Coherent Point Drift Research Articles

Track-to-Track Association by Coherent Point Drift

In this letter, we propose a probabilistic method, called the coherent point drift (CPD) algorithm, to address track-to-track association with sensor bias. In the CPD method for a pair of sensors, the local tracks of one sensor are represented by Gaussian mixture model centroids, and the local tracks of the other sensor are fitted to those of the first sensor by maximizing the likelihood. An expectation–maximization algorithm is proposed to find the correspondence matrix between the local tracks. Experiments illustrate the effectiveness of our method.

Mitral Valve Prolapse Classification from an Echocardiography Sequence using Coherent Point Drift Method based on Fractal Dimension

Background: Mitral Valve Prolapse (MVP) is now recognized as the most common cardiovalvular abnormality (CVA) in the USA, but there has been much less agreement about other aspects of its epidemiology, diagnosis and clinical features. CVA analysis still relies mainly on the visual assessment of echocardiographic imaging and manual measurements by experienced cardiologists. So, automating or semi-automating analysis of echocardiographic images for MVP detection is, therefore, highly desirable, but also challenging due to low image quality and high amount of speckle noise. Objective: The main objective of this paper was to test the hypothesis that fractal dimension (FD) values are significantly higher in severe MVP and moderate MVP cases than those of healthy subjects in motion pattern of their mitral valves. Materials and Methods: In this paper, we present a noninvasive algorithm that does not require any segmentation. This approach has three steps: first, we extracted corners as landmarks from echocardiographic sequences based on SUSAN corner detector. Then, landmarks were tracked using Coherent Point Drift (CPD) non-rigid registration. After that, the motion patterns of the landmarks were analyzed to extract features (FD) in order to classify the mitral valve behavior of 46 patients and 25 normals as normal, moderate or severe MVP. Results: The results show that moderate MVP detection has a relatively good sensitivity (82%) and specificity (82%). Conclusion: The motion pattern of landmarks in MVP patients, obtained by CPD method, differed from that of normals in such a way that the difference can be quantified and analyzed by FD.

Accurate point correspondences using a modified coherent point drift algorithm

A crucial challenge of statistical shape modeling is to find corresponding points. The task is much more difficult especially in cases of objects with greater shape diversities (such as liver). In this paper, we propose a new fast algorithm to find corresponding points based on modified Coherent Point Drift technique which is comparable to the state-of-the-art “Minimum Description Length” (MDL) algorithm. Combining fuzzy correspondence and deterministic annealing method together with non-rigid registration of shapes helps to find corresponding points of different liver shapes. We optimized the algorithm parameters to prevent it from producing unacceptable results. Evaluation of the results was performed using Compactness, Generality, Specificity, and run-time measures. We compared our method using both conventional and state-of-the-art techniques including “Iterative Closest Point” (ICP), “Thin Plate Spline-Robust Point Matching” (TPS-RPM) and MDL. The performance of our method is superior to ICP and TPS-RPM algorithms and our results are close to the MDL results. The Generality of ICP, TPS-RPM, MDL and our method are 7.1±1.80, 3.78±0.96, 2.64±0.65 and 3.64±0.85 respectively. The Specificity of MDL and TPS-RPM is the same as ours (0.21±0.06) and the ICP stands in the fourth rank (0.30±0.18). The Compactness of ICP, TPS-RPM, MDL and our method are 23, 19, 16 and 18 respectively. The run-time of ICP, TPS-RPM, MDL and our method are 30, 390, 3600 and 68s. Contrary to the MDL, our algorithm does not trap into degenerate cases.

