B-spline Algorithm Research Articles

Fuzzy B-spline optimization for urban slum three-dimensional reconstruction using ENVISAT satellite data

A critical challenges in urban aeras is slums. In fact, they are considered a source of crime and disease due to poor-quality housing, unsanitary conditions, poor infrastructures and occupancy security. The poor in the dense urban slums are the most vulnerable to infection due to (i) inadequate and restricted access to safety, drinking water and sufficient quantities of water for personal hygiene; (ii) the lack of removal and treatment of excreta; and (iii) the lack of removal of solid waste. This study aims to investigate the capability of ENVISAT ASAR satellite and Google Earth data for three-dimensional (3-D) slum urban reconstruction in developed countries such as Egypt. The main objective of this work is to utilize some 3-D automatic detection algorithm for urban slum in ENVISAT ASAR and Google Erath images were acquired in Cairo, Egypt using Fuzzy B-spline algorithm. The results show that the fuzzy algorithm is the best indicator for chaotic urban slum as it can discriminate between them from its surrounding environment. The combination of Fuzzy and B-spline then used to reconstruct 3-D of urban slum. The results show that urban slums, road network, and infrastructures are perfectly discriminated. It can therefore be concluded that the fuzzy algorithm is an appropriate algorithm for chaotic urban slum automatic detection in ENVSIAT ASAR and Google Earth data.

SU‐C‐17A‐05: Quantification of Intra‐Fraction Motion of Breast Tumors Using Cine‐MRI

Purpose:Magnetic resonance imaging (MRI) enables direct characterization of intra‐fraction motion ofbreast tumors, due to high softtissue contrast and geometric accuracy. The purpose is to analyzethis motion in early‐stage breast‐cancer patients using pre‐operative supine cine‐MRI.Methods:MRI was performed in 12 female early‐stage breast‐cancer patients on a 1.5‐T Ingenia (Philips)wide‐bore scanner in supine radiotherapy (RT) position, prior to breast‐conserving surgery. Twotwodimensional (2D) T2‐weighted balanced fast‐field echo (cine‐MRI) sequences were added tothe RT protocol, oriented through the tumor. They were alternately acquired in the transverse andsagittal planes, every 0.3 s during 1 min. A radiation oncologist delineated gross target volumes(GTVs) on 3D contrast‐enhanced MRI. Clinical target volumes (CTV = GTV + 15 mm isotropic)were generated and transferred onto the fifth time‐slice of the time‐series, to which subsequents lices were registered using a non‐rigid Bspline algorithm; delineations were transformed accordingly. To evaluate intra‐fraction CTV motion, deformation fields between the transformed delineations were derived to acquire the distance ensuring 95% surface coverage during scanning(P95%), for all in‐plane directions: anteriorposterior (AP), left‐right (LR), and caudal‐cranial(CC). Information on LR was derived from transverse scans, CC from sagittal scans, AP fromboth sets.Results:Time‐series with registration errors – induced by motion artifacts – were excluded by visual inspection. For our analysis, 11 transverse, and 8 sagittal time‐series were taken into account. Themedian P95% calculated in AP (19 series), CC (8), and LR (11) was 1.8 mm (range: 0.9–4.8), 1.7mm (0.8–3.6), and 1.0 mm (0.6–3.5), respectively.Conclusion:Intra‐fraction motion analysis of breast tumors was achieved using cine‐MRI. These first results show that in supine RT position, motion amplitudes are limited. This information can be used for adaptive RT planning, and to develop preoperative partial‐breast RT strategies, such asablative RT for early‐stage breast‐cancer patients.

Computing global minimizers to a constrained B‐spline image registration problem from optimal l1 perturbations to block match data

Block matching is a well-known strategy for estimating corresponding voxel locations between a pair of images according to an image similarity metric. Though robust to issues such as image noise and large magnitude voxel displacements, the estimated point matches are not guaranteed to be spatially accurate. However, the underlying optimization problem solved by the block matching procedure is similar in structure to the class of optimization problem associated with B-spline based registration methods. By exploiting this relationship, the authors derive a numerical method for computing a global minimizer to a constrained B-spline registration problem that incorporates the robustness of block matching with the global smoothness properties inherent to B-spline parameterization. The method reformulates the traditional B-spline registration problem as a basis pursuit problem describing the minimall1-perturbation to block match pairs required to produce a B-spline fitting error within a given tolerance. The sparsity pattern of the optimal perturbation then defines a voxel point cloud subset on which the B-spline fit is a global minimizer to a constrained variant of the B-spline registration problem. As opposed to traditional B-spline algorithms, the optimization step involving the actual image data is addressed by block matching. The performance of the method is measured in terms of spatial accuracy using ten inhale/exhale thoracic CT image pairs (available for download atwww.dir-lab.com) obtained from the COPDgene dataset and corresponding sets of expert-determined landmark point pairs. The results of the validation procedure demonstrate that the method can achieve a high spatial accuracy on a significantly complex image set. The proposed methodology is demonstrated to achieve a high spatial accuracy and is generalizable in that in can employ any displacement field parameterization described as a least squares fit to block match generated estimates. Thus, the framework allows for a wide range of image similarity block match metric and physical modeling combinations.

