Direct Linear Transformation Research Articles

Improved Direct Linear Transformation for Parameter Decoupling in Camera Calibration

For camera calibration based on direct linear transformation (DLT), the camera’s intrinsic and extrinsic parameters are simultaneously calibrated, which may cause coupling errors in the parameters and affect the calibration parameter accuracy. In this paper, we propose an improved direct linear transformation (IDLT) algorithm for calibration parameter decoupling. This algorithm uses a linear relationship of calibration parameter errors and obtains calibration parameters by moving a three-dimensional template. Simulation experiments were conducted to compare the calibration accuracy of DLT and IDLT algorithms with image noise and distortion. The results show that the IDLT algorithm calibration parameters achieve higher accuracy because the algorithm removes the coupling errors.

Using rainbow trout cell lines to further study and understand the pathogenesis of the coldwater pathogen, Flavobacterium psychrophilum

Robust tracking is a crucial step in automatic swimmer evaluation from video sequences. We designed a robust swimmer tracking system using a new multi-related-targets approach. The main idea is to consider the swimmer as a bloc of connected subtargets that advance at the same speed. If one of the subtargets is partially or totally occluded, it can be localized by knowing the position of the others. In this paper, we first introduce the two-dimensional direct linear transformation technique that we used to calibrate the videos. Then, we present the classical tracking approach based on dynamic fusion. Next, we highlight the main contribution of our work, which is the multi-related-targets tracking approach. This approach, the classical head-only approach and the ground truth are then compared, through testing on a database of high-level swimmers in training, national and international competitions (French National Championships, Limoges 2015, and World Championships, Kazan 2015). Tracking percentage and the accuracy of the instantaneous speed are evaluated and the findings show that our new appraoach is significantly more accurate than the classical approach.

Co-registering satellite images and LIDAR DEMs through straight lines

Co-registration of optical and range data is a crucial step before they could be merged. Trustworthy correspondence between both data is determined via image registration models. These models are mainly built with points; however, with the aid of automated extraction tools for linear objects, photogrammetrists have been developing transformation models with lines. In this study, we propose to co-register satellite images and light detection and ranging (LIDAR) digital elevation models (DEMs) with straight lines. We developed a line extraction algorithm that was capable of extracting straight lines in both data sets. These lines were then utilised to register the LIDAR DEM with several high-resolution satellite images. We were able to reach one-pixel accuracy through the parallel projection transformation model and the direct linear transformation (DLT) model when geometric constraints among the lines were enforced. Our findings are similar to those reported with points and highlight the leverage of linear features in registering satellite imageries and LIDAR data.

Near-Infrared Camera Calibration for Optical Surgical Navigation

Near-infrared optical tracking devices, which are important components of surgical navigation systems, need to be calibrated for effective tracking. The calibration results has a direct influence on the tracking accuracy of an entire system. Therefore, the study of calibration techniques is of theoretical significance and practical value. In the present work, a systematic calibration method based on movable plates is established, which analyzes existing calibration theories and implements methods using calibration reference objects. First, the distortion model of near-infrared cameras (NICs) is analyzed in the implementation of this method. Second, the calibration images from different positions and orientations are used to establish the required linear equations. The initial values of the NIC parameters are calculated with the direct linear transformation method. Finally, the accurate internal and external parameters of the NICs are obtained by conducting nonlinear optimization. Analysis results show that the relative errors of the left and right NICs in the tracking system are 0.244 and 0.282 % for the focal lengths and 0.735 and 1.111 % for the principal points, respectively. The image residuals of the left and right image sets are both less than 0.01 pixel. The standard error of the calibration result is lower than 1, and the measurement error of the tracking system is less than 0.3 mm. The experimental data show that the proposed method of calibrating NICs is effective and can generate favorable calibration results.

A preliminary study for determination of three-dimensional root apex position of the maxillary teeth using camera calibration technology.

