비디오 프레임 영상으로부터 제작된 자유 입체 모자이크 영상의 실좌표 등록

Existing Gauss-Newton methods for solving the problem of 3D similarity transformation are all based on the method of numerical partial derivatives, which can linearize the 3D similarity transformation model by using Taylor expansion for approximated variables to the first order derivative. And by using the linearized 3D transformation model, all of the unknown variables can be obtained by an iterative process. In existing models, the model considering random errors of design matrix is called errors-in-variables (EIV) model. In contrast to the Gauss-Newton methods, a Gauss-quasi-Newton method for solving the problem of 3D similarity transformation is proposed in this paper. In the Gauss-quasi-Newton method, 3D similarity transformation model is linearized by a differential method, and based on the differential linearization model, an iterative robust estimation can be carried out by considering both random errors and gross errors in 3D coordinates of common points. The new method proposed in this paper can be applied to 3D similarity transformation of arbitrary rotational angles. Finally, the new method is validated by three cases, and results showed that the new method is effective and feasible.

3D similarity transformations are often used for datum transformation in Geomatic Engineering. The transformations are routinely performed between the point coordinates evaluated from GNSS (Global Navigation Satellite Systems) observations and the point coordinates given in national datum. A mathematical model established among two different 3D coordinate systems contains tree type datum parameters which are translations, rotations and a scale. Coefficients of the parameters reflect large variations from each other’s. So, the unknown coefficient matrix in normal equations is to be ill-conditioned. In this study, it is indicated how the ill-condition structure is reduced to acceptable level by means of choosing at different unit of unknown parameters. Finally, the transformation from Kocaeli Metropolitan Municipality GNSS network coordinates to Turkish Geodetic Datum is used as a numerical example.

The dynamic equations of multibody railroad vehicle systems can be formulated using different sets of generalized coordinates; examples of these sets of coordinates are the absolute Cartesian and trajectory coordinates. The absolute coordinate based formulations do not require introducing an intermediate track coordinate system since all the absolute coordinates are defined in the global system. On the other hand, when the trajectory coordinates are used, a track coordinate system that follows the motion of a body in the railroad vehicle system is introduced. This track coordinate system is defined by the track geometry and the distance traveled by the body along the track centerline. The configuration of the body with respect to the track coordinate system is defined using five coordinates; two translations and three Euler angles. In this paper, the formulations based on the absolute and trajectory coordinates are compared. It is shown that these two sets of coordinates require different degrees of differentiability and smoothness. When an elastic contact formulation is used to study the wheel/rail dynamic interaction, there are significant differences in the order of the derivatives required in both formulations. In fact, as demonstrated in this study, in the absence of a contact constraint formulation, higher order derivatives with respect to geometric parameters are still required when the equations are formulated using the trajectory coordinates. The formulation of the constraints used in the analysis of the wheel/rail contact is discussed and it is shown that when the absolute coordinates are used, only third order derivatives need to be evaluated. The relationship between the track frame used in railroad vehicle dynamics and the Frenet frame used in the theory of curves to describe the curve geometry is also discussed in this paper. Based on the analysis presented in this paper, the advantages and drawbacks of a hybrid method which employs both the absolute and trajectory coordinates and planar contact conditions in order to reduce the number of contact constraints and relax the differentiability requirements are discussed. In this method, the absolute coordinates are used to formulate the equations of motion of the railroad vehicle system. The absolute coordinate solution can be used to determine the trajectory coordinates and their time derivatives. Using the trajectory coordinates, the motion of the body in the vehicle with respect to the track coordinate system can be predicted and used in the formulation of the planar contact model.

