Bacakoglu, H., and M.S. Kamel, A three-step camera calibration method, Ieee Transactions On Instrumentation and Measurement, 46 (5), 1165-1172, 1997.

Camera calibration is a crucial problem for many industrial applications that incorporate visual sensing, In this paper, we compute the intrinsic and extrinsic calibration parameters in three steps, In the first step, the calibration parameters are approximated using the linear least-squares method, In the second step, we develop two alternative formulations to obtain an optimal rotation matrix from the calibration parameters computed in the first step, Further optimization of translational and perspective transformations is then performed based on the optimized rotation matrix, In the third step, a nonlinear optimization is performed to handle lens distortion, The solution of the nonlinear system not only minimizes the perspective transformation relations between the image points and the corresponding world coordinates, but also satisfies the orthonormality constraints on the rotational transformation, To assess the performance of our proposed method, the Euclidean norm of the error matrix between the calculated and the original 4 x 4 homogeneous transformation matrices is used as a basis for comparison with existing methods, Simulation results from applying the method show significant improvements both before and after the nonlinear optimization step.

Basu, A., Active Calibration of Cameras - Theory and Implementation, Ieee Transactions On Systems Man and Cybernetics, 25 (2), 256-265, 1995.

The problem of calibrating a camera has been widely addressed in the past. Almost all techniques described in the literature use a known calibrating pattern and a static camera. We introduce a novel technique, based on an active camera, which does not need any predefined patterns. All that is required is a scene with some strong and stable edges. Two alternative algorithms are presented and analysed-the second method is shown to be more robust to noise and useful in practical situations. Using our methods, an active camera can automatically calibrate itself. Experimental results are shown, demonstrating the validity of the algorithms.

Borghese, N.A., P. Cerveri, and G.C. Ferrigno, Statistical comparison of DLT versus ILSSC in the calibration of a photogrammetric stereo-system, Journal of Biomechanics, 30 (4), 409-413, 1997.

This paper compares the DLT and ILSSC approaches in the geometrical calibration of a photogrammetric stereo-system in terms of accuracy and speed. To come up with an unbiased quantitative evaluation of the accuracy of the algorithms, the concept of reliable estimate has been introduced: the statistical distribution of the accuracy is assessed over different calibration experiments performed with the same data but with different noise distribution and different test sets. Results show that in the simulations where the only error on the two-dimensional points was Gaussian, zero mean, and on real data which were corrected for distortions through polynomial or linear interpolation, the accuracy of the two methods was quite similar. DLT showed more accurate than ILSSC on simulated data with residual distortion errors and on real data which were not corrected for distortions. As far as speed is concerned, a fast triangulation algorithm is associated with ILSSC while the simultaneous solution of two pairs of DLT equations is associated to DLT. The first algorithm is much faster, requiring 113 flops per point versus 259 of DLT; the fast triangulation with DLT parameters does not achieve the same accuracy on the reconstructed three-dimensional position. Taken all together the results suggest that ILSSC can be theoretically considered the best approach to three-dimensional reconstruction, provided that distortions are corrected in advance. The statistical evaluation of the accuracy allows a fair judgement of the performances of the algorithms to be obtained, unbiased by particular distributions of measurement errors and test points. (C) 1997 Elsevier Science Ltd.

Chatterjee, C., V.P. Roychowdhury, and E.K.P. Chong, A nonlinear Gauss-Seidel algorithm for noncoplanar and coplanar camera calibration with convergence analysis, Computer Vision and Image Understanding, 67 (1), 58-80, 1997.

In this study, we discuss the nonlinear structure of the camera calibration problem and present new and provably convergent algorithms for noncoplanar and coplanar cases. From the perspective of optimization theory, we have included the following features in solving this nonlinear problem: (1) An initialization algorithm that computes an approximate solution as a starting value close to the global minimum. (2) A main estimation method that partitions the parameter space and uses a Gauss-Seidel optimization procedure for block components, For the noncoplanar case, the extrinsic and lens distortion parameters are computed by linear iterations or in closed form in each iteration, Nonlinear optimization is performed on a reduced parameter space of dimension three. For the coplanar case, the lens distortion parameters are computed by linear iterations. In both cases, the orthonormality condition of the camera vectors is satisfied. Thus, while performing nonlinear optimization over all parameters, we still retain many advantages of the linear methods, and in the process obtain an optimal solution. (3) A Lyapunov type convergence analysis is given for the algorithms. The structure of the objective function is analyzed in each iteration. In addition, for the coplanar case, we discuss new methods for obtaining starting estimates of image center and scale factor parameters. Furthermore, we consider lens distortion with radial, decentering, and thin prism distortion models. (C) 1997 Academic Press.

Chatterjee, C., and V.P. Roychowdhury, Algorithms for coplanar camera calibration, Machine Vision and Applications, 12 (2), 84-97, 2000.

Coplanar camera calibration is the process of determining the extrinsic and intrinsic camera parameters from a given set of image and world points, when the world points lie on a two- dimensional plane. Noncoplanar calibration, on the other hand, involves world points that do not lie on a plane. While optimal solutions for both the camera-calibration procedures can be obtained by solving a set of constrained nonlinear optimization problems, there are significant structural differences between the two formulations. We investigate the computational and algorithmic implications of such underlying differences, and provide a set of efficient algorithms that are specifically tailored for the coplanar case. More specifically, we offer the following: (1) four algorithms for coplanar calibration that use linear or iterative linear methods to solve the underlying nonlinear optimization problem, and produce sub-optimal solutions. These algorithms are motivated by their computational efficiency and are useful for real-time low-cost systems. (2) Two optimal solutions for coplanar calibration, including one novel non linear algorithm. A constraint for the optimal estimation of extrinsic parameters is also given. (3) A Lyapunov type convergence analysis for the new nonlinear algorithm. We test the validity and performance of the calibration procedures with both synthetic and real images. The results consistently show significant improvements over less complete camera models.