Movable type printing identification based on Tangut characters registration

Scientific identification of the movable type printing provides favorable evidence to research the invention and dissemination of movable printing technique. However, the methods used to identify movable type printing are either unscientific or time-consuming. To solve those problems, a new method based on registration is introduced in this paper. Firstly, the boundary points of each character image are extracted, and the affine iterative closest point (ICP) with bidirectional distance is used to measure the shape similarity between two character point sets. Secondly, a heuristic tree of Tangut characters based on shape similarity is constructed, which connects two point sets with small deformation. In this way, the large deformation between characters is divided into several small differences. After that, the coherent point drift (CPD) algorithm is used to achieve the registration between these character point sets along the heuristic tree. Finally, after comparing the registrations errors between the subject character point sets and model character point set carefully and observing their character images as well as the registration images between them, the judgment of whether these characters are printed with the same movable character model is to be made. Experimental results demonstrate that the identification method of movable printing proposed has the advantages of being automatic, fast and accurate.

Spinal pedicle screw planning using deformable atlas registration

Spinal screw placement is a challenging task due to small bone corridors and high risk of neurological or vascular complications, benefiting from precision guidance/navigation and quality assurance (QA). Implicit to both guidance and QA is the definition of a surgical plan—i.e. the desired trajectories and device selection for target vertebrae—conventionally requiring time-consuming manual annotations by a skilled surgeon. We propose automation of such planning by deriving the pedicle trajectory and device selection from a patient’s preoperative CT or MRI.An atlas of vertebrae surfaces was created to provide the underlying basis for automatic planning—in this work, comprising 40 exemplary vertebrae at three levels of the spine (T7, T8, and L3). The atlas was enriched with ideal trajectory annotations for 60 pedicles in total. To define trajectories for a given patient, sparse deformation fields from the atlas surfaces to the input (CT or MR image) are applied on the annotated trajectories. Mean value coordinates are used to interpolate dense deformation fields. The pose of a straight trajectory is optimized by image-based registration to an accumulated volume of the deformed annotations. For evaluation, input deformation fields were created using coherent point drift (CPD) to perform a leave-one-out analysis over the atlas surfaces.CPD registration demonstrated surface error of 0.89 ± 0.10 mm (median ± interquartile range) for T7/T8 and 1.29 ± 0.15 mm for L3. At the pedicle center, registered trajectories deviated from the expert reference by 0.56 ± 0.63 mm (T7/T8) and 1.12 ± 0.67 mm (L3). The predicted maximum screw diameter differed by 0.45 ± 0.62 mm (T7/T8), and 1.26 ± 1.19 mm (L3). The automated planning method avoided screw collisions in all cases and demonstrated close agreement overall with expert reference plans, offering a potentially valuable tool in support of surgical guidance and QA.

Force-Controlled Exploration for Updating Virtual Fixture Geometry in Model-Mediated Telemanipulation

This paper proposes an approach for using force-controlled exploration data to update and register an a priori virtual fixture geometry to a corresponding deformed and displaced physical environment. An approach for safe exploration implementing hybrid motion/force control is presented on the slave robot side. During exploration, the shape and the local surface normals of the environment are estimated and saved in an exploration data set. The geometric data collected during this exploration scan are used to deform and register the a priori environment model to the exploration data set. The environment registration is achieved using a deformable registration based on the coherent point drift method. The task-description of the high-level assistive telemanipulation law, called a virtual fixture (VF), is then deformed and registered in the new environment. The new model is updated and used within a model-mediated telemanipulation framework. The approach is experimentally validated using a da-Vinci research kit (dVRK) master interface, a dVRK patient side manipulator, and a Cartesian stage robot. Experiments demonstrate that the updated VF and the updated model allow the users to improve their path following performance and to shorten their completion time when the updated path following VF is applied. The approach presented has direct bearing on a multitude of surgical applications including force-controlled ablation.