Background:Knee positions involved in noncontact anterior cruciate ligament (ACL) injury have been studied via analysis of injury videos. Positions of high ACL strain have been identified in vivo. These methods have supported different hypotheses regarding the role of knee abduction in ACL injury.Purpose/Hypothesis:The purpose of this study was to compare knee abduction angles measured by 2 methods: using a 3-dimensional (3D) coordinate system based on anatomic features of the bones versus simulated 2-dimensional (2D) videographic analysis. We hypothesized that knee abduction angles measured in a 2D videographic analysis would differ from those measured from 3D bone anatomic features and that videographic knee abduction angles would depend on flexion angle and on the position of the camera relative to the patient.Study Design:Descriptive laboratory study.Methods:Models of the femur and tibia were created from magnetic resonance images of 8 healthy male participants. The models were positioned to match biplanar fluoroscopic images obtained as participants posed in lunges of varying flexion angles (FLAs). Knee abduction angle was calculated from the positioned models in 2 ways: (1) varus-valgus angle (VVA), defined as the angle between the long axis of the tibia and the femoral transepicondylar axis by use of a 3D anatomic coordinate system; and (2) coronal plane angle (CPA), defined as the angle between the long axis of the tibia and the long axis of the femur projected onto the tibial coronal plane to simulate a 2D videographic analysis. We then simulated how changing the position of the camera relative to the participant would affect knee abduction angles.Results:During flexion, when CPA was calculated from a purely anterior or posterior view of the joint—an ideal scenario for measuring knee abduction from 2D videographic analysis—CPA was significantly different from VVA (P < .0001). CPA also varied substantially with the position of the camera relative to the participant.Conclusion:How closely CPA (derived from 2D videographic analysis) relates to VVA (derived from a 3D anatomic coordinate system) depends on FLA and camera orientation.Clinical Relevance:This study provides a novel comparison of knee abduction angles measured from 2D videographic analysis and those measured within a 3D anatomic coordinate system. Consideration of these findings is important when interpreting 2D videographic data regarding knee abduction angle in ACL injury.

Conventional open-tray impression versus intraoral digital scan for implant-level complete-arch impression

The 3D Pelvic Inclination Correction System (PICS): A universally applicable coordinate system for isovolumetric imaging measurements, tested in women with pelvic organ prolapse (POP)

Aim: To explore an accurate method to calculate acetabular cup anteversion after total hip arthroplasty. Method: 1) A 3D coordinate system was established with the center of the hip joint rotation center base as coordinate center. The acetabular exit plane and Pettersson formula acetabular anteversion and Riten Pradhan formula acetabular anteversion and acetabular true anteversion were drawn; 2) Determine the mathematical expression of Pettersson formula acetabular anteversion α and Riten Pradhan formula acetabular anteversion β in the coordinate system. The true acetabular anteversion is projection angle of Pettersson formula acetabular anteversion α on cross-section in the presence of acetabular abduction δ, determining mathematical expression of the acetabular anteversion θ by trigonometric functions. Results: Real acetabular cup anteversion θ = arctg (tgβ/cosδ). Conclusion: The true acetabular cup anteversion and Pettersson formula anteversion and Riten Pradhan for mula anteversion were quite different. The difference was increased with the acetabular cup abduction angle increased. The formula was simple and accurate and worthy of clinical reference.

The European Datum 1950 (ED50) of the Turkish national geodetic network (TNGN) and the World Geodetic System 1984 (WGS84) of the Turkish national fundamental GPS network (TNFGN) are in use as geodetic reference frames in Turkey. According to the use of two reference systems, it is necessary to transform the three-dimensional (3D) coordinate data from ED50 to WGS84 or vice versa. The seven-parameter similarity transformation method is frequently used for 3D coordinate transformation in geodesy. In this study, a back propagation artificial neural network (BPANN) that has been more widely applied in engineering among all other neural network models is evaluated as an alternative 3D coordinate transformation method. BPANN is compared with a popular seven-parameter similarity transformation (Molodensky-Badekas) method over a test area, in terms of root mean square error (RMSE). The results indicated that the employment of BPANN transformed 3D coordinates (X, Y, Z) more accurate than Molodensky-Badekas method and can be useful for 3D coordinate transformation between ED50 and WGS84. Key words: 3D coordinate transformation, back propagation artificial neural network, seven-parameter similarity transformation, BPANN, Molodensky-Badekas.

Type of wave breaking - plunging or spilling - depends on symmetry of waves. The spilling waves are asymmetric against horizontal axis and are practically symmetric against vertical axis so the phase shift between first and second nonlinear harmonics (or biphase) is close to zero. The plunging breaking waves have larger asymmetry against vertical axis, (biphase is close to -pi/2), and near symmetric on horizontal axis (close to saw-toothed form). Non-linear wave transformation influences on depth-induced wave breaking. Breaking index depends on relation of wave energy in frequency range of second nonlinear harmonics to wave energy in frequency range of main harmonic and on biphase. The dissipation rate of spilling breaking waves energy quadratically depends on frequency, while in plunging breaking, this dependency is practically linear for all frequencies.

