Comparative assessment of two algorithms for calibrating stereophotogrammetric systems

In this paper, a comparison is carried out between two photogrammetric algorithms aimed at camera calibration and three-dimensional target point reconstruction by ‘absolute’ distributions of control points; the first is Marzan and Karara's DLT, the second is CESNO, by the author, an algorithm quite close to Hatze's modified DLT (MDLT). The comparative assessment is especially aimed at testing the capability of the two methods to produce good results when calibration data are to be extrapolated beyond the space spanned by the control distribution. The assessment was carried out not by a real stereophotogrammetric system, but by the computer simulation of a two-camera set-up. Various combinations of internal camera parameters, such as the scaled principal distances, were tried out. As for the magnitude of the simulated non-linear lens distortion, three configurations were used which produced ‘low’, ‘medium’ and ‘strong’ distortion. The influence of decreasing the number of control (calibration) points on the accuracy performance of the two algorithms was also investigated. The results show the superiority of CESNO, especially with medium or strong lens distortion, or when the two camera principal distances sensibly differ.     

Quantitative underwater 3D motion analysis using submerged video cameras: accuracy analysis and trajectory reconstruction

In this study we aim at investigating the applicability of underwater 3D motion capture based on submerged video cameras in terms of 3D accuracy analysis and trajectory reconstruction. Static points with classical direct linear transform (DLT) solution, a moving wand with bundle adjustment and a moving 2D plate with Zhang's method were considered for camera calibration. As an example of the final application, we reconstructed the hand motion trajectories in different swimming styles and qualitatively compared this with Maglischo's model. Four highly trained male swimmers performed butterfly, breaststroke and freestyle tasks. The middle fingertip trajectories of both hands in the underwater phase were considered. The accuracy (mean absolute error) of the two calibration approaches (wand: 0.96 mm – 2D plate: 0.73 mm) was comparable to out of water results and highly superior to the classical DLT results (9.74 mm). Among all the swimmers, the hands' trajectories of the expert swimmer in the style were almost symmetric and in good agreement with Maglischo's model. The kinematic results highlight symmetry or asymmetry between the two hand sides, intra- and inter-subject variability in terms of the motion patterns and agreement or disagreement with the model. The two outcomes, calibration results and trajectory reconstruction, both move towards the quantitative 3D underwater motion analysis.     

Improved RSA accuracy with DLT and balanced calibration marker distributions with an assessment of initial-calibration

Roentgen stereophotogrammetric analysis (RSA) has been used for over 25 years for accurate micromotion measurement in a wide variety of orthopaedic applications. This study investigated two possible improvements to the method. First, direct linear transformation (DLT) was compared to the traditional RSA reconstruction algorithm. The two methods were considered with respect to standard extrapolation and interpolation calibration cages. Matlab simulations showed that reconstruction accuracy was greatly improved (>60%) by combining DLT with an even distribution of enclosing calibration markers. Second, a benchtop study using phantoms translated at 0.0254-mm intervals showed initial-calibration, followed by removal of the interpolation cage for subsequent exposures, was potentially twice as accurate as self-calibration with an extrapolation cage. These results showed optimizations for the application of RSA when unobstructed space is required.     

Accuracy of femur reconstruction from sparse geometric data using a statistical shape model

Sparse geometric information from limited field-of-view medical images is often used to reconstruct the femur in biomechanical models of the hip and knee. However, the full femur geometry is needed to establish boundary conditions such as muscle attachment sites and joint axes which define the orientation of joint loads. Statistical shape models have been used to estimate the geometry of the full femur from varying amounts of sparse geometric information. However, the effect that different amounts of sparse data have on reconstruction accuracy has not been systematically assessed. In this study, we compared shape model and linear scaling reconstruction of the full femur surface from varying proportions of proximal and distal partial femur geometry in combination with morphometric and landmark data. We quantified reconstruction error in terms of surface-to-surface error as well as deviations in the reconstructed femur’s anatomical coordinate system which is important for biomechanical models. Using a partial proximal femur surface, mean shape model-based reconstruction surface error was 1.8 mm with 0.15° or less anatomic axis error, compared to 19.1 mm and 2.7–5.6° for linear scaling. Similar results were found when using a partial distal surface. However, varying amounts of proximal or distal partial surface data had a negligible effect on reconstruction accuracy. Our results show that given an appropriate set of sparse geometric data, a shape model can reconstruct full femur geometry with far greater accuracy than simple scaling.     