Crawford, A.M., and A.E. Hay, A simple system for laser-illuminated video imaging of sediment suspension and bed topography, Ieee Journal of Oceanic Engineering, 23 (1), 12-19, 1998.

A simple underwater video system has been developed for simultaneously imaging sediment suspension and monitoring bed profiles under waves and combined wave-current hows, This consists of a diode-laser-generated light plane and a a black- and-white underwater video camera, The laser light illuminates suspended material in section and also provides a bed profile at the bottom, Orthogonal laser/camera pairs are used to obtain both cross-shore and alongshore views. During deployments, the system has been augmented by acoustic backscatter devices for measurement of sediment concentration, As with all video techniques, visibility is a limiting factor, but where turbidity is low to moderate, the results are encouraging, Results on cross-shore and alongshore bed elevation variations and suspension event scales obtained with the video/laser system are presented for two experiments: one at the National Research Council wave Research Flume in Ottawa, Canada, and the other in the field at Queensland Beach, N.S., Canada.

Eleveld, M.A., S.T. Blok, and J.P.G. Bakx, Deriving relief of a coastal landscape with aerial video data, International Journal of Remote Sensing, 21 (1), 189-195, 2000.

Coastal geomorphological research benefits from visualization of heights. Videography, a cheap, simple and flexible airborne remote sensing technique, was used for derivation of relief. A hand-held Hi 8 camera and a small aeroplane were used to collect video data of a 1300 m x 320 m strip of beach and foredune area on Ameland (the Netherlands). Simultaneously, the ground control points (GCPs) were measured with laser electronic distance measurement (EDM) equipment. A series of overlapping frames was grabbed, contrast-stretched and corrected for interlacing effects. The resulting images were processed with software that has some photogrammetric capabilities, R-WEL's Desktop Mapping System (DMS). The images and the positions of the GCPs enabled computation of the camera orientation, and allowed for image rectification and stereo correlation. Stereo pairs form the basis for anaglyphs, which give a perception of height. In addition, the parallax in the stereo pairs allows a derivation of quantitative height information. Some of the derived height values are, however, incorrect. This was due to inaccuracies in the camera technology and the use of photogrammetric software that was not designed principally to process video imagery.

Ethrog, U., Non-Metric Camera Calibration and Photo Orientation Using Parallel and Perpendicular Lines of the Photographed Objects, Photogrammetria, 39 (1), 13-22, 1984.


Foote, M., and D. Horn, Video measurement of swash zone hydrodynamics, Geomorphology, 29 (1-2), 59-76, 1999.

A new technique for recording two-dimensional uprush and backwash depth profiles using standard analogue camcorder technology is introduced. This technique has the potential to provide low cost, high frequency, high resolution measurements of individual swash events. Analogue to digital data conversion using multimedia software is discussed, as is the derivation of metric data via image processing and geographical information systems techniques. A series of field and laboratory experiments are described which provided an opportunity to refine and test the technique. Data from the laboratory video record are compared against measurements from standard surface piercing resistance type wave gauges, and an assessment made of the next steps required for the enhancement of the technique. The comparison between video and probe data indicates that the technique shows promise as a means of deriving two-dimensional profiles of swash lens; however, further development and testing are necessary. (C) 1999 Elsevier Science B.V. All rights reserved.

Giakos, G.C., Key paradigms of emerging imaging sensor technologies, Ieee Transactions On Instrumentation and Measurement, 47 (6), 1406-1414, 1998.

In this paper, key paradigms of emerging imaging technologies from different technological areas, are presented. Examples of transfer, utilization, and exchange of the imaging technology are offered and discussed. These phenomena, will create advanced solutions for potential development in different areas of science and technology. Overall, new imaging technologies will merge and are expected to play an ever-expanding role in the civilian and military applications of the next century.

Heikkila, J., Geometric camera calibration using circular control points, Ieee Transactions On Pattern Analysis and Machine Intelligence, 22 (10), 1066-1077, 2000.

Modern CCD cameras are usually capable of a spatial accuracy greater than 1/50 of the pixel size. However, such accuracy is not easily attained due to various error sources that can affect the image formation process. Current calibration methods typically assume that the observations are unbiased, the only error is the zero-mean independent and identically distributed random noise in the observed image coordinates, and the camera model completely explains the mapping between the 3D coordinates and the image coordinates. in general, these conditions are not met, causing the calibration results to be less accurate than expected. In this paper, a calibration procedure for precise 3D computer vision applications is described. It introduces bias correction for circular control points and a nonrecursive method for reversing the distortion model. The accuracy analysis is presented and the error sources that can reduce the theoretical accuracy are discussed. The tests with synthetic images indicate improvements in the calibration results in limited error conditions. In real images, the suppression of external error sources becomes a prerequisite for successful calibration.

Hill, P.S., J.P. Syvitski, E.A. Cowan, and R.D. Powell, In situ observations of floc settling velocities in Glacier Bay, Alaska, Marine Geology, 145 (1-2), 85-94, 1998.