A Characteristic Statistic Based Femoral Contour Point-set Registration Algorithm

The point-set registration technology has been widely applied in the field of medical image registration. This paper proposed a characteristic statistic based femoral contour point-set registration algorithm, in order to overcome the flaw of getting into local extrema and of poor global performance in the iterative optimization process in existing registration algorithms. First, it uses the Gaussian mixture model to represent the correspondence of points between two point-sets, and selects the global parameter associated with the objective function as the characteristic statistical items. Then, it leverages the statistical variation in the optimization process to guide the optimal search, yielding the global optimal solution of statistical items, and realizing the registration of two point-sets. In the end, this algorithm is applied to solve the registration problem of femoral contour characteristic point-set. The experimental results reveal that the proposed registration method performs more effective, faster, and more accurate compared with Coherent Point Drift (CPD) algorithm.

Automated High-Resolution Satellite Image Registration Using Supraglacial Rivers on the Greenland Ice Sheet

High-resolution satellite imagery raises new prospects for detailed study of the Greenland ice sheet (GrIS) surface processes and ice discharge. However, dramatic spatiotemporal variability of ice surface reflectance and features poses significant challenges for registration of satellite imagery. This study proposes a new feature-based registration method to register high-resolution panchromatic images of the ice sheet ablation zone. Its idea is to use relatively stable supraglacial rivers as tie points for automated image registration. A first demonstration is made using WorldView-1/2/3 panchromatic images (spatial resolution 0.5 m) as follows: first, supraglacial rivers are delineated using spectral analysis, nonlocal means denoising, Gabor filtering, and path opening. Next, buffer and overlay tools are combined to generate an area of interest and eliminate tie point outliers, yielding subset of high-confidence tie points for registration. Finally, a coherent point drift algorithm is applied to match these tie points and implement registration. Results show that the proposed method demonstrates good performance, despite a heterogeneous ice surface background that complicates river delineation. Accuracy of image registration negatively correlates with seasonal spatiotemporal variability of supraglacial river patterns, suggesting that for the best results, repeat images and time-adaptive techniques should be used. For time-stable meltwater channels, however, the method offers a novel, automated way to register high-resolution satellite imagery of the GrIS ablation zone. Well-registered ice surface high-resolution images reveal that short-term (1-2 week) variations in surface melting rate affect channel morphology (drainage densities and channel widths) significantly, whereas a signal from background advection by flowing ice is not apparent.

Falx Cerebri Segmentation via Multi-atlas Boundary Fusion.

The falx cerebri is a meningeal projection of dura in the brain, separating the cerebral hemispheres. It has stiffer mechanical properties than surrounding tissue and must be accurately segmented for building computational models of traumatic brain injury. In this work, we propose a method to segment the falx using T1-weighted magnetic resonance images (MRI) and susceptibility-weighted MRI (SWI). Multi-atlas whole brain segmentation is performed using the T1-weighted MRI and the gray matter cerebrum labels are extended into the longitudinal fissure using fast marching to find an initial estimate of the falx. To correct the falx boundaries, we register and then deform a set of SWI with manually delineated falx boundaries into the subject space. The continuous-STAPLE algorithm fuses sets of corresponding points to produce an estimate of the corrected falx boundary. Correspondence between points on the deformed falx boundaries is obtained using coherent point drift. We compare our method to manual ground truth, a multi-atlas approach without correction, and single-atlas approaches.

Matching Misaligned Two-Resolution Metrology Data

Multiresolution metrology devices coexist in today’s manufacturing environment, producing coordinate measurements complementing each other. Typically, the high-resolution (HR) device produces a scarce but accurate data set, whereas the low-resolution (LR) one produces a dense but less accurate data set. Research has shown that combining the two data sets of different resolutions makes better predictions of the geometric features of a manufactured part. A challenge, however, is how to effectively match each HR data point to an LR counterpart that measures approximately the same physical location. A solution to this matching problem appears a prerequisite to a good final prediction. We solved this problem by formulating it as a quadratic integer program, aiming at minimizing the maximum interpoint distance difference among all potential correspondences. Due to the combinatorial nature of the optimization model, solving it to optimality is computationally prohibitive even for a small problem size. We therefore propose a two-stage matching framework capable of solving real-life-sized problems within a reasonable amount of time. This two-stage framework consists of downsampling the full-size problem, solving the downsampled problem to optimality, extending the solution of the downsampled problem to the full-size problem, and refining the solution using iterative local search. Numerical experiments show that the proposed approach outperforms two popular point set registration alternatives, the iterative closest point and coherent point drift methods, using different performance metrics. The numerical results also show that our approach scales much better as the instance size increases, and is robust to the changes in initial misalignment between the two data sets.