Non-linear cancer classification using a modified radial basis function classification algorithm

Summary This paper proposes a modified radial basis function classification algorithm for non-linear cancer classification. In the algorithm, a modified simulated annealing method is developed and combined with the linear least square and gradient paradigms to optimize the structure of the radial basis function (RBF) classifier. The proposed algorithm can be adopted to perform non-linear cancer classification based on gene expression profiles and applied to two microarray data sets involving various human tumor classes: (1) Normal versus colon tumor; (2) acute myeloid leukemia (AML) versus acute lymphoblastic leukemia (ALL). Finally, accuracy and stability for the proposed algorithm are further demonstrated by comparing with the other cancer classification algorithms.     

Side-chain modeling with an optimized scoring function

Modeling side-chain conformations on a fixed protein backbone has a wide application in structure prediction and molecular design. Each effort in this field requires decisions about a rotamer set, scoring function, and search strategy. We have developed a new and simple scoring function, which operates on side-chain rotamers and consists of the following energy terms: contact surface, volume overlap, backbone dependency, electrostatic interactions, and desolvation energy. The weights of these energy terms were optimized to achieve the minimal average root mean square (rms) deviation between the lowest energy rotamer and real side-chain conformation on a training set of high-resolution protein structures. In the course of optimization, for every residue, its side chain was replaced by varying rotamers, whereas conformations for all other residues were kept as they appeared in the crystal structure. We obtained prediction accuracy of 90.4% for chi(1), 78.3% for chi(1 + 2), and 1.18 A overall rms deviation. Furthermore, the derived scoring function combined with a Monte Carlo search algorithm was used to place all side chains onto a protein backbone simultaneously. The average prediction accuracy was 87.9% for chi(1), 73.2% for chi(1 + 2), and 1.34 A rms deviation for 30 protein structures. Our approach was compared with available side-chain construction methods and showed improvement over the best among them: 4.4% for chi(1), 4.7% for chi(1 + 2), and 0.21 A for rms deviation. We hypothesize that the scoring function instead of the search strategy is the main obstacle in side-chain modeling. Additionally, we show that a more detailed rotamer library is expected to increase chi(1 + 2) prediction accuracy but may have little effect on chi(1) prediction accuracy.     

Age estimation of Norway spruce using incomplete increment cores: Testing new and improved methods

Information on tree age is often vital for dendrochronological studies, especially when the Regional Curve Standardisation technique is used. Several linear and non-linear methods of tree age estimation using partial increment cores (without the presence of pith) were evaluated and modified to provide more accurate estimations than are currently used. To achieve the objective, core samples from 142 Norway spruce trees (Picea abies [L.] Karst.) were collected from an altitudinal gradient in the Western Carpathians. The samples in which the pith was included were then used for further analyses. Several known age estimation approaches were adjusted to combine the advantages of direct increment- and indirect age-diameter-based methods. Inverse differential forms of non-linear growth functions were tested and proposed as a new advanced approach for age estimation. The results show that most of the modified linear methods achieved a mean square error of less than 10% when the length of the partial core exceeded 90% of the stem radius and less than 20% when the length of the core was at least 60% of the stem radius. Using an appropriate differential form of the non-linear growth functions, a mean square error of less than 20% was reached, even when the core length was shorter than 60% of the radius. The results show that current linear methods for age estimation can only be used if the missing part of the core sample is very short, with only a few rings absent. In the case of a large number of missing rings, a differential form of non-linear functions should preferably be used instead.     

