be used to optimize imaging for cancer detection. Such registration is challenging due to physical changes of the specimen during excision and fixation, and misalignment of the histological slices during preparation and digital scanning. In this work, we consider a multi-slice to volume registration method in which a stack of sparse, unaligned 2-D whole-mount histological slices is registered to a 3-D volumetric imaging of the prostate. We propose a particle filtering framework to contend with the high dimensionality of the search space and multimodal nature of the optimization. Such framework allows modeling of the uncertainty in the pose of the slices and in the imaged information, in order to derive optimal registration parameters in a Bayesian approach. Intensity-, region-, and point-based similarity metrics were incorporated into the registration algorithm to account for different imaging modalities. We demonstrate and evaluate our method on a diverse set of data that includes a synthetic volume, ex vivo and in vivo magnetic resonance imaging, and in vivo ultrasound.

Two-stage point-based registration method between ultrasound and CT imaging of the liver based on ICP and unscented Kalman filter: a phantom study

PURPOSE

In recent years, image-guided liver surgery based on intraoperative ultrasound (US) imaging has become common. Using an efficient point-based registration method to improve both accuracy and computational time for the registration of predeformation computer tomography, liver images with postdeformation US images are important during surgical procedure. Although iterative closest point (ICP) algorithm is widely used in surface-based registration, its performance strongly depends on the presence of noise and initial alignment. A registration technique based on unscented Kalman filter (UKF), which has been proposed recently, can used to overcome the noise and outliers on an incremental basis; however, the technique is associated with computational complexity.

METHODS

To overcome the limitations of ICP and UKF algorithms, we proposed an incremental two-stage registration method based on the combination of ICP and UKF algorithms to update the registration process with the acquired new points from US images. The registration is based on both the vessels and surface information of the liver.

RESULTS

The two-stage method was examined using numerical simulations and phantom data sets. The results of the phantom data set confirmed that the two-stage method outperforms the accuracy of ICP by 23% and reduces the running time of UKF by 60%.

CONCLUSION

The convergence rate, computational speed, and accuracy of the UKF algorithm can be improved using the two-stage method.

Improved multimodality data fusion of late gadolinium enhancement MRI to left ventricular voltage maps in ventricular tachycardia ablation

Electroanatomical voltage mapping (EAVM) is commonly performed prior to catheter ablation of scar-related ventricular tachycardia (VT) to locate the arrhythmic substrate and to guide the ablation procedure. EAVM is used to locate the position of the ablation catheter and to provide a 3-D reconstruction of left-ventricular anatomy and scar. However, EAVM measurements only represent the endocardial scar with no transmural or epicardial information. Furthermore, EAVM is a time-consuming procedure, with a high operator dependence and has low sampling density, i.e., spatial resolution. Late gadolinium enhancement (LGE) magnetic resonance imaging (MRI) allows noninvasive assessment of scar morphology that can depict 3-D scar architecture. Despite the potential use of LGE as a roadmap for VT ablation for identification of arrhythmogenic substrate, its utility has been very limited. To allow for identification of VT substrate, a correlation is needed between the substrates identified by EAVM as the gold standard and LGE-MRI scar characteristics. To do so, a system must be developed to fuse the datasets from these modalities. In this study, a registration pipeline for the fusion of LGE-MRI and EAVM data is presented. A novel surface registration algorithm is proposed, integrating the matching of global scar areas as an additional constraint in the registration process. A preparatory landmark registration is initially performed to expedite the convergence of the algorithm. Numerical simulations were performed to evaluate the accuracy of the registration in the presence of errors in identifying landmarks in EAVM or LGE-MRI datasets as well as additional errors due to respiratory or cardiac motion. Subsequently, the accuracy of the proposed fusion system was evaluated in a cohort of ten patients undergoing VT ablation where both EAVM and LGE-MRI data were available. Compared to landmark registration and surface registration, the presented method achieved significant improvement in registration error. The proposed data fusion system allows the fusion of EAVM and LGE-MRI data in VT ablation with registration errors less than 3.5  mm.

Filtering in the diffeomorphism group and the registration of point sets

The registration of a pair of point sets as well as the estimation of their pointwise correspondences is a challenging and important task in computer vision. In this paper, we present a method to estimate the diffeomorphic deformation, together with the pointwise correspondences, between a pair of point sets. Many of the registration problems are iteratively solved by estimating the correspondence, locally optimizing certain cost functionals over the rigid or similarity or affine transformation group, then estimating the correspondence again, and so on. This type of approach, however, is well-known to be susceptible to suboptimal local solutions. In this paper, we first adopt the perspective of treating the registration as a posterior estimation optimization problem and solve it accordingly via a particle-filtering framework. Second, within such a framework, the diffeomorphic registration is performed to correct the nonlinear deformation of the points. In doing so, we provide a solution less susceptible to local minima. We provide the experimental results, which include challenging medical data sets where the two point sets differ by 180 (°) rotation as well as local deformations, to highlight the algorithm's capability of robustly finding the more globally optimal solution for the registration task.