In situ floc settling velocities and diameters of particles ranging in size from 0.63 to 5.05 mm equivalent circular diameter were measured under a buoyant discharge plume by deploying a bottom-tripod-mounted Floc Camera Assembly (FCA) in Tarr Inlet, Glacier Bay, Alaska. These observations were used to estimate floc effective densities. Three results emerge from this work. First, fits of settling velocity and effective density to diameter are consistent with expressions published for other environments, suggesting that common controls on floc size and settling velocity operate across diverse marine environments. Second, the raw data show considerable scatter, with upper and lower 95% prediction intervals on settling velocity and excess density differing by about a factor of 7. Analysis of sources of error suggests that the variability is caused by differences in component-grain composition among flocs and turbulent stirring within the stilling box. Third, bin-averaged effective densities and settling velocities are highly correlated with diameter. Thus, while it is not possible, based on diameter, to predict accurately the settling velocity of a single floc, it is possible to estimate the mean settling velocity of a population of like-sized flocs. (C) 1998 Elsevier Science B.V.

Holland, K.T., and R.A. Holman, The Statistical Distribution of Swash Maxima On Natural Beaches, Journal of Geophysical Research-Oceans, 98 (C6), 10271-10278, 1993.

Cartwright and Longuet-Higgins (1956) describe the statistical distribution of maxima that would result from the linear superposition of random, Gaussian waves. The distribution function depends solely upon the relative width of the power spectrum and root-mean-square value of the process time series. Runup field data from three experiments are presented to determine the extent to which the distribution of swash maxima can be approximated using the Cartwright and Longuet-Higgins probability density function. The model is found to be satisfactory for describing various distribution statistics including the average maxima, the proportion of negative maxima, and the elevation at which one third of the swash maxima are exceeded. However, systematic discrepancies that scale as a function of time series skewness are observed in the statistics describing the upper tail of the distributions. Although we conclude that the linear model is incapable of delineating these apparent nonlinearities in the swash time series, the extent of the deviation can be estimated empirically for the purpose of constraining nonlinear models and nearshore engineering design.

Holland, K.T., and R.A. Holman, Video estimation of foreshore topography using trinocular stereo, Journal of Coastal Research, 13 (1), 81-87, 1997.

Previous researchers have shown that topographic response to swash processes is typically rapid and occasionally substantial. However, the methods used to document these fluctuations were often labor intensive and usually resulted in only a few estimates at a limited number of survey locations. We present an automated technique for the detection of small- and large-scale variations in foreshore topography that has both high spatial and temporal resolution. This technique utilizes trinocular (three view) stereogrammetry to recover topographic information from a set of synchronous, overlapping video images. The foreshore topography is mapped by following the movement of the sharply defined foamy runup edge that visibly contrasts with the darker, underlying, saturated beachface. Under field test conditions, the video method has a vertical accuracy of between 1 and 3 cm, comparable to that of traditional surveying methods and to theoretical expectations. The advantages of this new technique are that the topography estimates are extremely dense, on the order of thousands of estimates within a 100 m(2) region, that estimates can be made on a wave by wave basis, and that sampling requires minimal manpower. This method may prove useful in the study of rapid foreshore sediment transport dynamics, such as the formation of beach cusps.

Holland, K.T., R.A. Holman, T.C. Lippmann, J. Stanley, and N. Plant, Practical use of video imagery in nearshore oceanographic field studies, IEEE JOURNAL OF OCEANIC ENGINEERING, 22 (1), 81-92, 1997.


Holland, K.T., Beach cusp formation and spacings at Duck, USA, Continental Shelf Research, 18 (10), 1081-1098, 1998.

Approximately nine years of daily video images from Duck, NC, USA, were analyzed to determine the timing of cusp formation in relation to environmental forcing and the distances separating consecutive cusp horns. 57 independent cusp events (defined as transitions from visibly smooth to cuspate topography) were observed with most of the cusps forming after storms. The temporal lag between the peak in storm intensity and cusp development was typically 3 days. Approximately half of the cusp events had formations predicted by an empirical threshold relating storm presence, breaker angle, and beach reflectivity. This threshold and other statistical observations suggest that Duck cusps form as energy conditions become more reflective, as the offshore wave angle approaches normal incidence and as the directional spread of the incident wave field becomes narrower. The standard deviation of the observed spacings relative to the mean spacing for each event was around 15% with the range in spacings for each event being typically less than half the event's mean cusp width. There were no strong statistical relationships between mean cusp spacings and environmental parameters (such as swash excursion lengths). Copyright (C) 1998 Elsevier Science Ltd. All rights reserved.

Ito, M., and A. Ishii, A Noniterative Procedure For Rapid and Precise Camera Calibration, Pattern Recognition, 27 (2), 301-310, 1994.

A simple, rapid and precise camera calibration method is described by which the position and direction of a camera are calculated without using conventional iterative processes. Error parameters are defined as differences in the values of calculated intrinsic parameters from their fixed ones. Camera parameters are adjusted non-iteratively so that the error parameters become sufficiently small. The rotation matrix orthogonality constraints are completely preserved. Experimental error estimation using an actual mark image shows that the position error is less than 0.1 mm and that the direction error is less than 5 x 10(-4) rad, which correspond to relative errors of 5 x 10(-5) and 1 x 10(-4), respectively. These calibration procedures from the image acquisition to the result output are completed automatically within 6 s using a VAX11/780 (1 MIPS)

Izaguirre, A., P. Pu, and J. Summers, A New Development in Camera Calibration - Calibrating a Pair of Mobile Cameras, International Journal of Robotics Research, 6 (3), 104-116, 1987.


Kang, S.B., and R. Weiss, Characterization of errors in compositing panoramic images, Computer Vision and Image Understanding, 73 (2), 269-280, 1999.