Design of a marker-based human motion tracking system

In this paper a complete design of a high speed optical motion analyzer system has been described. The main core of the image processing unit has been implemented by the differential algorithm procedure. Some intelligent and conservative procedures that facilitate the search algorithm have also been proposed and implemented for the processing of human motions. Moreover, an optimized modified direct linear transformation (MDLT) method has been used to reconstruct 3D markers positions which are used for deriving kinematic characteristics of the motion. Consequently, a set of complete tests using some simple mechanical devices were conducted to verify the system outputs. Considering the system verification for human motion analysis, we used the system for gait analysis and the results including joint angles showed good compatibility with other investigations. Furthermore, a sport application example of the system has been quantitatively presented and discussed for Iranian National Karate-kas. The low computational cost, the high precision in detecting and reconstructing marker position with 2.39 mm error, and the capability of capturing from any number of cameras to increase the domain of operation of the subject, has made the proposed method a reliable approach for real-time human motion analysis. No special environment limitation, portability, low cost hardware and built in units for simulations and kinematic analysis are the other significant specifications of this system.     

Stereometry in very close-range stereophotogrammetry with non-metric cameras for human movement analysis

In this paper a stereophotogrammetric algorithm based on a black-box approach to the modelling of object to image spaces relationship is proposed. The algorithm is well suited for 'very close-range photogrammetry', with respect to experiments in which the measurement field is 0.5 X 0.5 X 0.5 m or smaller, as in the analysis of a few or small body segments movements. The attainable accuracy is high, better than 0.1% of the observation distance. Non-professional and even different cameras can be used. Consequently an inexpensive experimental set-up can be realized. A very simple, cheap and easily usable calibration object is needed. Computation time for the reconstruction of object-space co-ordinates of point body landmarks is one order of magnitude lower than in the case of the Direct Linear Transformation (DLT) (Abdel Aziz and Karara, Proceedings of the ASP/U1 Symposium on Close-Range Photogrammetry, pp. 1-18. American Society of Photogrammetry, 1971; Marzan and Karara, Proceedings of the Symposium on close-range Photogrammetric Systems, pp. 420-467. American Society of Photogrammetry, 1975). Computation time for calibration is two-fold in respect of the DLT. An example of application to the recording of the movements of the index finger with respect to the metacarpophalangeal joint is given.     

Comparison of different camera calibration approaches for underwater applications

The purpose of this study was to compare three camera calibration approaches applied to underwater applications: (1) static control points with nonlinear DLT; (2) moving wand with nonlinear camera model and bundle adjustment; (3) moving plate with nonlinear camera model. The DVideo kinematic analysis system was used for underwater data acquisition. The system consisted of two gen-locked Basler cameras working at 100 Hz, with wide angle lenses that were enclosed in housings. The accuracy of the methods was compared in a dynamic rigid bar test (acquisition volume-4.5×1×1.5 m(3)). The mean absolute errors were 6.19 mm for the nonlinear DLT, 1.16 mm for the wand calibration, 1.20 mm for the 2D plate calibration using 8 control points and 0.73 mm for the 2D plane calibration using 16 control points. The results of the wand and 2D plate camera calibration methods were less associated to the rigid body position in the working volume and provided better accuracy than the nonlinear DLT. Wand and 2D plate camera calibration methods presented similar and highly accurate results, being alternatives for underwater 3D motion analysis.     

Accuracy assessment and control point configuration when using the DLT for photogrammetry.

The direct linear transformation (DLT) is a common technique used to calibrate cameras and subsequently reconstruct points filmed with two or more cameras in a three-dimensional object space. The assessment of the accuracy of this technique, and of the influence of the distribution of control points on accuracy were examined. It was concluded that to obtain a true estimation of reconstruction accuracy, an independent assessment criterion is required, and that the use of control points distributed around the outside, rather than within the space to be calibrated, is preferred.     