To propose a novel method for determining the three-dimensional (3D) root apex position of maxillary teeth using a two-dimensional (2D) panoramic radiograph image and a 3D virtual maxillary cast model. The subjects were 10 adult orthodontic patients treated with non-extraction. The multiple camera matrices were used to define transformative relationships between tooth images of the 2D panoramic radiographs and the 3D virtual maxillary cast models. After construction of the root apex-specific projective (RASP) models, overdetermined equations were used to calculate the 3D root apex position with a direct linear transformation algorithm and the known 2D co-ordinates of the root apex in the panoramic radiograph. For verification of the estimated 3D root apex position, the RASP and 3D-CT models were superimposed using a best-fit method. Then, the values of estimation error (EE; mean, standard deviation, minimum error and maximum error) between the two models were calculated. The intraclass correlation coefficient values exhibited good reliability for the landmark identification. The mean EE of all root apices of maxillary teeth was 1.88 mm. The EE values, in descending order, were as follows: canine, 2.30 mm; first premolar, 1.93 mm; second premolar, 1.91 mm; first molar, 1.83 mm; second molar, 1.82 mm; lateral incisor, 1.80 mm; and central incisor, 1.53 mm. Camera calibration technology allows reliable determination of the 3D root apex position of maxillary teeth without the need for 3D-CT scan or tooth templates.

DLT와 부가변수에 의한 광속조정법을 활용한 근접사진측량의 3차원 위치정확도 분석

DLT와 부가변수에 의한 광속조정법을 활용한 근접사진측량의 3차원 위치정확도 분석

Application of composite small calibration objects in traffic accident scene photogrammetry.

In order to address the difficulty of arranging large calibration objects and the low measurement accuracy of small calibration objects in traffic accident scene photogrammetry, a photogrammetric method based on a composite of small calibration objects is proposed. Several small calibration objects are placed around the traffic accident scene, and the coordinate system of the composite calibration object is given based on one of them. By maintaining the relative position and coplanar relationship of the small calibration objects, the local coordinate system of each small calibration object is transformed into the coordinate system of the composite calibration object. The two-dimensional direct linear transformation method is improved based on minimizing the reprojection error of the calibration points of all objects. A rectified image is obtained using the nonlinear optimization method. The increased accuracy of traffic accident scene photogrammetry using a composite small calibration object is demonstrated through the analysis of field experiments and case studies.

The Relationship Between The Operation Of Kick Start And Isokinetic Knee Strength In Swimmers

PURPOSE: The purpose of this study was to examine the relationship between the operation of kick start and isokinetic knee strength in swimmers using three-dimensional (3D) analysis. METHODS: This study included 11 male university student swimmers, who usually used the kick-start technique. We filmed the operation of kick start using 3 high-speed cameras (300 scenes; shutter speed, 1/250 s). The cameras could record over an area measuring 6.05 × 1.90 × 2.00 m. After we took a video of operation, we vertically set up calibration-pole which applied the control-point at intervals of 0.5m at the seven places within the range of taking a picture as ground and the surface of the water. Motion analysis was performed using Frame-DIASIV System (DKH) software. The 3D coordinates of 23 points on each subject’s body were determined using direct linear transformation. Tests of isokinetic knee strength were performed using an isokinetic dynamometer (BIODEX, System 4). For each measurement, we set the angular velocity as 60, 180, and 300°/s, and repetitions were conducted 5, 10 and 15 times, respectively. In the analysis, we divided muscle strength by weight, for each participant. We used Spearman’s rank correlation coefficient to assess the relationship between the operation of kick start and isokinetic strength. Statistical significance was set at 5%. RESULTS: There was a significant relationship between the average center of gravity, horizontal acceleration before take-off, and flexion muscle strength of the front knee at 60°/s (r = 0.718) and 180°/s (r = 0.636) and extension muscle strength of the rear knee at 300°/s (r = 0.500). Similarly, there was a significant relationship between the time from the start signal to take-off and flexion muscle strength of the front knee at 60°/s (r = -0.651) and 180°/s (r = -0.651) and extension muscle strength of the rear knee at 300°/s (r = -0.433). CONCLUSION:These results suggest that swimmers with high muscle strength of the front knee at flexion can obtain a high horizontal acceleration in the acceleration phase, because they can quickly move the body forward. In addition, it is thought that this may shorten the take-off time