The accurate transformation of multi-camera 2D coordinates into 3D coordinates is critical for applications like animation, gaming, and medical rehabilitation. This study unveils an enhanced multi-camera calibration method that alleviates the shortcomings of existing approaches by incorporating a comprehensive cost function and Adaptive Iteratively Reweighted Least Squares (AIRLS) optimization. By integrating static error components (3D coordinate, distance, angle, and reprojection errors) with dynamic wand distance errors, the proposed comprehensive cost function facilitates precise multi-camera parameter calculations. The AIRLS optimization effectively balances the optimization of both static and dynamic error elements, enhancing the calibration’s robustness and efficiency. Comparative validation against advanced multi-camera calibration methods shows this method’s superior accuracy (average error 0.27 ± 0.22 mm) and robustness. Evaluation metrics including average distance error, standard deviation, and range (minimum and maximum) of errors, complemented by statistical analysis using ANOVA and post-hoc tests, underscore its efficacy. The method markedly enhances the accuracy of calculating intrinsic, extrinsic, and distortion parameters, proving highly effective for precise 3D reconstruction in diverse applications. This study represents substantial progression in multi-camera calibration, offering a dependable and efficient solution for intricate calibration challenges.

In cephalometric radiography a reduced dimensions radiograph system introduces a parallax effect. With the aid of a five-sided plexiglass phantom, we show that when the distance between the X-ray sources is lower than 4 metres from film and subject, the effect of parallax produces coordinates errors of a point in the space greater than the coordinate errors due to the capture on the radiographs. The objective is to improve the accuracy of the calculation of 3D coordinates of dentomaxillofacial points when the distance between patient and X-ray source is less than 6 metres. Using the stenope model of radiographic system, we describe a new method and we develop formulas, which permits the calculation of 3D real coordinates of a point viewed on any two out of the 3 radiographs, frontal, lateral and axial, from only one X-ray source. We test this method in comparing the known real coordinates of metallic markers fixed on the phantom to the computed coordinates given by this method. We test also this method by using a dried skull, we compare the computed coordinate errors to those due to capture on the radiograph by the operator and compare the dispersion of computed coordinate errors to errors due re-positioning the object on the radiographic system.

Unlike the traditional models, a new stereo photographic model requiring no sea control points that are difficult to lay on a sea surface is developed in this paper. It is realized according to the order of camera intrinsic parameters calibration, relative orientation and absolute orientation based on average sea surface, and we give the governing equations and its algorithms. First of all, in the paper we present an imaging model that adopts non-measurement camera with considering only the radial distortion coefficients, and then give the method that calculates the camera intrinsic parameters by combining the co-planar equations and the distance equations to form a closed system of equations. For verifying the convergence of the governing equations, we lay four parallel sand ridges on a level ground in laboratory, measure seven lines of different heights and take a pair of the images by two cameras. The intrinsic parameters are successfully calculated by using the method, and further analysis shows that the results are highly precise. When observing the ocean waves in offshore sea, we need to recalculate the relative orientation parameters. At this time the governing equations are the co-planar equations, but the accuracy of the image matching is seriously related to the accuracy of the relative orientation parameters. However, as the mirror reflection of the sea surface, the matching accuracy of the sea image is often low, so we select 407 optimal matching points from among 1600 conjugate points and calculate the parameters. It needs a sequence of sea image pairs to obtain the absolute orientation parameters, 256 pairs in the paper. For each pair, we select firstly 300300 feature points on the left image approximately evenly, then find the conjugate points on the right image by image matching, calculate the coordinates of the corresponding sea surface points in the left camera coordinate system, and then fit the points into a plane; thus a plane sequence can be obtained. We establish a special object coordinate system on the average sea surface that is obtained by summing the plane sequence, and calculate the absolute orientation parameters by the geometric relationship between the two coordinate systems. And it is proved that the methods of relative orientation and absolute orientation proposed in this paper are feasible by reconstructing sea surface height field. The model greatly reduces the difficulty in calibrating the stereoscopic photography for ocean wave measurement, which is beneficial to its popularization and application.