Fiducial optimization for minimal target registration error in image-guided neurosurgery

This paper presents new methods for the optimal selection of anatomical landmarks and optimal placement of fiducial markers in image-guided neurosurgery. These methods allow the surgeon to optimally plan fiducial marker locations on routine diagnostic images before preoperative imaging and to intraoperatively select the set of fiducial markers and anatomical landmarks that minimize the expected target registration error (TRE). The optimization relies on a novel empirical simulation-based TRE estimation method built on actual fiducial localization error (FLE) data. Our methods take the guesswork out of the registration process and can reduce localization error without additional imaging and hardware. Our clinical experiments on five patients who underwent brain surgery with a navigation system show that optimizing one marker location and the anatomical landmarks configuration reduced the TRE. The average TRE values using the usual fiducials setup and using the suggested method were 4.7 mm and 3.2 mm, respectively. We observed a maximum improvement of 4 mm. Reducing the target registration error has the potential to support safer and more accurate minimally invasive neurosurgical procedures.

3D ultrasound-CT registration in orthopaedic trauma using GMM registration with optimized particle simulation-based data reduction

Accurate real-time registration of intra-operative ultrasound (US) to computed tomography (CT) remains a challenging problem. In orthopedic applications, a recent promising approach proposed the use of Gaussian mixture modeling for bone surface registration. Though relatively successful, the method relied on naive and error prone subsampling of the surfaces registered to reduce computational cost and also heavily relied on heuristically-set parameters for bone surface generation. In this paper, we present an improved approach employing a novel point simplification method that redistributes surface points to better represent the surface achieving near real-time registration with higher accuracy and robustness. We also present a framework for automating the parameter selection in the bone surface extraction step. For validation, we present extensive quantitative tests on phantom and clinical data obtained by scanning patients with pelvic ring fractures in the operating room. We show an 89% average improvement in target registration error over the recent GMM registration based method.

Target and Trajectory Clinical Application Accuracy in Neuronavigation

BACKGROUND:

Catheter, needle, and electrode misplacement in navigated neurosurgery can result in ineffective treatment and severe complications.

OBJECTIVE:

To assess the Ommaya ventricular catheter localization accuracy both along the planned trajectory and at the target.

METHODS:

We measured the localization error along the ventricular catheter and on its tip for 15 consecutive patients who underwent insertion of the Ommaya catheter surgery with a commercial neuronavigation system. The preoperative computed tomography/magnetic resonance images and the planned trajectory were aligned with the postoperative computed tomography images showing the Ommaya catheter. The localization errors along the trajectory and at the target were then computed by comparing the preoperative planned trajectory with the actual postoperative catheter position. The measured localization errors were also compared with the error reported by the navigation system.

RESULTS:

The mean localization errors at the target and entry point locations were 5.9 ± 4.3 and 3.3 ± 1.9 mm, respectively. The mean shift and angle between planned and actual trajectories were 1.6 ± 1.9 mm and 3.9 ± 4.7°, respectively. The mean difference between the localization error at the target and entry point was 3.9 ± 3.7 mm. The mean difference between the target localization error and the reported navigation system error was 4.9 ± 4.8 mm.

CONCLUSION:

The catheter localization errors have significant variations at the target and along the insertion trajectory. Trajectory errors may differ significantly from the errors at the target. Moreover, the single registration error number reported by the navigation system does not appropriately reflect the trajectory and target errors and thus should be used with caution to assess the procedure risk.

Integration of model-based weighting into an ICP variant to account for measurement errors in intra-operative A-Mode ultrasound-based registration

This paper addresses error modeling in A-Mode ultrasound- (US-) based registration and integration of model-based weighting into the Random-ICP (R-ICP) algorithm. The R-ICP is a variant of the Iterative Closest Point (ICP) algorithm, and it was suggested for surface-based registration using A-Mode US in the context of skull surgery. In that application area the R-ICP could yield high accuracy even in case of a small number of data points and a very inaccurate user-interactive pre-registration. However, it cannot cope with unequal point uncertainty, which is an important drawback in the context of hip surgery: Uncertainty about the average speed of sound is an error source, whose impact on the registration accuracy increases with the thickness of the scanned soft tissue. It can, therefore, lead to considerable localization errors if a thick soft tissue layer is scanned, and it might vary a lot from data point to data point as the soft tissue thickness is inhomogeneous. The present work investigates how to account for this error source considering also other error sources such as the establishment of point correspondences. Simulation results show that registration accuracy can be substantially improved when model-based weighting is integrated into the R-ICP.

A coupled global registration and segmentation framework with application to magnetic resonance prostate imagery

Extracting the prostate from magnetic resonance (MR) imagery is a challenging and important task for medical image analysis and surgical planning. We present in this work a unified shape-based framework to extract the prostate from MR prostate imagery. In many cases, shape-based segmentation is a two-part problem. First, one must properly align a set of training shapes such that any variation in shape is not due to pose. Then segmentation can be performed under the constraint of the learnt shape. However, the general registration task of prostate shapes becomes increasingly difficult due to the large variations in pose and shape in the training sets, and is not readily handled through existing techniques. Thus, the contributions of this paper are twofold. We first explicitly address the registration problem by representing the shapes of a training set as point clouds. In doing so, we are able to exploit the more global aspects of registration via a certain particle filtering based scheme. In addition, once the shapes have been registered, a cost functional is designed to incorporate both the local image statistics as well as the learnt shape prior. We provide experimental results, which include several challenging clinical data sets, to highlight the algorithm's capability of robustly handling supine/prone prostate registration and the overall segmentation task.