여자 높이뛰기에서 경기력 간 도움닫기와 발구름 동작의 운동역학적 분석

Objective : The purpose of this study was to find some kinetic variable’s relationships between personal records and low records in female high jump. Methods : Collected data of the subjects(N=8, ages: 25.5±1.85, height: 173±5.83, mass: 54.75±6.36 personal record: 1.71±0.04, low record: 162.±0.03) were used for the last three strides and take-off phase. Five video cameras set in 30frames/s were used for recording. After digitizing motion, the Direct Linear Transformation(DLT) technique was employed to obtain 3-D position coordinates. The kinematic and kinetic factors of distance, velocity, angle, impulse, jerk variables were calculated. A paired t-test was applied for the difference of variables between personal records and lower records and for correlation with performances and variables. The significance level was accepted at p<.05. Results : There was no relationship between pattern of stride and performance. However, rate of change of velocity was related with cental of mass height(CMH) at peak point(PP). Knee, hip, backward lean, foot plant, approach and take off angle showed no difference between best record and low record. Vertical impulse momentum also showed no difference between performances. Conclusion : According to a t-test result, there were significant differences in CMH at PP and jerk at touch down between best record and low record.

VLBI 안테나와 모바일폰 카메라를 활용한 근접수치사진측량의 캘리브레이션 초기값 결정에 따른 3차원 정확도 분석

본 논문에서는 세종시 우주측지관측센터에 위치한 VLBI 안테나를 대상으로 모바일폰 카메라의 캘리브레이션을 수행하고, 촬영된 스테레오 영상으로부터 3차원 위치좌표를 산출하였다. 모바일폰에 탑재된 카메라의 캘리브레이션을 위한 초기값으로 DLT방법과 상용 수치사진측량시스템인 PhotoModeler <TEX>$Scanner^{(R)}$</TEX> ver. 6.0을 활용하였다. DLT와 PhotoModeler방법으로 산출한 표정결과를 초기값으로 사용하여 광속조정을 통해 카메라 내 외부 표정요소를 계산하고, 두 결과의 정확도를 비교하였다. 두 가지 방법으로 산출한 표정결과는 상당한 편차가 발생하지만, 비선형의 공선조건식을 이용한 광속조정계산으로 두 가지 방법의 최종 표정결과가 거의 일치함을 알 수 있었다. 또한, 두 가지 방법으로 결정된 카메라 내 외부 표정요소들을 이용하여 VLBI 안테나 특징점에 대한 3차원 좌표를 계산하고 토탈스테이션을 통해 측정된 기준좌표들과 비교하였다. 그 결과, 두 가지 방법 모두 표준편차가 <TEX>$X=0.004{\pm}0.010m$</TEX>, <TEX>$Y=0.001{\pm}0.015m$</TEX>, <TEX>$Z=0.009{\pm}0.017m$</TEX>로서, cm급의 높은 정확도를 나타내었다. 이러한 결과를 통해 정밀 사진측량의 목적이 아닌 허용오차의 범위가 상대적으로 큰 다양한 사진측량 분야에 모바일폰 카메라를 활용할 수 있을 것이라 판단된다. This study had been aimed to conduct the camera calibration on VLBI antenna in the Space Geodetic Observation Center of Sejong City with a low-cost digital camera, which embedded in a mobile phone to determine the three-dimension position coordinates of the VLBI antenna, based on stereo images. The initial values for the camera calibration have been obtained by utilizing the Direct Linear Transformation algorithm and the commercial digital photogrammetry system, PhotoModeler <TEX>$Scanner^{(R)}$</TEX> ver. 6.0, respectively. The accuracy of camera calibration results was compared with that the camera calibration results, acquired by a bundle adjustment with nonlinear collinearity condition equation. Although two methods showed significant differences in the initial value, the final calibration demonstrated the consistent results whichever methods had been performed for obtaining the initial value. Furthermore, those three-dimensional coordinates of feature points of the VLBI antenna were respectively calculated using the camera calibration by the two methods to be compared with the reference coordinates obtained from a total station. In fact, both methods have resulted out a same standard deviation of <TEX>$X=0.004{\pm}0.010m$</TEX>, <TEX>$Y=0.001{\pm}0.015m$</TEX>, <TEX>$Z=0.009{\pm}0.017m$</TEX>, that of showing a high degree of accuracy in centimeters. From the result, we can conclude that a mobile phone camera opens up the way for a variety of image processing studies, such as 3D reconstruction from images captured.