A panoramic image has a 360 degrees horizontal field of view and it can provide the viewer the impression of being immersed in the scene, A panorama is created by first taking a sequence of images while rotating the camera about a vertical axis. These images are then projected onto a cylindrical surface before being seamlessly composited, The cross-sectional circumference of the cylindrical panorama is called the compositing length, This work characterizes the error in compositing panoramic images due to errors in some of the intrinsic parameters, The intrinsic camera parameters that are considered are the camera focal length and the radial distortion coefficient. We show that the error in the compositing length is more sensitive to the error in the camera focal length. Especially important is the discovery that the relative error in compositing length is always smaller than the relative error in the focal length. This means that the error in focal length can be corrected by iteratively using the composited length to compute a new and more correct focal length, This compositing approach to camera calibration has the advantages of not requiring both feature detection and separate prior calibration, (C) 1999 Academic Press.

Kingston, K.S., B.G. Ruessink, I.M.J. van Enckevort, and M.A. Davidson, Artificial neural network correction of remotely sensed sandbar location, Marine Geology, 169 (1-2), 137-160, 2000.

This contribution details an accurate method for the remote sensing of submerged sandbar location through the application of an artificial neural network to video data. Lippmann and Holman (Lippmann T.C., Holman, R.A., 1989. Quantification of sandbar morphology: a video technique based on wave dissipation. J. Geophys. Res. 94(C1), 995-1011) have shown that the intensity maxima seen in time-averaged video images of the nearshore zone provide a reasonable proxy for sandbar location. However, recent studies have indicated that there may be a large deviation (up to 30-40 m) between the measured bar position and predictions based on the intensity maximum in the cross-shore direction. These deviations occur largely due to modulations of the breakpoint by the tide, and variations in the incident wave energy. This paper utilises an artificial neural network to model the cross-shore movement in the intensity maximum due to tides and waves. The resulting signal is then removed from the Video estimates to provide an accurate estimation of the sand bar location. Unique field data sets collected as part of the Coast3D experiment are used to train and test the neural network model. These data consist of simultaneous measurements of the nearshore bathymetry and video imagery of the double bar system at Egmond aan Zee, the Netherlands. The resulting model yields accurate estimates of sandbar location with residual errors of less than 5 m for the outer bar and less than 10 m for the inner bar. The artificial neural network model is utilised to extend the bathymetric data set for Egmond aan Zee for times when wave conditions were too large to allow physical measurement. (C) 2000 Elsevier Science B.V. All rights reserved.

Kocak, D.M., N.D. Lobo, and E.A. Widder, Computer vision techniques for quantifying, tracking, and identifying bioluminescent plankton, Ieee Journal of Oceanic Engineering, 24 (1), 81-95, 1999.

This paper applies computer vision techniques to underwater video images of bioluminescent biota for quantifying, tracking, and identification. Active contour models are adapted for computerized image segmentation, labeling, tracking, and mapping of the bioluminescent plankton recorded by low-light- level video techniques. The system automatically identifies luminous events and extracts features such as duration, size, and coordinates of the point of impact, and uses this information to taxonomically classify the plankton species. This automatic classification can aid oceanographic researchers in characterizing the in situ spatial and temporal relationships of these organisms in their underwater environment. Experiments with real oceanographic data are reported. The results indicate that the approach yields performance comparable to human expert level capability. Furthermore, because the described technique has the potential to rapidly process vast quantities of video data, it may prove valuable for other similar applications.

Lenz, R.K., and R.Y. Tsai, Techniques For Calibration of the Scale Factor and Image Center For High-Accuracy 3-D Machine Vision Metrology, Ieee Transactions On Pattern Analysis and Machine Intelligence, 10 (5), 713-720, 1988.


Lynch, M.B., C.H. Dagli, and M. Vallenki, The use of feedforward neural networks for machine vision calibration, International Journal of Production Economics, 60-1, 479-489, 1999.

Machine vision calibration is an important step to obtaining usable measurements in inspection and automation operations. Conventional calibration techniques require the development of elaborate mathematical models and have prior knowledge of many parameters. Creating a suitable model and obtaining reasonable values for some calibration parameters is often difficult and error prone. In this article, a neural network approach is presented as an indirect non-linear optimization method to machine vision calibration. This approach does not require a mathematical model be developed nor any prior knowledge about the setup or calibration parameters. A universal calibration approach is developed and utilized in various applications. The applications are discussed and results from experiments are presented. It is shown that a neural network approach can provide an accurate machine vision calibration. (C) 1999 Published by Elsevier Science B.V. All rights reserved.

Naftel, A.J., and J.C. Boot, An Iterative Linear Transformation Algorithm For Solution of the Collinearity Equations, Photogrammetric Engineering and Remote Sensing, 57 (7), 913-919, 1991.

A modification of the direct linear transformation (DLT) technique for solving the collinearity equations is proposed. The iterative linear transformation (ILT) procedure involves incorporating photo-coordinate observations of non-control points in the least-squares adjustment leading to the determination of the calibration parameters. The reconstructed object-space coordinates so obtained in a subsequent adjustment are then treated as "approximate" control and the computation is repeated until convergence is obtained. In a study utilizing check-point control, the algorithm reduced the average root-mean-square (RMS) error in the conventional DLT solution from 3.3mm to 0.9mm in 16 iterations. This equates to a spatial resolution of 0.047 percent (about 1 part in 2130) in object-space dimensions. Applications to two test surfaces requiring reconstruction of a much larger number of spatial points yielded similar reductions in average RMS errors in 50 and 140 iterations, respectively.

Navab, N., and O.D. Faugeras, The critical sets of lines for camera displacement estimation: A mixed euclidean-projective and constructive approach, International Journal of Computer Vision, 23 (1), 17-44, 1997.