The role of registration in accurate surgical guidance

Registration is presented as the central issue of surgical guidance. The focus is on the accuracy of approaches employed today, all of which use pre-operative images to guide surgery on rigid anatomy. The three most well-established approaches to guidance, namely the stereotactic frame, point fiducials, and surface matching, are examined in detail, together with two new approaches based on microstereotactic frames. It is shown that each method relies on the registration of points in the image to corresponding points in the operating room, and therefore that the error patterns associated with point registration are similar for all of them. Three types of registration error, namely fiducial localization error (FLE), fiducial registration error (FRE), and target registration error (TRE), are highlighted, as well as two additional guidance errors, namely target localization error and total targeting error, the latter of which is the overall error of the guidance system. Statistical relationships between TRE and FLE, between FRE and FLE, and between TRE, TLE, and TTE are given. Finally some myths concerning fiducial registration are highlighted.

Point set registration via particle filtering and stochastic dynamics

In this paper, we propose a particle filtering approach for the problem of registering two point sets that differ by a rigid body transformation. Typically, registration algorithms compute the transformation parameters by maximizing a metric given an estimate of the correspondence between points across the two sets of interest. This can be viewed as a posterior estimation problem, in which the corresponding distribution can naturally be estimated using a particle filter. In this work, we treat motion as a local variation in pose parameters obtained by running a few iterations of a certain local optimizer. Employing this idea, we introduce stochastic motion dynamics to widen the narrow band of convergence often found in local optimizer approaches for registration. Thus, the novelty of our method is threefold: First, we employ a particle filtering scheme to drive the point set registration process. Second, we present a local optimizer that is motivated by the correlation measure. Third, we increase the robustness of the registration performance by introducing a dynamic model of uncertainty for the transformation parameters. In contrast with other techniques, our approach requires no annealing schedule, which results in a reduction in computational complexity (with respect to particle size) as well as maintains the temporal coherency of the state (no loss of information). Also unlike some alternative approaches for point set registration, we make no geometric assumptions on the two data sets. Experimental results are provided that demonstrate the robustness of the algorithm to initialization, noise, missing structures, and/or differing point densities in each set, on several challenging 2D and 3D registration scenarios.

Estimation of optimal fiducial target registration error in the presence of heteroscedastic noise

We study the effect of point dependent (heteroscedastic) and identically distributed anisotropic fiducial localization noise on fiducial target registration error (TRE). We derive an analytic expression, based on the concept of mechanism spatial stiffness, for predicting TRE. The accuracy of the predicted TRE is compared to simulated values where the optimal registration transformation is computed using the heteroscedastic errors in variables algorithm. The predicted values are shown to be contained by the 95% confidence intervals of the root mean square TRE obtained from the simulations.

Distribution of fiducial registration error in rigid-body point-based registration

Rigid-body point-based registration is frequently used in computer assisted surgery to align corresponding points, or fiducials, in preoperative and intraoperative data. This alignment is mostly achieved by assuming the same homogeneous error distribution for all the points; however, due to the properties of the medical instruments used in measuring the point coordinates, the error distribution might be inhomogeneous and different for each point. In this paper, in an effort to understand the effect of error distribution in the localized points on the performed registration, we derive a closed-form solution relating the error distribution of each point with the performed registration accuracy. The solution uses maximum likelihood estimation to calculate the probability density function of registration error at each fiducial point. Extensive numerical simulations are performed to validated the proposed solution.

Distribution of target registration error for anisotropic and inhomogeneous fiducial localization error

In point-based rigid-body registration, target registration error (TRE) is an important measure of the accuracy of the performed registration. The registration's accuracy depends on the fiducial localization error (FLE) which, in turn, is due to the measurement errors in the points (fiducials) used to perform the registration. FLE may have different characteristics and distributions at each point of the registering data sets, and along each orthogonal axis. Previously, the distribution of TRE was estimated based on the assumption that FLE has an independent, identical, and isotropic or anisotropic distribution for each point in the registering data sets. In this article, we present a general solution based on the Maximum Likelihood (ML) algorithm that estimates the distribution of TRE for the cases where FLE has an independent, identical or inhomogeneous, isotropic or anisotropic, distribution at each point in the registering data sets, and when an algorithm is available that is capable of calculating the optimum registration to first order. Mathematically, we show that the proposed algorithm simplifies to the one proposed by Fitzpatrick and West when FLE has an independent, identical, and isotropic distribution in the registering data sets. Furthermore, we use numerical simulations to show that the proposed algorithm accurately estimates the distribution of TRE when FLE has an independent, inhomogeneous, and anisotropic distribution in the registering data sets.