Kinematic analysis of video-captured falls experienced by older adults in long-term care

Falls cause 95% of hip and wrist fractures and 60% of head injuries in older adults. Risk for such injuries depends in part on velocity at contact, and the time available during the fall to generate protective responses. However, we have no information on the impact velocities and durations of falls in older adults. We addressed this barrier through kinematic analysis of 25 real-life falls (experienced by 23 individuals of mean age 80 years (SD=9.8)) captured on video in two long-term facilities.All 25 falls involved impact to the pelvis, 12 involved head impact, and 21 involved hand impact. We determined time-varying positions by digitizing each video, using direct linear transformations calibrated for each fall, and impact velocities through differentiation.The vertical impact velocity averaged 2.14m/s (SD=0.63) for the pelvis, 2.91m/s (SD=0.86) for the head, and 2.87m/s (SD=1.60) for the hand. These values are 38%, 28%, and 4% lower, respectively, than predictions from an inverted pendulum model. Furthermore, the average pelvis impact velocity was 16% lower than values reported previously for young individuals in laboratory falling experiments. The average fall duration was 1271ms (SD=648) from the initiation of imbalance to pelvis impact, and 583ms (SD=255) from the start of descent to pelvis impact.These first measures of the kinematics of falls in older adults can inform the design and testing of fall injury prevention interventions (e.g., hip protectors, helmets, and flooring).

Direct Linear Transformation from Comparator Coordinates into Object Space Coordinates in Close-Range Photogrammetry

The January 8-9, 2015 Frozen Uas Tour Blows Into Grand Forks, North Dakota A method for photogrammetric data reduction without the necessity for neither fiducial marks nor initial approximations for inner and outer orientation parameters of the camera has been developed. This approach is particularly suitable for reduction of data from non-metric photography, but has also distinct advantages in its application to metric photography. Preliminary fictitious data tests indicate that the approach is promising. Experiments with real data are underway.

Automatic Fusion of Hyperspectral Images and Laser Scans Using Feature Points

Automatic fusion of different kinds of image datasets is so intractable with diverse imaging principle. This paper presents a novel method for automatic fusion of two different images: 2D hyperspectral images acquired with a hyperspectral camera and 3D laser scans obtained with a laser scanner, without any other sensor. Only a few corresponding feature points are used, which are automatically extracted from a scene viewed by the two sensors. Extraction method of feature points relies on SURF algorithm and camera model, which can convert a 3D laser scan into a 2D laser image with the intensity of the pixels defined by the attributes in the laser scan. Moreover, Collinearity Equation and Direct Linear Transformation are used to create the initial corresponding relationship of the two images. Adjustment is also used to create corrected values to eliminate errors. The experimental result shows that this method is successfully validated with images collected by a hyperspectral camera and a laser scanner.

C-18 ボールの軌道からみたバスケットボールフリースローの投射方策に関する研究(投げ)

The purpose of this study was to elucidate strategy for accurate throw by focusing on trajectory of free throw in basketball. The subjects were the six skilled basketball players belonging to a university basketball club and the recreational basketball player. The subjects were required to sink a free throw. The behavior of the thrown ball was recorded by four normal-speed video cameras placed beside the shooter and analyzed using the three-dimensional direct linear transformation method. The results were as follows: 1) Initial velocity ranged 0.2 to 0.6 m/s, and release angle ranged 3 to 9 degrees. This result differed from previous research. Then, it is necessary to consider including not only initial velocity and release angle, but also release point. 2) All subjects tended to change release point forward as the distance to the ring increased. In order to increase initial velocity, it is thought to push the ball longer and carry the ball in a straight line.