Three-dimensional slum urban reconstruction in Envisat and Google Earth Egypt

This study aims to aim to investigate the capability of ENVISAT ASAR satellite and Google Earth data for three-dimensional (3-D) slum urban reconstruction in developed country such as Egypt. The main objective of this work is to utilize 3-D automatic detection algorithm for urban slum in ENVISAT ASAR and Google Erath images were acquired in Cairo, Egypt using Fuzzy B-spline algorithm. The results show that fuzzy algorithm is the best indicator for chaotic urban slum as it can discriminate them from its surrounding environment. The combination of Fuzzy and B-spline then used to reconstruct 3-D of urban slam. The results show that urban slums, road network, and infrastructures are perfectly discriminated. It can therefore be concluded that fuzzy algorithm is an appropriate algorithm for chaotic urban slum automatic detection in ENVSIAT ASAR and Google Earth data.

Evaluation of Dose Change by Using the Deformable Image Registration (DIR) on the Intensity Modulated Radiation Therapy (IMRT) with Glottis Cancer

The purpose of this study is to evaluate the variation of the dose which is delivered to the patients with glottis cancer under IMRT (intensity modulated radiation therapy) by using the 3D registration with CBCT (cone beam CT) images and the DIR (deformable image registration) techniques. The CBCT images which were obtained at a one-week interval were reconstructed by using B-spline algorithm in DIR system, and doses were recalculated based on the newly obtained CBCT images. The dose distributions to the tumor and the critical organs were compared with reference. For the change of volume depending on weight at 3 to 5 weeks, there was increased of 1.38∼2.04 kg on average. For the body surface depending on weight, there was decreased of 2.1 mm. The dose with transmitted to the carotid since three weeks was increased compared be more than 8.76% planned, and the thyroid gland was decreased to 26.4%. For the physical evaluation factors of the tumor, PITV, TCI, rDHI, mDHI, and CN were decreased to 4.32%, 5.78%, 4 4.54%, 12.32%, and 7.11%, respectively. Moreover, D max, Dmean, V67.50, and D95 for PTV were increased or decreased to 2.99%, 1.52%, 5.78%, and 11.94%, respectively. Although there was no change of volume depending on weight, the change of body types occurred, and IMRT with the narrow composure margin sensitively responded to such a changing. For the glottis IMRT, the patient's weight changes should be observed and recorded to evaluate the actual dose distribution by using the DIR techniques, and more the adaptive treatment planning during the treatment course is needed to deliver the accurate dose to the patients.

Deformable image registration for temporal subtraction of chest radiographs.

Temporal subtraction images constructed from image registration can facilitate the visualization of pathologic changes. In this study, we propose a deformable image registration (DIR) framework for creating temporal subtraction images of chest radiographs. We developed a DIR methodology using two different image similarity metrics, varying flow (VF) and compressible flow (CF). The proposed registration method consists of block matching, filtering, and interpolation. Specifically, corresponding point pairs between reference and target images are initially determined by minimizing a nonlinear least squares formulation using grid-searching optimization. A two-step filtering process, including least median of squares filtering and backward matching filtering, is then applied to the estimated point matches in order to remove erroneous matches. Finally, moving least squares is used to generate a full displacement field from the filtered point pairs. We applied the proposed DIR method to 10 pairs of clinical chest radiographs and compared it with the demons and B-spline algorithms using the five-point rating score method. The average quality scores were 2.7 and 3 for the demons and B-spline methods, but 3.5 and 4.1 for the VF and CF methods. In addition, subtraction images improved the visual perception of abnormalities in the lungs by using the proposed method. The VF and CF models achieved a higher accuracy than the demons and the B-spline methods. Furthermore, the proposed methodology demonstrated the ability to create clinically acceptable temporal subtraction chest radiographs that enhance interval changes and can be used to detect abnormalities such as non-small cell lung cancer.

