Automated 3D Cobb Angle Measurement Using U-Net in CT Images of Preoperative Scoliosis Patients.

To propose a deep learning framework "SpineCurve-net" for automated measuring the 3D Cobb angles from computed tomography (CT) images of presurgical scoliosis patients. A total of 116 scoliosis patients were analyzed, divided into a training set of 89 patients (average age 32.4 ± 24.5 years) and a validation set of 27 patients (average age 17.3 ± 5.8 years). Vertebral identification and curve fitting were achieved through U-net and NURBS-net and resulted in a Non-Uniform Rational B-Spline (NURBS) curve of the spine. The 3D Cobb angles were measured in two ways: the predicted 3D Cobb angle (PRED-3D-CA), which is the maximum value in the smoothed angle map derived from the NURBS curve, and the 2D mapping Cobb angle (MAP-2D-CA), which is the maximal angle formed by the tangent vectors along the projected 2D spinal curve. The model segmented spinal masks effectively, capturing easily missed vertebral bodies. Spoke kernel filtering distinguished vertebral regions, centralizing spinal curves. The SpineCurve Network method's Cobb angle (PRED-3D-CA and MAP-2D-CA) measurements correlated strongly with the surgeons' annotated Cobb angle (ground truth, GT) based on 2D radiographs, revealing high Pearson correlation coefficients of 0.983 and 0.934, respectively. This paper proposed an automated technique for calculating the 3D Cobb angle in preoperative scoliosis patients, yielding results that are highly correlated with traditional 2D Cobb angle measurements. Given its capacity to accurately represent the three-dimensional nature of spinal deformities, this method shows potential in aiding physicians to develop more precise surgical strategies in upcoming cases.

Discretization of Non-uniform Rational B-Spline (NURBS) Models for Meshless Isogeometric Analysis.

We present an algorithm for fast generation of quasi-uniform and variable-spacing nodes on domains whose boundaries are represented as computer-aided design (CAD) models, more specifically non-uniform rational B-splines (NURBS). This new algorithm enables the solution of partial differential equations within the volumes enclosed by these CAD models using (collocation-based) meshless numerical discretizations. Our hierarchical algorithm first generates quasi-uniform node sets directly on the NURBS surfaces representing the domain boundary, then uses the NURBS representation in conjunction with the surface nodes to generate nodes within the volume enclosed by the NURBS surface. We provide evidence for the quality of these node sets by analyzing them in terms of local regularity and separation distances. Finally, we demonstrate that these node sets are well-suited (both in terms of accuracy and numerical stability) for meshless radial basis function generated finite differences discretizations of the Poisson, Navier-Cauchy, and heat equations. Our algorithm constitutes an important step in bridging the field of node generation for meshless discretizations with isogeometric analysis.

Using Deep Learning and B-Splines to Model Blood Vessel Lumen from 3D Images.

Accurate geometric modeling of blood vessel lumen from 3D images is crucial for vessel quantification as part of the diagnosis, treatment, and monitoring of vascular diseases. Our method, unlike other approaches which assume a circular or elliptical vessel cross-section, employs parametric B-splines combined with image formation system equations to accurately localize the highly curved lumen boundaries. This approach avoids the need for image segmentation, which may reduce the localization accuracy due to spatial discretization. We demonstrate that the model parameters can be reliably identified by a feedforward neural network which, driven by the cross-section images, predicts the parameter values many times faster than a reference least-squares (LS) model fitting algorithm. We present and discuss two example applications, modeling the lower extremities of artery-vein complexes visualized in steady-state contrast-enhanced magnetic resonance images (MRI) and the coronary arteries pictured in computed tomography angiograms (CTA). Beyond applications in medical diagnosis, blood-flow simulation and vessel-phantom design, the method can serve as a tool for automated annotation of image datasets to train machine-learning algorithms.

Cooperative Dynamic Motion Planning for Dual Manipulator Arms Based on RRT*Smart-AD Algorithm.