The problem of the recovery of the motion, and the structure from motion is relevant to many computer vision applications. Many algorithms have been proposed to solve this problem. Some of these use line correspondences. For obvious practical reasons, it is important to study the limitation of such algorithms. In this paper, we are concerned with the problem of recovering the relative displacements of a camera by using line matches in three views. In particular, we want to know whether there exist sets of 3D lines such that no matter how many lines we observe there will always be several solutions to the relative displacement estimation problem. Such sets of lines may be called critical in the sense that they defeat the corresponding algorithm. This question has been studied in detail in the case of point matches by early-century Austrian photogrammeters and, independently, in the mid-seventies and early-eighties by computer vision scientists. The answer lies in the idea of a critical surface. The case of lines has been much less studied. Recently, Buchanan (1992a, 1992b) provided a first analysis of the problem in which he gave a positive answer: there exist critical sets of lines and they are pretty big (infinity(2) lines). In general these sets are algorithm dependent, for example the critical set of lines for the Liu- Huang algorithm introduced in (Buchanan, 1992a), but Buchanan has shown that there is a critical set that defeats any algorithm. This paper is an attempt to build on his work and extend it in several directions. First, we cast his purely projective analysis in a more euclidean framework better suited to applications and, currently, more familiar to most of the computer vision community. Second, we clearly relate his critical set to those of previously published algorithms, in particular (Liu and Huang, 1988a, 1988b). Third, we provide an effective, i.e., computational, approach for describing these critical sets in terms of simple geometric properties. This has allowed us to scrutinize the structure of the critical sets which we found to be both intricate and beautiful.

Okamoto, A., The Model Construction Problem Using the Collinearity Condition, Photogrammetric Engineering and Remote Sensing, 50 (6), 705-711, 1984.


Park, K.S., and C.J. Lim, An efficient camera calibration method for vision-based head tracking, International Journal of Human-Computer Studies, 52 (5), 879-898, 2000.

The aim of this study is to develop and evaluate an efficient camera calibration method for vision-based head tracking. Tracking head movements is important in the design of an eye- controlled human/computer interface. A vision-based head tracking system is proposed to allow the user's head movements in the design of the eye-controlled human/computer interface. We propose an efficient camera calibration method to track the three-dimensional position and orientation of the user's head accurately. We also evaluate the performance of the proposed method and the influence of the configuration of calibration points on the performance. The experimental error analysis results showed that the proposed method can provide more accurate and stable pose (i.e. position and orientation) of the camera than the direct linear transformation method which has been used in camera calibration. The results for this study can be applied to the tracking of head movements related to the eye-controlled human/computer interface and the virtual reality technology. (C) 2000 Academic Press.

Plant, N.G., and R.A. Holman, Intertidal beach profile estimation using video images, Marine Geology, 140 (1-2), 1-24, 1997.

In this paper, we present a technique suitable for measurement of intertidal bathymetry over a broad range of length scales (10(1) to 10(3) m) and time scales (days to decades). A series of time-averaged images of the swash zone are used to map contour lines of the beach surface. In each image, contours are identified using bands of maximum brightness associated with breaking waves at the shoreline. By mapping the location of these bands in a sequence of images collected over one tidal cycle, contour maps of the intertidal bathymetry are generated. We expect this technique to work best (smallest absolute error) under waves which are nearly reflective at the shoreline, but break enough to be observed visually. This is typical of a barred beach since the wave height at the shoreline is limited by wave breaking over the bar crest. The ability of the measurements made with this technique to resolve actual beach elevation variation depends on the ratio of the measurement error variance to the true beach elevation variance. Thus, large measurement errors may be compensated by either large tidal ranges or large temporal changes of the beach itself. In a comparison to bathymetry surveyed using a Differential Global Positioning System (DGPS) during the Duck94 experiment, in Duck, N.C., the image-based elevation estimates were well correlated with the actual bathymetry. The deviations (image- based vs. DGPS measurements) may be partially attributed to effects scaled by wave height at the shoreline, wave-induced setup, and wave height saturation over the sand bar. In particular, setup was important during dissipative conditions. The rms deviation (vertical) between the DGPS and image-based bathymetry was reduced from 0.24 m to 0.06 m by correcting for the systematic deviations due to variations in setup and wave height saturation. Further improvement of the elevation estimates resulted from parameterizing the actual bathymetry with a simple plane beach surface, which reduced random (or unresolvable) measurement errors. This led to estimates of the beach slope that were accurate to within 10% of the actual slope and estimates of the cross-shore location of the mean sea level line accurate to about 0.50 m. (C) 1997 Elsevier Science B.V.

Prescott, B., and G.F. McLean, Line-based correction of radial lens distortion, Graphical Models and Image Processing, 59 (1), 39-47, 1997.

A method for determining the radial distortion parameters of a camera is presented. The technique is based on the analysis of distorted images of straight lines and does not require the determination of point correspondence between a scene and an image of that scene. The method is described in detail, including information on the line detection method and the optimization procedure used to estimate the distortion parameters. Quantitative and qualitative experimental results using both synthetic and real image data show that the technique is effective. (C) 1997 Academic Press.

Shah, S., and J.K. Aggarwal, Intrinsic parameter calibration procedure for a (high- distortion) fish-eye lens camera with distortion model and accuracy estimation, Pattern Recognition, 29 (11), 1775-1788, 1996.