Volumetric Dose Summation Between Brachytherapy Fractions in Patients Treated for Cervical Cancer: Feasibility of Using Deformable Registration

Volumetric Dose Summation Between Brachytherapy Fractions in Patients Treated for Cervical Cancer: Feasibility of Using Deformable Registration

Biomechanical Model as a Registration Tool for Image-Guided Neurosurgery: Evaluation Against BSpline Registration

In this paper we evaluate the accuracy of warping of neuro-images using brain deformation predicted by means of a patient-specific biomechanical model against registration using a BSpline-based free form deformation algorithm. Unlike the BSpline algorithm, biomechanics-based registration does not require an intra-operative MR image which is very expensive and cumbersome to acquire. Only sparse intra-operative data on the brain surface is sufficient to compute deformation for the whole brain. In this contribution the deformation fields obtained from both methods are qualitatively compared and overlaps of Canny edges extracted from the images are examined. We define an edge based Hausdorff distance metric to quantitatively evaluate the accuracy of registration for these two algorithms. The qualitative and quantitative evaluations indicate that our biomechanics-based registration algorithm, despite using much less input data, has at least as high registration accuracy as that of the BSpline algorithm.

The extended cubic B-spline algorithm for a modified regularized long wave equation

A collocation method based on an extended cubic B-spline function is introduced for the numerical solution of the modified regularized long wave equation. The accuracy of the method is illustrated by studying the single solitary wave propagation and the interaction of two solitary waves of the modified regularized long wave equation.

H and He atoms in strong magnetic fields

We develop a B-spline algorithm to investigate problems of strongly magnetized atoms. Energy levels for both H and He atoms are presented for a wider field range.

DInSAR technique for three-dimensional coastal spit simulation from radarsat-1 fine mode data

This work presents a new approach to 3D spit simulation using differential synthetic aperture interferometry (DInSAR). In doing so, conventional DInSAR procedures are implemented to three repeat passes of RADARSAT-1 SAR fine mode data (F1). Further, a new application of using fuzzy B-spline algorithm is implemented with phase unwrapping technique. The study shows that the performance of DInSAR method using fuzzy B-spline is better than the DInSAR technique, which is validated by the coefficient of determination r 2 of 0.96, probability p of 0.002, and accuracy (RMSE) of ± 0.034 m, with 90% confidence intervals. In conclusion, integration of fuzzy B-spline with phase unwrapping produces an accurate 3D coastal geomorphology reconstruction.

Calculation of Excited States of He Atoms in a Strong Magnetic Field

A recently developed B-spline algorithm is extended and utilized to calculate excited states of He atoms in the presence of strong magnetic fields. Binding energies are presented for He in the five excited atomic states 210+, 110−, 210−, 11(−1)+, and 21(−1)+ with magnetic field strength ranging from 0.0001 to 10 a.u. The obtained energies are compared with available theoretical data, and found to be in good agreement. We investigate influence of magnetic fields on atomic structures of multielectron atoms, and illustrate that how electron probability density distributions change with increasing magnetic field strength. The current approach is directly applicable to simulations of discrete spectra for He atoms in the atmospheres of magnetized white dwarf stars.

B-Spline Registration Based on New Concept of an Intelligent Masking Procedure and GPU Computations for the Head and Neck Adaptive Tomotherapy

The deformable image registration (DIR) procedure has been optimized for helical tomotherapy. The data on registration shifts obtained on matching planning image with pre-treatment megavoltage CT are used in our software for acceleration of the first step (rigid registration) of the DIR procedure and for implementation of the B-Spline algorithm with intelligent masking. Priorities of the masks were automatically calculated based on disagreement detected during rigid registration. Evaluation tasks included: (a) comparison of accuracy and rate for schemes of pre-registered and non-registered images; (b) qualification of the effectiveness of the intelligent masking process, and (c) determination of acceleration of achievable with GPU computing. A specially designed head and neck phantom used for evaluation included structures with controlled changes of position, volume, density, and shape. Re-contouring procedures were performed with an Adaptive Planning software (Tomotherapy Inc.). No statistical difference was observed in accuracy of DIR based on structure position match on the tomotherapy unit and non pre-registered images (p > 0.7). Using pre-registered data reduces the total time required for execution of the elastic registration procedure by 5%. These data are also necessary for intelligent masking procedure during B-Spine registration. Intelligent masking procedure increases accuracy of the registration for a masked structure (p < 0.04) without decreasing the accuracy in non-masked tissues and additionally reduces the total time by 13%. GPU computations speed up procedure 30 times. GPU computing of the DIR in current status of our investigation could be realized in a relatively short time after pre-treatment imaging. The proposed approach can be used in the routine assessment of anatomic changes occurring in healthy tissue during the course of radiotherapy. Further developments will be concentrated on the full integration of DIR computations in the imaging and treatment process of helical tomotherapy.