Intelligent manufacturing requires robots to adapt to increasingly complex tasks, and dual-arm cooperative operation can provide a more flexible and effective solution. Motion planning serves as a crucial foundation for dual-arm cooperative operation. The rapidly exploring random tree (RRT) algorithm based on random sampling has been widely used in high-dimensional manipulator path planning due to its probability completeness, handling of high-dimensional problems, scalability, and faster exploration speed compared with other planning methods. As a variant of RRT, the RRT*Smart algorithm introduces asymptotic optimality, improved sampling techniques, and better path optimization. However, existing research does not adequately address the cooperative motion planning requirements for dual manipulator arms in terms of sampling methods, path optimization, and dynamic adaptability. It also cannot handle dual-manipulator collaborative motion planning in dynamic scenarios. Therefore, in this paper, a novel motion planner named RRT*Smart-AD is proposed to ensure that the dual-arm robot satisfies obstacle avoidance constraints and dynamic characteristics in dynamic environments. This planner is capable of generating smooth motion trajectories that comply with differential constraints and physical collision constraints for a dual-arm robot. The proposed method includes several key components. First, a dynamic A* cost function sampling method, combined with an intelligent beacon sampling method, is introduced for sampling. A path-pruning strategy is employed to improve the computational efficiency. Strategies for dynamic region path repair and regrowth are also proposed to enhance adaptability in dynamic scenarios. Additionally, practical constraints such as maximum velocity, maximum acceleration, and collision constraints in robotic arm applications are analyzed. Particle swarm optimization (PSO) is utilized to optimize the motion trajectories by optimizing the parameters of quintic non-uniform rational B-splines (NURBSs). Static and dynamic simulation experiments verified that the RRT*Smart-AD algorithm for cooperative dynamic path planning of dual robotic arms outperformed biased RRT* and RRT*Smart. This method not only holds significant practical engineering significance for obstacle avoidance in dual-arm manipulators in intelligent factories but also provides a theoretical reference value for the path planning of other types of robots.

NURBS Interpolator with Minimum Feedrate Fluctuation Based on Two-Level Parameter Compensation.

Feedrate plays a crucial role in determining the machining quality, tool life, and machining time. Thus, this research aimed to improve the accuracy of NURBS interpolator systems by minimizing feedrate fluctuations during CNC machining. Previous studies have proposed various methods to minimize these fluctuations. However, these methods often require complex calculations and are not suitable for real-time and high-precision machining applications. Given the sensitivity of the curvature-sensitive region to feedrate variations, this paper proposed a two-level parameter compensation method to eliminate the feedrate fluctuation. First, in order to address federate fluctuations in non-curvature sensitive areas with low computational costs, we employed the first-level parameter compensation (FLPC) using the Taylor series expansion method. This compensation allows us to achieve a chord trajectory for the new interpolation point that matches the original arc trajectory. Second, even in curvature-sensitive areas, feedrate fluctuations can still occur because of truncation errors in the first-level parameter compensation. To address this, we employed the Secant-based method for second-level parameter compensation (SLPC), which does not require derivative calculations and can regulate feedrate fluctuation within the fluctuation tolerance. Finally, we applied the proposed method to the simulation of butterfly-shaped NURBS curves. These simulations demonstrated that our method achieved maximum feedrate fluctuation rates below 0.01% with an average computational time of 360 us, which is sufficient for high-precision and real-time machining. Additionally, our method outperformed four other feedrate fluctuation elimination methods, highlighting its feasibility and effectiveness.

An Adaptive Hybrid Sampling Method for Free-Form Surfaces Based on Geodesic Distance.