A Study of Coronary Bifurcation Shape in a Normal Population

During percutaneous coronary intervention, stents are placed in narrowings of the arteries to restore normal blood flow. Despite improvements in stent design, deployment techniques and drug-eluting coatings, restenosis and stent thrombosis remain a significant problem. Population stent design based on statistical shape analysis may improve clinical outcomes. Computed tomographic (CT) coronary angiography scans from 211 patients with a zero calcium score, no stenoses and no intermediate artery, were used to create statistical shape models of 446 major coronary artery bifurcations (left main, first diagonal and obtuse marginal and right coronary crux). Coherent point drift was used for registration. Principal component analysis shape scores were tested against clinical risk factors, quantifying the importance of recognised shape features in intervention including size, angles and curvature. Significant differences were found in (1) vessel size and bifurcation angle between the left main and other bifurcations; (2) inlet and curvature angle between the right coronary crux and other bifurcations; and (3) size and bifurcation angle by sex. Hypertension, smoking history and diabetes did not appear to have an association with shape. Physiological diameter laws were compared, with the Huo-Kassab model having the best fit. Bifurcation coronary anatomy can be partitioned into clinically meaningful modes of variation showing significant shape differences. A computational atlas of normal coronary bifurcation shape, where disease is common, may aid in the design of new stents and deployment techniques, by providing data for bench-top testing and computational modelling of blood flow and vessel wall mechanics.

Bladder accumulated dose in image-guided high-dose-rate brachytherapy for locally advanced cervical cancer and its relation to urinary toxicity

The purpose of this study was to estimate locally accumulated dose to the bladder in multi-fraction high-dose-date (HDR) image-guided intracavitary brachytherapy (IG-ICBT) for cervical cancer, and study the locally-accumulated dose parameters as predictors of late urinary toxicity.A retrospective study of 60 cervical cancer patients who received five HDR IG-ICBT sessions was performed. The bladder outer and inner surfaces were segmented for all sessions and a bladder-wall contour point-set was created in MATLAB. The bladder-wall point-sets for each patient were registered using a deformable point-set registration toolbox called coherent point drift (CPD), and the fraction doses were accumulated. Various dosimetric and volumetric parameters were calculated using the registered doses, including (minimum dose to the most exposed n-cm3 volume of bladder wall), r Vn Gy (wall volume receiving at least m Gy), and (minimum equivalent biologically weighted dose to the most exposed n-cm3 of bladder wall), where n = 1/2/5/10 and m = 3/5/10. Minimum dose to contiguous 1 and 2 cm3 hot-spot volumes was also calculated. The unregistered dose volume histogram (DVH)-summed equivalent of and parameters (i.e. and ) were determined for comparison. Late urinary toxicity was assessed using the LENT-SOMA scale, with toxicity Grade 0–1 categorized as Controls and Grade 2–4 as Cases. A two-sample t-test was used to identify the differences between the means of Control and Case groups for all parameters. A binomial logistic regression was also performed between the registered dose parameters and toxicity grouping. Seventeen patients were in the Case and 43 patients in the Control group. Contiguous values were on average 16 and 18% smaller than parameters for 1 and 2 cm3 volumes, respectively. Contiguous values were on average 26 and 27% smaller than parameters. The only statistically significant finding for Case versus Control based on both methods of analysis was observed for r V3 Gy (p = 0.01).DVH-summed parameters based on unregistered structure volumes overestimated the bladder dose in our patients, particularly when contiguous high dose volumes were considered. The bladder-wall volume receiving at least 3 Gy of accumulated dose may be a parameter of interest in further investigations of Grade 2+ urinary toxicity.