Reconstruction of Composite Surface Based on CMM Point Data

In this paper, a novel surface reconstruction method is presented to creat a composite surface with point data on surface obtained by CMM. In this method, the 3th non-uniform B-spline algorithm is proposed to reconstruct every single free-form surface on the whole composite surface, and the algorithm for surface blending is proposed to merge every single surface together to achieve the level of G1 continuity. Furthermore, in order to check and visualize the reconstruction model, a special closed-loop RE system is developd by VC++ to constantly guide to measure and reconstruct untill the model fits in with requirements. Examples are included to illustrate the approach.

Fuzzy B-spline algorithm for 3-D lineament reconstruction

Lineaments are vital geological features that play the role of a key indicator for ground water and petroleum searching. At present, there is no study that has utilised remote sensing satellite data to reconstruct three dimensional (3-D) lineament visualization in the Uinted Arab Emirates (UAE). This work aimed at reconstructing a (3-D) lineament visualization from multispectral remote sensing such as LANDSAT TM. In doing so, the fuzzy B-spline algorithm was used to reconstruct 3-D from two dimensional (2-D) LANDSAT TM 7 satellite data. Prior to the fuzzy B-spline algorithm, image enhancement contrast, stretching and linear enhancements were applied to acquire an excellent visualization. In addition, automatic detection algorithm of Canny was performed to extract linear features in multispectral remote sensing data, that is, lineaments, fractures. Uncertainty digital elevation model (DEM) was performed by using fuzzy B-spline algorithm to map spatial lineament variation in 3-D. Further, a fuzzy B-spline algorithm was used to reconstruct 3-D visualization of lieament with standard error of mean of 0.12 and bias of 0.23. In conclusion, fuzzy B-spline provides excellent promising for 3-D geological features reconstruction from two dimensional (2-D) remote sensing satellite data. Key words: Lineament, 3D visualizations, DEM, multispectral remotely sensed data, LANDSAT TM.

Shadow Removal Using B-Spline for Edges Reconstruction in Surveillance

Shadows are one of the major problems in objects detection and tracking for automated video surveillance systems. In such systems accurate detection is required even under variable weather conditions. The majority of shadow removal algorithms in the literature suffer from misclassification errors because of inaccurate shadow detection, thus resulting in distorted object shapes. In this paper, a novel technique is proposed for shadow detection and removal using both edge detecting and B-spline algorithm. This technique is capable of correcting such errors by using B-spline algorithm for object's edges reconstruction so that the object shapes remain well defined along most part of their contours. Experimental results in PETS2006 benchmark dataset show that the proposed technique increases the shadow detection reliability compared to some existing shadow detection algorithms.

Three-dimensional visualisation of coastal geomorphology using fuzzy B-spline of dinsar technique

This paper introduces a new approach for mapping coastal geomorphology by using differential synthetic aperture radar interferometry (DInSAR). Fuzzy B-spline is used to accelerate and improve the accuracy of 3-D map from DInSAR. The DInSAR algorithm involved two parts: 3-D map simulation and interferogram simulation with discrete element method (DEM) and satellite orbit parameters. 3-D coastal geomorphology reconstruction is realised by the fuzzy B-spline algorithm with the midpoint displacement method and the terrain roughness, and average slope are determined by two describing parameters of the model. Furthermore, fuzzy B-spline was used to eliminate topographic phase from the interferograms. Three RADARSAT-1 data sets of fine beam mode (F1) had been obtained between November 1999 and March 2004. The study shows incomplete fringe interferometry pattern because of decorrelation. Furthermore, fuzzy B-spline of DInSAR performs higher overall accuracy of 95% compared to DInSAR technique and ground data. Finally, prefect fringe pattern is clearly produced in ocean water body that refers to ocean water InSAR or liqui-InSAR. In conclusion, fuzzy B-spline of DInSAR provide accurate map of 3-D coastal geomorphology construction from historical RADARSAT-1 SAR fine mode data and can be also tool for liqui-InSAR. Key words: RADARSAT-1 SAR, differential synthetic aperture radar interferometry (DInSAR), fuzzy B-spline, 3-D, coastal geomorphology.