High precision geometric measurement of free-form surfaces has become the key to high-performance manufacturing in the manufacturing industry. By designing a reasonable sampling plan, the economic measurement of free-form surfaces can be realized. This paper proposes an adaptive hybrid sampling method for free-form surfaces based on geodesic distance. The free-form surfaces are divided into segments, and the sum of the geodesic distance of each surface segment is taken as the global fluctuation index of free-form surfaces. The number and location of the sampling points for each free-form surface segment are reasonably distributed. Compared with the common methods, this method can significantly reduce the reconstruction error under the same sampling points. This method overcomes the shortcomings of the current commonly used method of taking curvature as the local fluctuation index of free-form surfaces, and provides a new perspective for the adaptive sampling of free-form surfaces.

Fast NURBS-based parametric modeling of human calves with high-accuracy for personalized design of graduated compression stockings.

BACKGROUND AND OBJECTIVES: Accurate human body models are increasingly demanded by high-quality human-centered ergonomic applications, especially the design and manufacturing of compressive functional apparels. However, existing parametric models in related works are not capable to accurately describe detailed local shape features of human. METHODS: In this work, a high-accuracy parametric modeling approach for human limb was proposed. 3D Scans of human calves were studied. Key data points of the scanned human calves were identified according to human anatomy, forming a quasi-triangular mesh of feature points. Then, non-uniform rational B-splines (NURBS) method was implemented. Control points were calculated from the key data points, with which the human calf shapes can be reconstructed by the smooth NURBS surface, giving rise to a new parametric model of human calves. Error between the scanned and reconstructed calf shapes were analyzed to verify the effectiveness of this model. RESULTS: Error analysis showed that, this proposed method delivers a high-efficiency and high-accuracy parametric shape modeling approach with averaged error observed as only 0.37% for all the 260 subjects, much less compared to previous relative works (around 5%). For tentative application, customized medical compression stockings were designed based on this model and proved as valid to exert desired gradient compression on the according calf mannequin. CONCLUSIONS: By introducing the non-uniform rational B-splines method, a parametric model capable of characterizing human limbs with high-accuracy was proposed. Using very small amount of data, this model is expected to highly facilitate remote customized design and provide 3D shape references for design of compressive garments. Moreover, the proposed methods can inspire developments of other mixed modeling methods for high-accuracy applications.

3D Reality-Based Survey and Retopology for Structural Analysis of Cultural Heritage.

Cultural heritage's structural changes and damages can influence the mechanical behaviour of artefacts and buildings. The use of finite element methods (FEM) for mechanical analysis is largely used in modelling stress behaviour. The workflow involves the use of CAD 3D models and the use of non-uniform rational B-spline (NURBS) surfaces. For cultural heritage objects, altered by the time elapsed since their creation, the representation created with the CAD model may introduce an extreme level of approximation, leading to wrong simulation results. The focus of this work is to present an alternative method intending to generate the most accurate 3D representation of a real artefact from highly accurate 3D reality-based models, simplifying the original models to make them suitable for finite element analysis (FEA) software. The approach proposed, and tested on three different case studies, was based on the intelligent use of retopology procedures to create a simplified model to be converted to a mathematical one made by NURBS surfaces, which is also suitable for being processed by volumetric meshes typically embedded in standard FEM packages. This allowed us to obtain FEA results that were closer to the actual mechanical behaviour of the analysed heritage asset.

Effect of Various Edge Configurations on the Accuracy of the Modelling Shape of Shell Structures Using Spline Functions.

Spline functions are a useful tool for modelling the shape of shell structures. They have curvature continuity that allows good approximation accuracy for various objects, including hyperboloid cooling towers, spherical domes, paraboloid bowls of radio telescopes, or many other types of smooth free surfaces. Spline models can be used to determine the displacement of structures based on point clouds from laser scanning or photogrammetry. The curvature continuity of splines may, however, cause local distortions in models that have edges. Edges may appear in point clouds where surface patches are joined, on surfaces equipped with additional technical infrastructure or with cracks and shifts in the structure. Taking the properties of spline functions into account, several characteristic types of edge configurations can be distinguished, which may, to a different extent, affect the values of modelling errors. The research conducted below was aimed at identifying such configurations based on theoretical considerations and then assessing their effect on the accuracy of modelling shell structures measured by laser scanning. It turned out to be possible to distinguish between edge configurations, based on the deviation values.