This paper presents a calibration procedure for a fish-eye lens (a high-distortion lens) mounted on a CCD TV camera. The method is designed to account for the differences in images acquired via a distortion-free lens camera setup and the images obtained by a fish-eye lens camera. The calibration procedure essentially defines a mapping between points in the world coordinate system and their corresponding point locations in the image plane. This step is important for applications in computer vision which involve quantitative measurements. The objective of this mapping is to estimate the internal parameters of the camera, including the effective focal length, one-pixel width on the image plane, image distortion center, and distortion coefficients. The number of parameters to be calibrated is reduced by using a calibration pattern with equally spaced dots and assuming a pin-hole model camera behavior for the image center, thus assuming negligible distortion at the image distortion center. Our method employs a non-linear transformation between points in the world coordinate system and their corresponding location on the image plane. A Lagrangian minimization method is used to determine the coefficients of the transformation. The validity and effectiveness of our calibration and distortion correction procedure are confirmed by application of this procedure on real images. Copyright (C) 1996 Pattern Recognition Society.

Shen, T.S., J.B. Huang, and C.H. Menq, Multiple-sensor integration for rapid and high-precision coordinate metrology, Ieee-Asme Transactions On Mechatronics, 5 (2), 110-121, 2000.

In this paper, the development of a multiple-sensor coordinate measuring system is introduced and its applications to automated part localization and rapid surface digitization are experimentally demonstrated. The developed multiple-sensor coordinate measuring machine (CMM) is characterized by an integrated use of a high-precision CMM equipped with a motorized touch probe, and a three-dimensional (3-D) active vision system, advanced computational software, and the associated electronics. The 3-D active vision system consists of three components: a charge-coupled device camera, a digital light professing (DLP) projector, and a personal computer with an image processing board. The DLP projector is based on the innovative digital micro-mirror device, which can be controlled by the personal computer to project various structured light patterns. With the flexibility of the DLP projector, the orientation, range, density, and colors of the structured light patterns are programmable and adaptable to different needs. Consequently, the active vision system is capable of digitizing surface coordinates of objects having multiple features. With the coordinate data acquired using the 3-D active vision system, intelligent feature recognition algorithms can be applied to extract the global surface information of the object. The obtained information can be subsequently used to automatically guide the touch probe for rapid coordinate data acquisition and to strategically control the coordinate measuring machine for high precision sampling of critical surface area. In this paper, the information automation for the multiple-sensor integrated system is demonstrated in part localization when computer-aided design models are available, and rapid and high-precision surface digitization in reverse engineering. By integrating the developed technology with the state of the art equipment, a highly automated high-speed high- precision 3-D coordinate acquisition system can be developed. It has potential applications in a whole spectrum of manufacturing problems with a major impact on metrology, inspection, and reverse engineering.

Shih, S.W., Y.P. Hung, and W.S. Lin, Accurate Linear Technique For Camera Calibration Considering Lens Distortion By Solving an Eigenvalue Problem, Optical Engineering, 32 (1), 138-149, 1993.

A new technique for calibrating a camera with high accuracy and low computational cost is proposed. The geometric camera parameters considered include camera position, orientation, focal length, radial lens distortion, pixel size, and optical axis piercing point. With this method, the camera parameters to be estimated are divided into two parts: the radial lens distortion coefficient kappa and a composite parameter vector c composed of all the above-mentioned geometric camera parameters other than kappa. Instead of using nonlinear optimization techniques, the estimation Of kappa is transformed into an eigenvalue problem of an 8 x 8 matrix. The method is fast because it requires only linear computation; it is accurate because the effect of the lens distortion is considered and because all the information contained in the calibration points is used. Computer simulations and real experiments show that the calibration method can achieve an accuracy of 1 part in 10,000 in 3-D measurement, which is better than that of the well-known method proposed by R. Y. Tsai.

Shih, S.W., Y.P. Hung, and W.S. Lin, When Should We Consider Lens Distortion in Camera Calibration, Pattern Recognition, 28 (3), 447-461, 1995.

This work investigates the effect of neglecting lens distortion in camera calibration, and presents a theoretical analysis of the calibration accuracy. We derived an approximate upper envelope for the 2D prediction error, which is a function of a few factors including the number of calibration points, the observation error of 2D image points, the radial lens distortion coefficient, the image size and resolution. This error envelope provides a guide line for selecting both a proper camera calibration configuration and an appropriate camera model while satisfying the desired accuracy. Experimental results from both computer simulations and real experiments are included in this paper.

Shih, S.W., Y.P. Hung, and W.S. Lin, Calibration of an active binocular head, Ieee Transactions On Systems Man and Cybernetics Part a-Systems and Humans, 28 (4), 426-442, 1998.

In this paper, we shelf how an active binocular head, the IIS head, can be easily calibrated with very high accuracy. Our calibration method can also be applied to many other binocular heads. In addition to the proposal and demonstration of a four- stage calibration process, there are three major contributions in this paper. First, we propose a motorized-focus lens (MFL) camera model which assumes constant nominal extrinsic parameters. The advantage of having constant extrinsic parameters is to having a simple head/eye relation, Second, a calibration method for the MFL camera model is proposed in this paper, which separates estimation of the image center and effective focal length from estimation of the camera orientation and position. This separation has been proved to be crucial; otherwise, estimates of camera parameters would be very noise-sensitive. Thirdly, we show that, once the parameters of the MFL camera model is calibrated, a nonlinear recursive least-square estimator can be used to refine all the 35 kinematic parameters. Real experiments have shown that the proposed method can achieve accuracy of one pixel prediction error and 0.2 pixel epipolar error, even when all the joints, including the left and right focus motors, are moved simultaneously. This accuracy is good enough for many three- dimensional (3-D) vision applications, such as 3-D navigation, 3-D object tracking, and even 3-D reconstruction.

Sidahmed, M.A., and M.T. Boraie, Dual Camera Calibration For 3-D Machine Vision Metrology, Ieee Transactions On Instrumentation and Measurement, 39 (3), 512-516, 1990.