Attenuation Correction Methods Suitable for Brain Imaging with a PET/MRI Scanner: A Comparison of Tissue Atlas and Template Attenuation Map Approaches

Modeled attenuation correction (AC) will be necessary for combined PET/MRI scanners not equipped with transmission scanning hardware. We compared 2 modeled AC approaches that use nonrigid registration with rotating (68)Ge rod-based measured AC for 10 subjects scanned with (18)F-FDG. Two MRI and attenuation map pairs were evaluated: tissue atlas-based and measured templates. The tissue atlas approach used a composite of the BrainWeb and Zubal digital phantoms, whereas the measured templates were produced by averaging spatially normalized measured MR image and coregistered attenuation maps. The composite digital phantom was manually edited to include 2 additional tissue classes (paranasal sinuses, and ethmoidal air cells or nasal cavity). In addition, 3 attenuation values for bone were compared. The MRI and attenuation map pairs were used to generate subject-specific attenuation maps via nonrigid registration of the MRI to the MR image of the subject. SPM2 and a B-spline free-form deformation algorithm were used for the nonrigid registration. To determine the accuracy of the modeled AC approaches, radioactivity concentration was assessed on a voxelwise and regional basis. The template approach produced better spatial consistency than the phantom-based atlas, with an average percentage error in radioactivity concentration across the regions, compared with measured AC, of -1.2% ± 1.2% and -1.5% ± 1.9% for B-spline and SPM2 registration, respectively. In comparison, the tissue atlas method with B-spline registration produced average percentage errors of 0.0% ± 3.0%, 0.9% ± 2.9%, and 2.9% ± 2.8% for bone attenuation values of 0.143 cm(-1), 0.152 cm(-1), and 0.172 cm(-1), respectively. The largest errors for the template AC method were found in parts of the frontal cortex (-3%) and the cerebellar vermis (-5%). Intersubject variability was higher with SPM2 than with B-spline. Compared with measured AC, template AC with B-spline and SPM2 achieved a correlation coefficient (R(2)) of 0.99 and 0.98, respectively, for regional radioactivity concentration. The corresponding R(2) for the tissue atlas approach with B-spline registration was 0.98, irrespective of the bone attenuation coefficient. Nonrigid registration of joint MRI and attenuation map templates can produce accurate AC for brain PET scans, particularly with measured templates and B-spline registration. Consequently, these methods are suitable for AC of brain scans acquired on combined PET/MRI systems.

Optical digital sensor for three-dimensional turbulent flow visualization

The Nikon Coolpix885® conventional digital camera is utilized to reform three-dimensional (3-D) turbulent pattern on lake that is situated in University Technology Malaysia (UTM).The main objective of this study is to use fuzzy arithmetic to reduce the errors arising from noise in digital camera data when constructing turbulent pattern flow. In doing so, the fuzzy B-spline algorithm, which assemble a global topological between the data points, are used to support an approximation to the real surface. Further, the fuzzy B-spline is performed to water surface information which estimated from 2-D digital camera images. Key words: Digital camera, turbulent flow, fuzzy B-spline, three-dimensional (3D) reconstruction.

A new approach to quantifying lung damage after stereotactic body radiation therapy

Radiological pneumonitis and fibrosis are common after stereotactic body radiotherapy (SBRT) but current scoring systems are qualitative and subjective. We evaluated the use of CT density measurements and a deformable registration tool to quantitatively measure lung changes post-SBRT. Material and methods. Four-dimensional CT datasets from 25 patients were imported into an image analysis program. Deformable registration was done using a B-spline algorithm (VelocityAI) and evaluated by landmark matching. The effects of respiration, contrast, and CT scanner on density measurements were evaluated. The relationship between density and clinician-scored radiological pneumonitis was assessed. Results. Deformable registration resulted in more accurate image matching than rigid registration. CT lung density was maximal at end-expiration, and most deformation with breathing occurred in the lower thorax. Use of contrast increased mean lung density by 18 HU (range 16–20 HU; p = 0.004). Diagnostic scans had a lower mean lung density than planning scans (mean difference 57 HU in lung contralateral to tumor; p = 0.048). Post-treatment CT density measurements correlated strongly with clinician-scored radiological pneumonitis (r = 0.75; p < 0.001). Conclusions. Quantitative analysis of changes in lung density correlated strongly with physician-assigned radiologic pneumonitis scores. Deformable registration and CT density measurements permit objective assessment of treatment toxicity.