Hybrid computational pregnant female phantom construction for radiation dosimetry applications.

The number of patients undergoing diagnostic radiology and radiation therapy procedures has increased drastically owing to improvements in cancer diagnosis and treatment, and consequently, patient survival. However, the risk of secondary malignancies owing to radiation exposure remains a matter of concern. We previously published three hybrid computational fetal phantoms, which contained 27 fetal organs, as a starting point for developing the whole hybrid computational pregnant phantom set, which is the final objective of this study. An International Commission on Radiological Protection (ICRP) reference female voxel model was converted to a non-uniform rational B-spline (NURBS) surface model to construct a hybrid computational female phantom as a pregnant mother for each fetal model. Both fetal and maternal organs were matched with the ICRP- 89 reference data. To create a complete standard pregnant computational phantom set at 20, 30, and 35 weeks of pregnancy, the model mother's reproductive organs were removed, and fetal phantoms with appropriate placental and uterine models were added to the female pelvis using a 3D-modeling software. With the aid of radiological image sets that had originally been used to construct the fetal models, each fetal position and rotation inside the uterus were carefully adjusted to represent the real fetal locations inside the uterus. The major abdominal soft tissue organs below the diaphragm, namely the small intestine, large intestine, liver, gall bladder, stomach, pancreas, uterus, and urinary bladder, were removed from non-pregnant females. The resulting fetal phantom was positioned in the appropriate location, matching the original radiological image sets. An obstetrician-gynecologist reviewed the complete internal anatomy of all fetus phantoms and the pregnant women for accuracy, and suggested changes were implemented as needed. The remaining female anatomical tissues were reshaped and modified to accommodate the location of the fetus inside the uterus. This new series of hybrid computational pregnant phantom models provides realistic anatomical details that can be useful in evaluating fetal radiation doses in pregnant patients undergoing diagnostic imaging or radiotherapy procedures where realistic fetal computational human phantoms are required.

A Novel Algorithm for Thickness Prediction in Incremental Sheet Metal Forming.

Incremental sheet metal forming characterized as increased flexibility and local plastic deformation is well suitable for low-production-run manufacturing and a new sample trial production of complex shapes. Thickness thinning is still an obstacle to the application of incremental forming. In this study, a novel mathematical algorithm based on a non-uniform rational B-spline (NURBS) surface was proposed and implemented which focuses on predicting and calculating the final thickness for arbitrary parts in incremental forming. In order to evaluate the validity of the proposed model, the finite element simulation and forming experiments of three kinds of parts, such as truncated cones, truncated pyramids and ellipsoid parts, were conducted. The thickness of theoretical prediction was compared with that of finite element simulation and experiment, and good agreements were obtained. The results show that the proposed model and the method are effective and robust for predicting the thickness of the formed parts in incremental sheet metal forming.

A 3D nano scale IGA for free vibration and buckling analyses of multi-directional FGM nanoshells.

This article explores a three-dimensional solid isogeometric analysis (3D-IGA) approach based on a nonlocal elasticity theory to investigate size effects on natural frequency and critical buckling load for multi-directional functionally graded (FG) nanoshells. The multi-directional FG material uses a power law rule with three power exponent indexes concerning three parametric coordinates. Nanoshell's geometries include the square plate, cylindrical and spherical panels with the side length considered in a nanoscale with various thickness ratios. Because 3D-IGA utilizes an approximation of NURBS basic functions to integrate from geometry modeling to discretized domain, it does not require any hypotheses for deformations distribution and stress component through the plate's thickness. Therefore, the results from the 3D solution are obtained accurately with any thickness ratio of the shells. The numerical solutions are verified by those published in several pieces of literature to determine the current approach's accuracy and reliability. After a convergence solution is examined, a quartic NURBS basic function can yield ultra-converged and high-accurate results with a low computational cost. The findings show the size effect parameters which significantly impact the frequencies and the critical buckling factors of the multi-directional FG nanoshells. Generally, increases in the size effect parameters will cause declines in the frequencies and the critical buckling factors of the nanoshells.