Robust non-rigid point set registration via building tree dynamically

The non-rigid registration methods, such as coherent point drift (CPD) method can deal with similar point sets, but it is difficult for them to achieve the non-rigid registration of point sets with large deformations. To overcome the problem, a novel approach via building dynamic tree is proposed in this paper. First of all, the similarity between the model and subject point sets is evaluated by the affine iterative closest point (ICP) algorithm with bidirectional distance, and the models and their similar subjects are connected. Secondly, the non-rigid registration is conducted on every two similar point sets. The subjects with accurate registration results are added to the model sets and wrong pairs are cut off based on a bidirectional distance. These steps are repeated and a dynamic tree is built up. In this way, a large deformation between two images is decomposed into a series of small deformations and the elimination of the wrong pairs in the dynamic tree guarantees the registration results are precise and satisfactory. Experimental results on several image datasets demonstrate that our method improves the accuracy of the point set registration results with large shape difference compared with existing approaches.

Evaluation of a Coherent Point Drift Algorithm for Breast Image Registration via Surface Markers

Breast Magnetic Resonance Imaging (MRI) is a reliable imagingtool for localization and evaluation of lesions prior to breast conservingsurgery (BCS). MR images typically will be used to determinethe size and location of the tumours before making the incisionin order to minimize the amount of tissue excised.The arm position and configuration of the breast during andprior to surgery are different and one question is whether it wouldbe possible to match the two configurations. This matching processcan potentially be used in development of tools to guide surgeonsin the incision process.Recently, a Thin-Plate-Spline (TPS) algorithm has been proposedto assess the feasibility of breast tissue matching using fiducialsurface markers in two different arm positions. The registrationalgorithm uses the surface markers only and does not employ theimage intensities.In this manuscript, we apply and evaluate a coherent point drift(CPD) algorithm for registration of three-dimensional breast MR imagesof six patient volunteers. In particular, we evaluate the resultsof the previous TPS registration technique to the proposed rigidCPD, affine CPD, and deformable CPD registration algorithms onthe same patient datasets.The preliminary results suggest that the CPD deformable registrationalgorithm is superior in correcting the motion of the breastcompared to CPD rigid, affine and TPS registration algorithms.

A robust coherent point drift approach based on rotation invariant shape context

Point set matching is a common problem in many domains, such as medical image analysis, object recognition, 3D reconstruction, and motion tracking. Coherent point drift (CPD) appears as an efficient algorithm to align two point sets. It treated point set matching as a problem of Gaussian mixture density estimation. But there are four drawbacks in the CPD method: outlier ratio given manually, equal prior probability for the mixture model, lack of shape information and failure for large rotation transformations. To deal with these limitations, we propose a robust CPD approach based on rotation invariant shape context. First, a rotation invariant shape context (RISC) is constructed for each point of the two sets to keep the rotation invariance of shape features. Then an adaptive prior probability and outlier ratio are computed based on RISC. For each Gaussian mixture model (GMM) component, the prior probability is linked to the number of the sample points derived from this component. Finally, the correspondence and transformation are achieved through expectation-maximization (EM) process. The results on synthetic and real data show that our method is a robust and effective non-rigid point matching approach.