We present a new experimental system of monodisperse, soft, frictionless, fluorescent labeled elastic shells for the characterization of structure, universal scaling laws and force networks in 3D jammed matter. The elastic shells in a jammed packing are deformed in such a way that at each contact one of the shells buckles with a dimple and the other remain spherical, closely resembling overlapping spheres. Using confocal microscopy, we obtained 3D stacks of images of shells at different volume fractions which were subsequently processed in ImageJ software to find their coordinates. The determination of 3D coordinates involved three steps: locating the edges of shells in all 2D slices, analyzing their shape and subsequently finding their 2D coordinates, and finally determining their 3D centers by grouping the corresponding 2D coordinates. From this analysis routine we obtained particle coordinates with sub-pixel accuracy. In a contact pair we also identified the shell that underwent buckling forming a dimple by analyzing the intensity profile of a line that connects the centers of particle pairs. The amorphous structure of the packing was analyzed as a function of distance to the jamming threshold by investigating the radial distribution function, bond order parameters, contact numbers and the number of dimples per particle (buckling number), which is a unique property of this system. We find that the power law scaling of the contact number with excess volume fraction deviated from theoretical and computer simulation predictions. In addition, the buckling number also showed a similar scaling as that of the contact number with distance to the jamming transition.

Presentation of multiple interactions is of vital importance in the new field of cytomics. Quantitative analysis of multi- and polychromatic stained cells in tissue will serve as a basis for medical diagnosis and prediction of disease in forthcoming years. A major problem associated with huge interdependent data sets is visualization. Therefore, alternative and easy-to-handle strategies for data visualization as well as data meta-evaluation (population analysis, cross-correlation, co-expression analysis) were developed. To facilitate human comprehension of complex data, 3D parallel coordinate systems have been developed and used in automated microscopy-based multicolor tissue cytometry (MMTC). Frozen sections of human skin were stained using the combination anti-CD45-PE, anti-CD14-APC, and SytoxGreen as well as the appropriate single and double negative controls. Stained sections were analyzed using automated confocal laser microscopy and semiquantitative MMTC-analysis with TissueQuest 2.0. The 3D parallel coordinate plots are generated from semiquantitative immunofluorescent data of single cells. The 2D and 3D parallel coordinate plots were produced by further processing using the Matlab environment (Mathworks, USA). Current techniques in data visualization primarily utilize scattergrams, where two parameters are plotted against each other on linear or logarithmic scales. However, data evaluation on cartesian x/y-scattergrams is, in general, only of limited value in multiparameter analysis. Dot plots suffer from serious problems, and in particular, do not meet the requirements of polychromatic high-context tissue cytometry of millions of cells. The 3D parallel coordinate plot replaces the vast amount of scattergrams that are usually needed for the cross-correlation analysis. As a result, the scientist is able to perform the data meta-evaluation by using one single plot. On the basis of 2D parallel coordinate systems, a density isosurface is created for representing the event population in an intuitive way. The proposed method opens new possibilities to represent and explore multidimensional data in the perspective of cytomics and other life sciences, e.g., DNA chip array technology. Current protocols in immunofluorescence permit simultaneous staining of up to 17 markers. Showing the cross-correlation between these markers requires 136 scattergrams, which is a prohibitively high number. The improved data visualization method allows the observation of such complex patterns in only one 3D plot and could take advantage of the latest developments in 3D imaging.

ABSTRACTThis article presents a Gaussian process (GP)-based approach to model a tunnel’s inner surface profile with high frequency sensing data provided by a Terrestrial Laser Scanner (TLS). We introduce a reading-surface profile that uniquely determines a three-dimensional tunnel in a Cartesian coordinate system. This reading-surface transforms the cylindrical tunnel to a two-dimensional surface profile, hence allowing us to model the tunnel profile by GP. To account for coordinate errors induced by TLS, we take repeated measurements at designed coordinates. We apply a Taylor approximation to extract mean and gradient estimations from the repeated measurements and then fit the GP model with both estimations to obtain a more robust reconstruction of the tunnel profile. We validate our method through numerical examples. The simulation results show that with the help of derivative estimations, our method outperforms the conventional GP regression with noisy observations in terms of mean-squared prediction error. We also present a case study to demonstrate that our method provides a more accurate result than the existing cylinder-fitting approach and has great potential for deformation monitoring in the presence of coordinate errors.