Study of Optimal Cam Design of Dual-Axle Spring-Loaded Camming Device.

The spring-loaded camming device (SLCD), also known as "friend", is a simple mechanism used to ensure the safety of the climber through fall prevention. SLCD consists of two pairs of opposing cams rotating separately, with one (single-axle SLCD) or two (dual-axle SLCD) pins connecting the opposing cams, a stem, connected to the pins, providing the attachment of the climbing rope, springs, which simultaneously push cams to a fully expanded position, and an operating element controlling the cam position. The expansion of cams is thus adaptable to allow insertion or removal of the device into/from a rock crack. While the pins, stem, operating element, and springs can be considered optimal, the (especially internal) shape of the cam allows space for improvement, especially where the weight is concerned. This paper focuses on optimizing the internal shape of the dual-axle SLCD cam from the perspective of the weight/stiffness trade-off. For this purpose, two computational models are designed and multi-step topology optimization (TOP) are performed. From the computational models' point of view, SLCD is considered symmetric and only one cam is optimized and smoothened using parametric curves. Finally, the load-bearing capacity of the new cam design is analyzed. This work is based on practical industry requirements, and the obtained results will be reflected in a new commercial design of SLCD.

Attenuation correction in single-photon emission computed tomography for NURBS-based cardiac-torso phantom using dual-energy acquisition.

Single photon emission tomography is widely used to detect photons emitted from the patient. Some of these emitted photons suffer from scattering and absorption because of the attenuation occurred through their path in patient's body. Therefore, the attenuation is the most important problem in single-photon emission computed tomography (SPECT) imaging. Some of the radioisotopes emit gamma rays in different energy levels, and consequently, they have different counts and attenuation coefficients. Calculation of the parameters used in the attenuation equation N out=αNin = e- µ l Nin by mathematical methods is useful for the attenuation correction. Nurbs-based cardiac-torso (NCAT) phantom with an adequate attenuation coefficient and activity distribution is used in this study. Simulations were done using SimSET in 20-70 and 20-167 keV. A total of 128 projections were acquired over 360°. The corrected and reference images were compared using a universal image quality index (UIQI). The simulation repeated using NCAT phantom by SimSET. In the first group, no attenuation correction was used, but the Zubal coefficients were used for attenuation correction in the second image group. After the image reconstruction, a comparison between image groups was done using optimized UIQI to determine the quality of used reconstruction methods. Similarities of images were investigated by considering the average sinogram for every block size. The results showed that the proposed method improved the image quality. This study showed that simulation studies are useful tools in the investigation of nuclear medicine researches. We produced a nonattenuated model using Monte Carlo simulation method and compared it with an attenuated model. The proposed reconstruction method improved image resolution and contrast. Regional and general similarities of images could be determined, respectively, from acquired UIQI of small and large block sizes. Resulted curves from both small and large block sizes showed a good similarity between reconstructed and ideal images.

Optimal Design of CNT-Nanocomposite Nonlinear Shells.

Carbon nanotube/polymer nanocomposite plate- and shell-like structures will be the next generation lightweight structures in advanced applications due to the superior multifunctional properties combined with lightness. Here material optimization of carbon nanotube/polymer nanocomposite beams and shells is tackled via ad hoc nonlinear finite element schemes so as to control the loss of stability and overall nonlinear response. Three types of optimizations are considered: variable through-the-thickness volume fraction of random carbon nanotubes (CNTs) distributions, variable volume fraction of randomly oriented CNTs within the mid-surface, aligned CNTs with variable orientation with respect to the mid-surface. The collapse load, which includes both limit points and deformation thresholds, is chosen as the objective/cost function. An efficient computation of the cost function is carried out using the Koiter reduced order model obtained starting from an isogeometric solid-shell model to accurately describe the point-wise material distribution. The sensitivity to geometrical imperfections is also investigated. The optimization is carried out making use of the Global Convergent Method of Moving Asymptotes. The extensive numerical analyses show that varying the volume fraction distribution as well as the CNTs orientation can lead to significantly enhanced performances towards the loss of elastic stability making these lightweight structures more stable. The most striking result is that for curved shells, the unstable postbuckling response of the baseline material can be turned into a globally stable response maintaining the same amount of nanostructural reinforcement but simply tailoring strategically its distribution.