Reconstruction Accuracy Assessment of Surface and Underwater 3D Motion Analysis: A New Approach.

This study assessed accuracy of surface and underwater 3D reconstruction of a calibration volume with and without homography. A calibration volume (6000 × 2000 × 2500 mm) with 236 markers (64 above and 88 underwater control points—with 8 common points at water surface—and 92 validation points) was positioned on a 25 m swimming pool and recorded with two surface and four underwater cameras. Planar homography estimation for each calibration plane was computed to perform image rectification. Direct linear transformation algorithm for 3D reconstruction was applied, using 1600000 different combinations of 32 and 44 points out of the 64 and 88 control points for surface and underwater markers (resp.). Root Mean Square (RMS) error with homography of control and validations points was lower than without it for surface and underwater cameras (P ≤ 0.03). With homography, RMS errors of control and validation points were similar between surface and underwater cameras (P ≥ 0.47). Without homography, RMS error of control points was greater for underwater than surface cameras (P ≤ 0.04) and the opposite was observed for validation points (P ≤ 0.04). It is recommended that future studies using 3D reconstruction should include homography to improve swimming movement analysis accuracy.

6DOF Simulation of a Floating Structure Model Using a Single Video

This paper purposes on stimulating the dynamic behavior of a floating structure model with the image processing and the close-range photogrammetry, instead of the contact sensors. Previously, the movement of structures was presented by the exterior orientation estimation from a single camera following the space resection. The inverse resection yields to 6 orientation parameters of the floating structure, with respect to the camera coordinates system. The single camera solution of interest in applications is characterized by the restriction in terms of costs, unfavorable observation conditions, or synchronization demands when using multiple cameras. This paper discusses the theoretical determinations of camera exterior orientation by using the least squares adjustment, applied of the values from the DLT (Direct Linear Transformation) and the photogrammetric resection. This proposed method is applied to monitor motions of a floating model. The results of 6DOF (Six Degrees of Freedom) from the inverse resection were signified that applying appropriate initial values from DLT in the least square adjustment is effective in obtaining precise exterior orientation parameters. Therefore, the proposed method can be concluded as an efficient solution to simulate movements of the floating structure.

Texture reconstruction of 3D sculpture using non-rigid transformation

Abstract Sculptures, one of the most important forms of cultural heritage, exist in numerous temples, towers and grottoes. The current generation of high precision 3D digital sculpture models is a primary reality-based modeling tool for digital documentation, archaeological research, virtual restoration, and digital exhibition. However, high precision texture mapping remains a challenge in high fidelity digital reconstruction of complex sculptures, especially in the areas of rich geometrical details. This paper proposes a method to texture mapping one image onto the sculpture model to deal with the mapping problem problems caused by the image distortion and the model deformation. Firstly, we use a rigid pinhole camera model to project the image onto the geometric model to acquire primary texture mapping, where direct linear transformation is employed to estimate the elements of exterior orientation of the texture image. Then, we propose a non-rigid transformation model, called weighted thin-plate spline (W-TPS), discuss the theoretical derivation and the establishment of the W-TPS function, and apply this model to adjust the primary texture mapping results. The proposed method can precisely project the image onto the geometrical model both globally and locally. We conduct three experiments to verify the efficiency and feasibility of the proposed method using the sculptures in Dunhuang Mogao Grottoes in western China, which was inscribed on World Heritage List by UNESCO in 1987.

Rigorous geometric self-calibrating bundle adjustment for a dual fluoroscopic imaging system.