A constrained linear regression optimization algorithm for diaphragm motion tracking with cone beam CT projections

PurposeWe presented a feasibility study to extract the diaphragm motion from the inferior contrast cone beam computed tomography (CBCT) projection images using a constrained linear regression optimization algorithm.MethodsThe shape of the diaphragm was fitted by a parabolic function which was initialized by five manually placed points on the diaphragm contour of a pre-selected projection. A constrained linear regression model by exploiting the spatial, algebraic, and temporal constraints of the diaphragm, approximated by a parabola, was employed to estimate the parameters. The algorithm was assessed by a fluoroscopic movie acquired at anterior-posterior (AP) fixed direction and kilovoltage CBCT projection image sets from four lung and two liver patients using the Varian 21iX Clinac. The automatic tracing by the proposed algorithm and manual tracking were compared in both space and frequency domains for the algorithm evaluations.ResultsThe error between the results estimated by the proposed algorithm and those by manual tracking for the AP fluoroscopic movie was 0.54 mm with standard deviation (SD) of 0.45 mm. For the detected projections the average error was 0.79 mm with SD of 0.64 mm for all six enrolled patients and the maximum deviation was 2.5 mm. The mean sub-millimeter accuracy outcome exhibits the feasibility of the proposed constrained linear regression approach to track the diaphragm motion on rotational fluoroscopic images.ConclusionThe new algorithm will provide a potential solution to rendering diaphragm motion and possibly aiding the tumor target tracking in radiation therapy of thoracic/abdominal cancer patients.     

基于Renyi熵滤波的光声图像重建算法设计与实现

针对光声图像重建过程中存在的原始光声信号信噪比差、重建图像对比度低、分辨率不足等问题,提出了基于Renyi熵的光声图像重建滤波算法.该算法首先根据原始光声信号的Renyi熵分布情况,确定分割阈值,并滤除杂波信号;再利用滤波后的光声数据进行延时叠加光声图像重建.利用该滤波算法分别处理铅笔芯横截面(零维)、头发丝(一维)以及小鼠大脑皮层血管(二维)等不同维度样本的光声信号,实验结果表明:相比Renyi熵处理之前,重建图像对比度平均增强了32.45%,分辨率平均提高了30.78%,信噪比提高了47.66%,均方误差降低了35.01%;相比典型的滤波处理算法(模极大值法和阈值去噪法),本研究中图像的对比度、分辨率和信噪比分别提高了25.94%/10.60%、27.90%/19.48%、35.21%/10.60%,均方误差减小了28.57%/16.66%.因此,选择利用Renyi熵滤波算法处理光声信号,从而使光声图像重建质量得到大幅改善.     

Accounting for radiotelemetry signal flux in triangulation point estimation

Triangulation by radiotelemetry is a method commonly used to estimate locations of wildlife. Despite the importance of the accuracy of resulting location estimates, there has been little development and comparison of alternative methods for point-location estimation for 25 years. Most methods assume that signal transmissions as they are received are consistent, but signal heterogeneity and fluxing is common. Using data from a beacon study, we determined that a subjective ranking of confidence in the accuracy of a signal was correlated with absolute bearing error. Using this factor and the distance from a telemetry station to the error triangle incenter, we developed an algorithm to place a weighted point-location estimate in relative proximity to each error triangle leg. We have termed this the weighted-incenter method. Despite previous findings that the major confidence ellipse axis of Lenth’s maximum likelihood estimator (MLE) correlated best to linear distance error, our beacon test data indicated that total bearing angle difference was the best single predictor of linear error with an optimal total angle of about 100°. The new and intuitive weighted-incenter method offered some improvement over previous methods such as the MLE estimator, but only with suboptimal angle bearings that may be common in field studies. By using a MATLAB function to produce data for site-specific regression analyses, one can determine which method should produce the more accurate point-location estimate for each triangulation observation. Further significance of this study for field biologists is discussed.     