Material-Oriented Shape Functions for FGM Plate Finite Element Formulation.

A four-noded finite element of a moderately thick plate made of functionally graded material (FGM) is presented. The base element is rectangular and can be extended to any shape using a transformation based on NURBS functions. The proposed 2D shape functions are consistent with the physical interpretation and describe the states of element displacement caused by unit displacements of nodes. These functions depend on the FGM's material parameters and are called material-oriented. The shape function matrix is based on a superposition displacement field of two plate strips with 1D exact shape functions. A characteristic feature of the proposed formulation is full coupling of the membrane and bending states in the plate. The analytical form of the stiffness matrix and the nodal load vector was obtained, which leads to the numerical efficiency of the formulation. The element has been incorporated into Abaqus software with the use of Maple program. The finite element shows good convergence properties for different FGM models in the transverse direction to the middle plane of the plate. During derivation of the 2D plate element the formally exact 1D finite element for transverse nonhomogeneous FGM plate strip was developed.

Integration of Terrestrial Laser Scanning and NURBS Modeling for the Deformation Monitoring of an Earth-Rock Dam.

A complete picture of the deformation characteristics (distribution and evolution) of the geotechnical infrastructures serves as superior information for understanding their potential instability mechanism. How to monitor more completely and accurately the deformation of these infrastructures (either artificial or natural) in the field expediently and roundly remains a scientific topic. The conventional deformation monitoring methods are mostly carried out at a limited number of discrete points and cannot acquire the deformation data of the whole structure. In this paper, a new monitoring methodology of dam deformation and associated results interpretation is presented by taking the advantages of the terrestrial laser scanning (TLS), which, in contrast with most of the conventional methods, is capable of capturing the geometric information at a huge amount of points over an object in a relatively fast manner. By employing the non-uniform rational B-splines (NURBS) technology, the high spatial resolution models of the monitored geotechnical objects can be created with sufficient accuracy based on these point cloud data obtained from application of the TLS. Finally, the characteristics of deformation, to which the geotechnical infrastructures have been subjected, are interpreted more completely according to the models created based on a series of consecutive monitoring exercises at different times. The present methodology is applied to the Changheba earth-rock dam, which allows the visualization of deformation over the entire dam during different periods. Results from analysis of the surface deformation distribution show that the surface deformations in the middle are generally larger than those on both sides near the bank, and the deformations increase with the increase of the elevations. The results from the present application highlight that the adhibition of the TLS and NURBS technology permits a better understanding of deformation behavior of geotechnical objects of large size in the field.

Surface Fitting for Quasi Scattered Data from Coordinate Measuring Systems.

Non-uniform rational B-spline (NURBS) surface fitting from data points is wildly used in the fields of computer aided design (CAD), medical imaging, cultural relic representation and object-shape detection. Usually, the measured data acquired from coordinate measuring systems is neither gridded nor completely scattered. The distribution of this kind of data is scattered in physical space, but the data points are stored in a way consistent with the order of measurement, so it is named quasi scattered data in this paper. Therefore they can be organized into rows easily but the number of points in each row is random. In order to overcome the difficulty of surface fitting from this kind of data, a new method based on resampling is proposed. It consists of three major steps: (1) NURBS curve fitting for each row, (2) resampling on the fitted curve and (3) surface fitting from the resampled data. Iterative projection optimization scheme is applied in the first and third step to yield advisable parameterization and reduce the time cost of projection. A resampling approach based on parameters, local peaks and contour curvature is proposed to overcome the problems of nodes redundancy and high time consumption in the fitting of this kind of scattered data. Numerical experiments are conducted with both simulation and practical data, and the results show that the proposed method is fast, effective and robust. What's more, by analyzing the fitting results acquired form data with different degrees of scatterness it can be demonstrated that the error introduced by resampling is negligible and therefore it is feasible.