High-speed dual fluoroscopy is a noninvasive imaging technology for three-dimensional skeletal kinematics analysis that finds numerous biomechanical applications. Accurate reconstruction of bone translations and rotations from dual-fluoroscopic data requires accurate calibration of the imaging geometry and the many imaging distortions that corrupt the data. Direct linear transformation methods are commonly applied for performing calibration using a two-step process that suffers from a number of potential shortcomings including that each X-ray source and corresponding camera must be calibrated separately. Consequently, the true imaging set-up and the constraints it presents are not incorporated during calibration. A method to overcome such drawbacks is the single-step self-calibrating bundle adjustment method. This procedure, based on the collinearity principle augmented with imaging distortion models and geometric constraints, has been developed and is reported herein. Its efficacy is shown with a carefully controlled experiment comprising 300 image pairs with 48 507 image points. Application of all geometric constraints and a 31 parameter distortion model resulted in up to 91% improvement in terms of precision (model fit) and up to 71% improvement in terms of 3-D point reconstruction accuracy (0.3-0.4 mm). The accuracy of distance reconstruction was improved from 0.3±2.0 mm to 0.2 ±1.1 mm and angle reconstruction accuracy was improved from -0.03±0.55(°) to 0.01±0.06(°). Such positioning accuracy will allow for the accurate quantification of in vivo arthrokinematics crucial for skeletal biomechanics investigations.

The Effect of Ankle Taping to Restrict Plantar Flexion on Ball and Foot Velocity During an Instep Kick in Soccer.

Posterior ankle impingement syndrome is a common disorder in soccer players and ballet dancers. In soccer players, it is caused by the repetitive stress of ankle plantar flexion due to instep kicking. Protective ankle dorsiflexion taping is recommended with the belief that it prevents posterior ankle impingement. However, the relationship between ankle taping and ball-kicking performance remains unclear. To demonstrate the relationship between the restrictions of ankle taping and performance of an instep kick in soccer. Laboratory-based repeated-measures. University laboratory. 11 male university soccer players. The subjects' ankle plantar flexion was limited by taping. Four angles of planter flexion (0°, 15°, 30°, and without taping) were formed by gradation limitation. The subjects performed maximal instep kicks at each angle. The movements of the kicking legs and the ball were captured using 3 high-speed cameras at 200 Hz. The direct linear-transformation method was used to obtain 3-dimensional coordinates using a digitizing system. Passive ankle plantar-flexion angle, maximal plantar-flexion angle at ball impact, ball velocity, and foot velocity were measured. The data were compared among 4 conditions using repeated-measures ANOVA, and the correlations between ball velocity and foot velocity and between ball velocity and toe velocity were calculated. Ankle dorsiflexion taping could gradually limit both passive plantar flexion and plantar flexion at the impact. Furthermore, limitation of 0° and 15° reduced the ball velocity generated by instep kicks. Plantar-flexion-limiting taping at 30° has a potential to prevent posterior ankle impingement without decreasing the ball velocity generated by soccer instep kicks.

As-Projective-As-Possible Image Stitching with Moving DLT

The success of commercial image stitching tools often leads to the impression that image stitching is a "solved problem". The reality, however, is that many tools give unconvincing results when the input photos violate fairly restrictive imaging assumptions; the main two being that the photos correspond to views that differ purely by rotation, or that the imaged scene is effectively planar. Such assumptions underpin the usage of 2D projective transforms or homographies to align photos. In the hands of the casual user, such conditions are often violated, yielding misalignment artifacts or "ghosting" in the results. Accordingly, many existing image stitching tools depend critically on post-processing routines to conceal ghosting. In this paper, we propose a novel estimation technique called Moving Direct Linear Transformation (Moving DLT) that is able to tweak or fine-tune the projective warp to accommodate the deviations of the input data from the idealized conditions. This produces as-projective-as-possible image alignment that significantly reduces ghosting without compromising the geometric realism of perspective image stitching. Our technique thus lessens the dependency on potentially expensive postprocessing algorithms. In addition, we describe how multiple as-projective-as-possible warps can be simultaneously refined via bundle adjustment to accurately align multiple images for large panorama creation.