3D reconstruction of the pelvis from bi-planar radiography

3D personalized models are more and more requested for clinical and biomechanical studies. Techniques based on bi-planar X-rays present the advantage of a low radiation dose for the patient. However, up to now, such techniques have shown limited accuracy in the case of pelvis reconstruction. This study proposes and validates a method providing accurate 3D personalized model of the pelvis from bi-planar X-rays. The algorithm is based on the fast computation of an initial solution followed by local deformations based on 2D anatomical points and contours that are digitized in both radiographs. Results were close to CT-scan reconstructions (mean difference 1.6 mm and differences under 4.3 mm for 95% of the points). Moreover, 3D morphometry of the pelvis could be obtained with an accuracy of 5%. This technique provides 3D patient specific model with a low radiation dose.     

Exploring Variability in CT Characterization of Tumors: A Preliminary Phantom Study

PURPOSE: To explore the effects of computed tomography (CT) slice thickness and reconstruction algorithm on quantification of image features to characterize tumors using a chest phantom. MATERIALS AND METHODS: Twenty-two phantom lesions of known sizes (10 and 20 mm), shapes (spherical, elliptical, lobulated, and spiculated), and densities [-630, -10, and +100 Hounsfield Unit (HU)] were inserted into an anthropomorphic thorax phantom and scanned three times with relocations. The raw data were reconstructed using six imaging settings, i.e., a combination of three slice thicknesses of 1.25, 2.5, and 5 mm and two reconstruction kernels of lung and standard. Lesions were segmented and 14 image features representing lesion size, shape, and texture were calculated. Differences in the measured image features due to slice thickness and reconstruction algorithm were compared using linear regression method by adjusting three confounding variables (size, density, and shape). RESULTS: All 14 features were significantly different between 1.25 and 5 mm slice images. The 1.25 and 2.5 mm slice thicknesses were better than 5 mm for volume, density mean, density SD gray-level co-occurrence matrix (GLCM) energy and homogeneity. As for the reconstruction algorithm, there was no significant difference in uni-dimension, volume, shape index 9, and compactness. Lung reconstruction was better for density mean, whereas standard reconstruction was better for density SD. CONCLUSIONS: CT slice thickness and reconstruction algorithm can significantly affect the quantification of image features. Thinner (1.25 and 2.5 mm) and thicker (5 mm) slice images should not be used interchangeably. Sharper and smoother reconstructions significantly affect the density-based features.     

Progressive search in tandem mass spectrometry

A cell exhibits a variety of responses to internal and external cues. These responses are possible, in part, due to the presence of an elaborate gene regulatory network (GRN) in every single cell. In the past 20 years, many groups worked on reconstructing the topological structure of GRNs from large-scale gene expression data using a variety of inference algorithms. Insights gained about participating players in GRNs may ultimately lead to therapeutic benefits. Mutual information (MI) is a widely used metric within this inference/reconstruction pipeline as it can detect any correlation (linear and non-linear) between any number of variables (n-dimensions). However, the use of MI with continuous data (for example, normalized fluorescence intensity measurement of gene expression levels) is sensitive to data size, correlation strength and underlying distributions, and often requires laborious and, at times, ad hoc optimization. In this work, we first show that estimating MI of a bi- and tri-variate Gaussian distribution using k-nearest neighbor (kNN) MI estimation results in significant error reduction as compared to commonly used methods based on fixed binning. Second, we demonstrate that implementing the MI-based kNN Kraskov–Stoögbauer–Grassberger (KSG) algorithm leads to a significant improvement in GRN reconstruction for popular inference algorithms, such as Context Likelihood of Relatedness (CLR). Finally, through extensive in-silico benchmarking we show that a new inference algorithm CMIA (Conditional Mutual Information Augmentation), inspired by CLR, in combination with the KSG-MI estimator, outperforms commonly used methods. Using three canonical datasets containing 15 synthetic networks, the newly developed method for GRN reconstruction—which combines CMIA, and the KSG-MI estimator—achieves an improvement of 20–35% in precision-recall measures over the current gold standard in the field. This new method will enable researchers to discover new gene interactions or better choose gene candidates for experimental validations.     