3D pose estimation of green pepper fruit for automated harvesting

This paper presents a novel pose estimation algorithm for stem position detection in Japanese green pepper automatic harvesting. When the available visual cues do not provide sufficient information to the harvesting robot, information about the pose of the fruit in space is necessary for accurate stem position detection. In the proposed method the orientation of a fruit in space is obtained by fitting a model to surface points of the fruit. These surface points are acquired using a Lidar type laser range finder, and the point matching is performed using a coherent point drift algorithm with two model transformation methods, rigid and affine. The performance of the proposed method was evaluated both under laboratory conditions and in a greenhouse. In the laboratory test, the mean total error for the affine transformation was less than 25mm in 42 of 49 positions, less than 20mm in 28 of 49 positions and less than 15mm in 19 of 49 positions. For the rigid transformation, the same error was less than 25mm in 39 of 49 positions, less than 20mm in 31 of 49 positions and less than 15mm in 11 of 49 positions. The total error of the affine transformation was found to be proportional to the inclination angle, as the mean error was 11mm, 15mm, and 23mm for inclination angles of 15, 30 and 45 degrees, respectively. No relationship was found between the mean total error and the inclination angle for the rigid transformation, as the calculated mean total error was 20mm, 18mm, and 20mm for inclination angles of 15, 30 and 45 degrees, respectively. In the greenhouse test, the stem was calculated to be within the cutting range for 81 of 107 instances for affine transformation and for 66 of 107 for rigid transformation. These results suggest that the proposed method is suitable for stem position detection in the automatic harvesting of green pepper, and could be adjusted for use with other fruits and vegetables.

Automated detection and labeling of high-density EEG electrodes from structural MR images

Objective. Accurate knowledge about the positions of electrodes in electroencephalography (EEG) is very important for precise source localizations. Direct detection of electrodes from magnetic resonance (MR) images is particularly interesting, as it is possible to avoid errors of co-registration between electrode and head coordinate systems. In this study, we propose an automated MR-based method for electrode detection and labeling, particularly tailored to high-density montages. Approach. Anatomical MR images were processed to create an electrode-enhanced image in individual space. Image processing included intensity non-uniformity correction, background noise and goggles artifact removal. Next, we defined a search volume around the head where electrode positions were detected. Electrodes were identified as local maxima in the search volume and registered to the Montreal Neurological Institute standard space using an affine transformation. This allowed the matching of the detected points with the specific EEG montage template, as well as their labeling. Matching and labeling were performed by the coherent point drift method. Our method was assessed on 8 MR images collected in subjects wearing a 256-channel EEG net, using the displacement with respect to manually selected electrodes as performance metric. Main results. Average displacement achieved by our method was significantly lower compared to alternative techniques, such as the photogrammetry technique. The maximum displacement was for more than 99% of the electrodes lower than 1 cm, which is typically considered an acceptable upper limit for errors in electrode positioning. Our method showed robustness and reliability, even in suboptimal conditions, such as in the case of net rotation, imprecisely gathered wires, electrode detachment from the head, and MR image ghosting. Significance. We showed that our method provides objective, repeatable and precise estimates of EEG electrode coordinates. We hope our work will contribute to a more widespread use of high-density EEG as a brain-imaging tool.

Robust image registration using adaptive coherent point drift method

Coherent point drift (CPD) method is a powerful registration tool under the framework of the Gaussian mixture model (GMM). However, the global spatial structure of point sets is considered only without other forms of additional attribute information. The equivalent simplification of mixing parameters and the manual setting of the weight parameter in GMM make the CPD method less robust to outlier and have less flexibility. An adaptive CPD method is proposed to automatically determine the mixing parameters by embedding the local attribute information of features into the construction of GMM. In addition, the weight parameter is treated as an unknown parameter and automatically determined in the expectation-maximization algorithm. In image registration applications, the block-divided salient image disk extraction method is designed to detect sparse salient image features and local self-similarity is used as attribute information to describe the local neighborhood structure of each feature. The experimental results on optical images and remote sensing images show that the proposed method can significantly improve the matching performance.