Stockdon, H.F., and R.A. Holman, Estimation of wave phase speed and nearshore bathymetry from video imagery, Journal of Geophysical Research-Oceans, 105 (C9), 22015-22033, 2000.

A new remote sensing technique based on video image processing has been developed for the estimation of nearshore bathymetry. The shoreward propagation of waves is measured using pixel intensity time series collected at a cross-shore array of locations using remotely operated video cameras. The incident band is identified, and the cross-spectral matrix is calculated for this band. The cross-shore component of wavenumber is found as the gradient in phase of the first complex empirical orthogonal function of this matrix. Water depth is then inferred from linear wave theory's dispersion relationship, Full bathymetry maps may be measured by collecting data in a large array composed of both cross-shore and longshore lines, Data are collected hourly throughout the day, and a stable, daily estimate of bathymetry is calculated from the median of the hourly estimates. The technique was tested using 30 days of hourly data collected at the SandyDuck experiment in Duck, North Carolina, in October 1997. Errors calculated as the difference between estimated depth and ground truth data show a mean bias of -35 cm (rms error = 91 cm). Expressed as a fraction of the true water depth, the mean percent error was 13% (rms error = 34%). Excluding the region of known wave nonlinearities over the bar crest, the accuracy of the technique improved, and the mean (rms) error was -20 cm (75 cm). Additionally, under low-amplitude swells (wave height H less than or equal to 1 m), the performance of the technique across the entire profile improved to 6% (29%) of the true water depth with a mean (rms) error of -12 cm (71 cm).

Swaminathan, R., and S.K. Nayar, Nonmetric calibration of wide-angle lenses and polycameras, Ieee Transactions On Pattern Analysis and Machine Intelligence, 22 (10), 1172-1178, 2000.

Images taken with wide-angle cameras tend to have severe distortions which pull points towards the optical center. This paper proposes a simple method for recovering the distortion parameters without the use of any calibration objects. Since distortions cause straight lines in the scene to appear as curves in the image, our algorithm seeks to find the distortion parameters that map the image curves to straight lines. The user selects a small set of points along the image curves. Recovery of the distortion parameters is formulated as the minimization of an objective function which is designed to explicitly account for noise in the selected image points. Experimental results are presented for synthetic data as well as real images. We also present the idea of a polycamera which is defined as a tightly packed camera cluster. Possible configurations are proposed to capture very large fields of view. Such camera clusters tend to have a nonsingle viewpoint. We therefore provide analysis of what we call the minimum working distance for such clusters. Finally, we present results for a polycamera consisting of four wide-angle sensors having a minimum working distance of about 4m. On undistorting the acquired images using our proposed technique, we create real- time high resolution panoramas.

Tsai, R.Y., A Versatile Camera Calibration Technique For High-Accuracy 3d Machine Vision Metrology Using Off-the-Shelf Tv Cameras and Lenses, Ieee Journal of Robotics and Automation, 3 (4), 323-344, 1987.


Wang, C.C., Extrinsic Calibration of a Vision Sensor Mounted On a Robot, Ieee Transactions On Robotics and Automation, 8 (2), 161-175, 1992.

A vision sensor is mounted on a robot to detect surrounding objects. Its mounting position and orientation must be identified, resulting in an extrinsic calibration problem. This paper presents three classes of extrinsic calibration procedures. All use closed-form solutions. The class A calibration procedure requires a reference object at a precalibrated location. The class B calibration procedure takes advantage of a robot's mobility. It requires a reference frame but not precalibration. The class C procedure, by taking full advantage of both robot mobility and dexterity, requires no reference object but the simplest one-a visible point. In simulation studies, the class A, B, and C calibration procedures have produced estimates successfully converging to true extrinsic parameter values. Except the class A calibration procedure, which yields biased results unless the precalibration is free from errors, field experiments have been carried out for class B and C calibration procedures. For comparison, two existing B-type calibration methods, namely, those of Tsai and Lenz and Shiu and Ahmad, have also been tested with real data. Individually, each method has achieved consistent results. Collectively, their results appear to be comparable. Standard deviations obtained by class B and the Tsai-Lenz methods have been smaller than those of the Shiu- Ahmad method. On average, the Tsai-Lenz method has achieved the smallest standard deviations.

Wang, C.C., A Low-Cost Calibration Method For Automated Optical Mensuration Using a Video Camera, Machine Vision and Applications, 7 (4), 259-266, 1994.

Automated optical mensuration gauges the acquired image of the inspected unit while assessing its actual size and shape. The mensuration requires the following preparations: (I) alignment of the video camera perpendicularly to the inspection table, and (2) calibration of the scale ratios of image acquisition, notably, the stretching ratio caused by signal conversion and the magnification ratio of optical coupling. This paper presents the unique two-stage calibration method. The first stage applies the parallelogram conservation property, a property very sensitive to misorientation, to test against the potential misalignment. Once detected, we adjust the misalignment towards orthogonal alignment using image patterns of the calibration template. Then, the second stage determines the scale ratios. The proposed calibration method is suitable for on-site applications, and its implementation cost is low. Sensitivity analysis and experimental results are reported.

Wang, C.C., J. Lee, L.W. Chen, and H.Y. Lai, A new method for circular grid analysis in the sheet metal forming lest, Experimental Mechanics, 40 (2), 190-196, 2000.

Computer vision systems are employed to determine the major and minor lengths of deformed elliptic grids while determining a sheet metal's workability. The existing method identifies the ellipse using the least squares analysis. It suffers two drawbacks: assumptions in direct conflict with the observed real-world processes and an undesirable property of orientation dependence. For the remedy, this paper presents a new method that, in addition to achieving the desired property of orientation invariance, discards assumptions that conflict with real-world processes. The proposed method is implemented and tested using simulated and real-world data. Results are reported and compared with those obtained by the existing method.