Topologically preserving straightening of spinal cord MRI.

PURPOSE: To propose a robust and accurate method for straightening magnetic resonance (MR) images of the spinal cord, based on spinal cord segmentation, that preserves spinal cord topology and that works for any MRI contrast, in a context of spinal cord template-based analysis. MATERIALS AND METHODS: The spinal cord curvature was computed using an iterative Non-Uniform Rational B-Spline (NURBS) approximation. Forward and inverse deformation fields for straightening were computed by solving analytically the straightening equations for each image voxel. Computational speed-up was accomplished by solving all voxel equation systems as one single system. Straightening accuracy (mean and maximum distance from straight line), computational time, and robustness to spinal cord length was evaluated using the proposed and the standard straightening method (label-based spline deformation) on 3T T2 - and T1 -weighted images from 57 healthy subjects and 33 patients with spinal cord compression due to degenerative cervical myelopathy (DCM). RESULTS: The proposed algorithm was more accurate, more robust, and faster than the standard method (mean distance = 0.80 vs. 0.83 mm, maximum distance = 1.49 vs. 1.78 mm, time = 71 vs. 174 sec for the healthy population and mean distance = 0.65 vs. 0.68 mm, maximum distance = 1.28 vs. 1.55 mm, time = 32 vs. 60 sec for the DCM population). CONCLUSION: A novel image straightening method that enables template-based analysis of quantitative spinal cord MRI data is introduced. This algorithm works for any MRI contrast and was validated on healthy and patient populations. The presented method is implemented in the Spinal Cord Toolbox, an open-source software for processing spinal cord MRI data. LEVEL OF EVIDENCE: 1 Technical Efficacy: Stage 1 J. Magn. Reson. Imaging 2017;46:1209-1219.

Feasibility of differential geometry-based features in detection of anatomical feature points on patient surfaces in range image-guided radiation therapy.

PURPOSE: To investigate the feasibility of differential geometry features in the detection of anatomical feature points on a patient surface in infrared-ray-based range images in image-guided radiation therapy. METHODS: The key technology was to reconstruct the patient surface in the range image, i.e., point distribution with three-dimensional coordinates, and characterize the geometrical shape at every point based on curvature features. The region of interest on the range image was extracted by using a template matching technique, and the range image was processed for reducing temporal and spatial noise. Next, a mathematical smooth surface of the patient was reconstructed from the range image by using a non-uniform rational B-splines model. The feature points were detected based on curvature features computed on the reconstructed surface. The framework was tested on range images acquired by a time-of-flight (TOF) camera and a Kinect sensor for two surface (texture) types of head phantoms A and B that had different anatomical geometries. The detection accuracy was evaluated by measuring the residual error, i.e., the mean of minimum Euclidean distances (MMED) between reference (ground truth) and detected feature points on convex and concave regions. RESULTS: The MMEDs obtained using convex feature points for range images of the translated and rotated phantom A were [Formula: see text] and [Formula: see text], respectively, using the TOF camera. For the phantom B, the MMEDs of the convex and concave feature points were [Formula: see text] and [Formula: see text] mm, respectively, using the Kinect sensor. There was a statistically significant difference in the decreased MMED for convex feature points compared with concave feature points [Formula: see text]. CONCLUSIONS: The proposed framework has demonstrated the feasibility of differential geometry features for the detection of anatomical feature points on a patient surface in range image-guided radiation therapy.