Assessment of the Implant Geometry in Fractionated Interstitial HDR Breast Brachytherapy

To determine the inter-fraction stability of the implant geometry in fractionated HDR interstitial brachytherapy (HDR-iBT) partial breast irradiations (PBI) by means of electromagnetic tracking (EMT). In our contemporary phantom study, an EMT protocol to track 6F catheters with an accuracy of 1±0.3 mm (maximum: 2 mm) in our typical clinical environment was established [Kellermeier et al. Med. Phys. 42(6):3533]. Based on that protocol, the implant geometry of 21 patients (17 patients: 9-fraction PBI and four patients: 2-fraction boost after teletherapy) was quantified during their iBT treatment. For each patient, the implant geometry was measured on the CT table just after acquiring the treatment planning scan (EMCT) and on the HDR treatment table directly after each treatment fraction (EMFx). Three 6 degrees of freedom (DoF) sensors were placed on the breast surface to obtain fiducial positions used to derive relative positions of a 5 DoF sensor manually and consecutively inserted in the catheters. To compensate for patient movements, e.g. respiratory motion, the implant sensor data were corrected against the mean position of the fiducial sensors. Using the catheter traces, dwell positions (DPs) were determined for each measurement. In analogy to the already published phantom studies, the rigid coherent point drift (CPD) algorithm was used to register corresponding DPs. For each patient, the determined DPs from EMCT and EMFx were compared against the CT-derived DPs from treatment planning (CTRef). In addition, to assess quantitatively the changes in the implant geometry - without the need for registration - the distances from each DP to all DPs within a 3 cm spherical range were determined. For each measured implant geometry, the change in these intra-implant DP distances (IIDD) was compared with those from CTRef. EMT of the whole catheter implant per patient (median: 17 catheters) took per fraction on average 6.8 minutes plus a few minutes for setup of the EMT system. The registered implant geometry from the CT table showed over all DPs a mean deviation of 1.3 mm (median: 1.1 mm, inter-quartile range IQR: 0.9 mm). Registration of the EMT-based DP from the fractions (EMFx) against CTRef resulted in an overall mean deviation of 2.4 mm (median: 2.2 mm, IQR: 1.7 mm). Throughout the fractionated treatment, no significant trend could be determined (see the Figure for the various measurement sessions). Regarding the change in IIDD over CTRef, EMCT showed a mean deviation of 0.9 mm (median: 0.6 mm, IQR: 1.1 mm). In the EMFx data, IIDD changed by 1.0 mm (median: 0.8 mm, IQR: 1.3 mm). EMT measurements in 21 HDR-iBT breast patients were feasible within the clinical workflow and well tolerated by the patients. EMT determined DPs based on the patient measurements on the CT table differed by 1.3 mm (mean) from the CT-derived DPs used for treatment planning. Throughout the fractionated treatment, the EMT determined DP deviation increased to 2.4 mm (mean) without a significant trend over the treatment duration.

Convex hull indexed Gaussian mixture model (CH-GMM) for 3D point set registration

To solve the problem of rigid/non-rigid 3D point set registration, a novel convex hull indexed Gaussian mixture model (CH-GMM) is proposed in this paper. The model works by computing a weighted Gaussian mixture model (GMM) response over the convex hull of each point set. Three conditions, proximity, area conservation and projection consistency, are incorporated into the model so as to improve its performance. Given that the convex hull is the tightest convex set of a point set, the combination of Gaussian mixture and convex hull can effectively preserve the topological structure of a point set. Furthermore, computational complexity can be significantly reduced since only the GMM of the convex hull (instead of the whole point set) needs to be calculated. Rigid registration is achieved by seeking the best rigid transformation parameters yielding the most similar CH-GMM responses. Non-rigid deformation is realized by optimizing the coordinates of the control points used by the thin-plate spline model for interpolating the entire point set. Experiments are designed to evaluate a method׳s robustness to rotational changes between two point sets, positional noise, differences in density and partial overlap. The results demonstrated better robustness and registration accuracy of CH-GMM based method over state-of-the-art methods including iterative closest point, coherent point drift and the GMM method. Besides, the computation of CH-GMM is efficient.