Wei, G.Q., and S. Dema, Implicit and Explicit Camera Calibration - Theory and Experiments, Ieee Transactions On Pattern Analysis and Machine Intelligence, 16 (5), 469-480, 1994.

By implicit camera calibration, we mean the process of calibrating a camera without explicitly computing its physical parameters. Implicit calibration can be used for both three- dimensional (3-D) measurement and generation of image coordinates. In this paper, we present a new implicit model based on the generalized projective mappings between the image plane and two calibration planes. The back-projection and projection processes are modelled separately to ease the computation of distorted image coordinates from known world points. A set of constraints of perspectivity is derived to relate the transformation parameters of the two calibration planes. Under the assumption of the radial distortion model, we present a computationally efficient method for explicitly correcting the distortion of image coordinates in frame buffer without involving the computation of camera position and orientation. By combining with any linear calibration techniques, this method makes explicit the camera physical parameters. Extensive experimental comparison of our methods with the classic photogrammetric method and Tsai's method in the aspects of 3-D measurement (both absolute and relative errors), the prediction of image coordinates, and the effect of the number of calibration points, is made using real images from 15 different depth values.

Wei, G.Q., K. Arbter, and G. Hirzinger, Active self-calibration of robotic eyes and hand-eye relationships with model identification, Ieee Transactions On Robotics and Automation, 14 (1), 158-166, 1998.

In this short paper, we first review research results of camera self-calibration achieved in photogrammetry, robotics and computer vision. Then we propose a method for self-calibration of robotic hand cameras by means of active motion. Through tracking a set of world points of unknown coordinates during robot motion, the internal parameters of the cameras (including distortions), the mounting parameters as well as the coordinates of the world points are estimated. The approach is fully autonomous, in that no initial guesses of the unknown parameters are to be provided from the outside by humans for the solution of a set of nonlinear equations. Sufficient conditions for a unique solution are derived in terms of controlled motion sequences. Methods to improve accuracy and robustness are proposed by means of best model identification and motion planning. Experimental results in both a simulated and a real environments are reported.

Weng, J.Y., P. Cohen, and M. Herniou, Camera Calibration With Distortion Models and Accuracy Evaluation, Ieee Transactions On Pattern Analysis and Machine Intelligence, 14 (10), 965-980, 1992.

The objective of stereo camera calibration is to estimate the internal and external parameters of each camera. Using these parameters, the 3-D position of a point in the scene, which is identified and matched in two stereo images, can be determined by the method of triangulation. In this paper, we present a camera model that accounts for major sources of camera distortion, namely, radial, decentering, and thin prism distortions. The proposed calibration procedure consists of two steps. In the first step, the calibration parameters are estimated using a closed-form solution based on a distortion- free camera model. In the second step, the parameters estimated in the first step are improved iteratively through a nonlinear optimization, taking into account camera distortions. According to minimum variance estimation, the objective function to be minimized is the mean-square discrepancy between the observed image points and their inferred image projections computed with the estimated calibration parameters. We introduce a type of measure that can be used to directly evaluate the performance of calibration and compare calibrations among different systems. The validity and performance of our calibration procedure are tested with both synthetic data and real images taken by tele- and wide-angle lenses. The results consistently show significant improvements over less complete camera models.

Zhang, Z.Y., Q.T. Luong, and O. Faugeras, Motion of an uncalibrated stereo rig: Self-Calibration and metric reconstruction, Ieee Transactions On Robotics and Automation, 12 (1), 103-113, 1996.

We address in this paper the problem of self-calibration and metric reconstruction (up to a scale factor) from one unknown motion of an uncalibrated stereo rig. The epipolar constraint is first formulated for two uncalibrated images. The problem then becomes one of estimating unknowns such that the discrepancy from the epipolar constraint, in terms of sum of squared distances between points and their corresponding epipolar lines, is minimized. Although the full self- calibration is theoretically possible, we assume in this paper that the coordinates of the principal point of each camera are known. Then, the initialization of the unknowns can be done based on our previous work on self-calibration of a single moving camera, which requires to solve a set of so-called Kruppa equations. Redundancy of the information contained in a sequence of stereo images makes this method more robust than using a sequence of monocular images. Real data has been used to test the proposed method, and the results obtained are quite good. We also show experimentally that it is very difficult to estimate precisely the coordinates of the principal points of cameras. A variation of as high as several dozen pixels in the principal point coordinates does not affect significantly the 3-D reconstruction.

Zhou, Y., and B.J. Nelson, Calibration of a parametric model of an optical microscope, Optical Engineering, 38 (12), 1989-1995, 1999.

In micro-domain applications, such as assembly of hybrid microelectromechanical systems, optical microscopes form a critical component of visually based microassembly systems. In order to effectively use vision feedback to guide manipulation strategies using a broad range of optical microscope configurations, accurately calibrated parametric models of optical microscopes are required. Although many calibration techniques exist for macroscopic camera-lens systems, there is a dearth of literature on calibration of parametric microscope models. Optical microscope calibration has unique characteristics that are quite different from normal camera calibration, including (1) unique calibration parameters; (2) calibration patterns that must be parallel to the image plane, and (3) restriction to single-plane calibration. In this paper, we propose a parametric microscope model and calibration algorithm specifically for optical microscopes. Our approach extends existing camera calibration techniques to include the unique parameters of optical microscopes and also allows the use of a single calibration plane perpendicular to the optical axis. The validity and accuracy of our proposed microscope calibration method are tested by experiments. (C) 1999 Society of Photo-Optical Instrumentation Engineers. [S0091- 3286(99)02412-5].