A new calibration method for 3-D position measurement in biomedical applications.

Aim of the study was to determine practicality and to test accuracy of a new calibration technique firstly introduced in 1998 by Schmid and Bess for biomechanical human tests. This technique enables three-dimensional calibration of camera positions as well as the calculation of internal and external camera parameters. It can be performed unlike other three-dimensional calibration techniques as the first with a planar calibration grid and only one single video image (of each camera) to calculate all 3-D reconstruction parameters. The tests were performed using two albavision ACAM G-Cameras with a resolution of 480 (h) by 420 (v) pixels. The achievable accuracy of distance measurements in recent commercially available motion measurement systems usually ranges from about 0.09% to 1.77% and higher. Accuracy of 0.0373% was determined with the new calibration technique. The 95% confidence interval ranged at +/- 0.02322 mm, the RMS (root mean square) error at 0.18776 mm. Better accuracy, easier and faster calibration are features of this new calibration technique. Required time for complete calibration ranged below one minute. Anticipating this new method will have good practicality in gait analysis or in research and industry due to increased accuracy and ease of use.     

The appropriate use of regression equations for the estimation of segmental inertia parameters

Linear regression equations are commonly used in conjunction with experimental data to provide linear relationships between quantities which are dimensionally distinct. In many cases theoretical relationships between such quantities are known and can be used as a basis for non-linear regression equations. This study compares linear and non-linear approaches for estimating the segmental moments of inertia from anthropometric measurements using the data of Chandler et al. [Chandler et al. (1975) Investigation of inertial properties of the human body. AMRL Technical Report 74-137, Wright Patterson Air Force Base. OH.] Right limb data were used to derive the equations while left limb data were used as a cross-validation sample to evaluate the inertia estimates calculated from the equations. For the limb segments the standard error estimates had average values of 21% for the linear equations and 13% for the non-linear equations. Data on a 10 yr-old boy was used to compare the two approaches outside the sample range. The mean percentage residuals were 286% for the linear equations and 20% for the non-linear equations. A set of non-linear equations is provided.     

The robustness and accuracy of in vivo linear wear measurements for knee prostheses based on model-based RSA

Accurate in vivo measurements methods of wear in total knee arthroplasty are required for a timely detection of excessive wear and to assess new implant designs. Component separation measurements based on model-based Roentgen stereophotogrammetric analysis (RSA), in which 3-dimensional reconstruction methods are used, have shown promising results, yet the robustness of these measurements is unknown. In this study, the accuracy and robustness of this measurement for clinical usage was assessed. The validation experiments were conducted in an RSA setup with a phantom setup of a knee in a vertical orientation. 72 RSA images were created using different variables for knee orientations, two prosthesis types (fixed-bearing Duracon knee and fixed-bearing Triathlon knee) and accuracies of the reconstruction models. The measurement error was determined for absolute and relative measurements and the effect of knee positioning and true seperation distance was determined. The measurement method overestimated the separation distance with 0.1mm on average. The precision of the method was 0.10mm (2*SD) for the Duracon prosthesis and 0.20mm for the Triathlon prosthesis. A slight difference in error was found between the measurements with 0° and 10° anterior tilt. (difference=0.08mm, p=0.04). The accuracy of 0.1mm and precision of 0.2mm can be achieved for linear wear measurements based on model-based RSA, which is more than adequate for clinical applications. The measurement is robust in clinical settings. Although anterior tilt seems to influence the measurement, the size of this influence is low and clinically irrelevant.