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1. Camera Calibration with a Simulated Three Dimensional Calibration Object

Hynek Bakstein, Radim Halir (2000)

A new camera calibration method based on DLT model is presented in this

paper. Full set of camera parameters can be obtained from multiple views of

coplanar calibration object with coordinates of control points measured in 2D.

The proposed approach is numerically stable and robust in comparison with

calibration techniques based on non-linear optimisation of all camera

parameters.

2. A Four-step Camera Calibration Procedure with Implicit Image Correction

Janne Heikkila and Olli Silven

In geometrical camera calibration the objective is to determine set of camera

parameters that describe the mapping between 3-D reference coordinates and 2-

D image coordinates. In this paper a four-step calibration procedure that is an

extension to the two-step method. There is an additional step to compensate for

distortion caused by circular features, and a step for correcting the distorted

image coordinates. The image correction is performed with an empirical

inverse model that accurately compensates for radial and tangential distortions.

Finally, a linear method for solving the parameters of the inverse model is

presented.

3. Plane-based Calibration of a Camera with Varying focal Length: the Center

Line Constraint Pierre GURDJOS and Rene PAYRISSAT

This paper deals with the problem of calibrating a (moving) camera with

varying

focal length, from views of a planar pattern with a known Euclidean structure.

They relate this calibration problem to the Center Line (CL) constraint, that is

the principal point locus when planar figures are in perspective

correspondence. They demonstrate that the CL equation is irrespective of the

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focal length and holds for each view, with only three unknown parameters

whose values are constant in the images. They define its analytic equation with

coefficients computed from the world-plane to image homography matrices

.The simulations on synthetic data and an application with real images.

4. A Simple Camera Calibration Method

Aldo Cumani

In this paper he discusses a calibration method based on a simple and

inexpensive setup. Their approach allows a substantial decoupling of the

distortion model from the rest of the camera model, which means that

distortion estimation can make a better use of the available image data.

Preliminary experimental tests show promising results.

5. Using Angles for Internal Camera Calibration and Calibration Update

Marina Kolesnik

Standard camera calibration technique is based on the relationship between 3D

point coordinates in the object space and their respective 2D coordinates in the

image plane. Thus precise distance measurements for a set of reference points

are a necessary burden of the calibration. The idea presented in the paper is to

perform internal camera calibration using angular information for a set of

reference points in the image plane. This approach is angular calibration. In this

they use a special laser projector that generates reference pattern with known

angular characteristics. Angular calibration uses known angles to distinguished

3-D points in the laser pattern viewed by the camera. The calculation is done in

the camera standard coordinate system; only the intrinsic camera parameters

are of importance. They show how angular calibration approach can be used

for the camera with changing focal length. They give calibration results of the

camera internal parameters.

6. 3-D reconstruction of articulated objects from uncalibrated images Fabio

Remondino 2002

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In this paper a system for the reconstruction of 3-D models of articulated

objects, like human bodies, from uncalibrated images is presented. The scene is

seen from different viewpoints and no pre-set knowledge is considered. To

extract precise 3-D information from imagery, a calibration procedure must be

performed. Therefore, first a camera calibration with Direct Linear

Transformation (DLT) is done assuming few control points on the subject. The

initial approximations of the interior and exterior orientation computed with

DLT are then improved in a general photogrammetric bundle adjustment with

self-calibration. Additionally a stereo matching process based on least squares

matching extracts a dense set of image correspondences from the sequence.

Finally a 3-D point cloud is computed by forward intersection using the

calibration data and the matched points. The resulting 3-D model of human

body is presented.

7. Photogrammetric Transformation with Panning K.A. Stivers, G.B. Ariel, A.

Vorobiev, M.A. Penny, A. Gouskov, N. Yakunin

This paper is to present a technique called physical parameter transformation

(PPT) which allows the use of panning cameras. The PPT is built upon the co

linearity photogrammetric relations from which the DLT is derived. Like the

MDLT, PPT is implemented such that orthogonality of the orientation matrix

of the image to object coordinate system is guaranteed. PPT with panning will

be demonstrated to have greater accuracy than the DLT.

8.Two new algorithms to retrieve the calibration matrix from the 3-d projective

camera model Gamal H. Seedahmed and Ayman F. Habib

This paper presents two new algorithms to retrieve the calibration matrix from

the projective camera model. In both algorithms, a collective approach was

adopted, using matrix factorization. The calibration matrix was retrieved from a

quadratic matrix term. The two algorithms were framed around a correct

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utilization of Cholesky factorization to decompose the quadratic matrix term.

The first algorithm used an iterative Cholesky factorization to retrieve the

calibration matrix from the quadratic matrix term. The second algorithm used

Cholesky factorization to factor the quadratic matrix term but after its

inversion. The basic argument behind the two algorithms is that: the direct use

of Cholesky factorization does not reveal the correct decomposition due to the

missing matrix structure in terms of lower-upper order. In both algorithms, a

successful retrieval of the calibration matrix was achieved. This paper explains

the key ideas behind the two algorithms, accommodated with a simulated

example to demonstrate their validity.

9. Linear recovery of the exterior orientation parameters in a planar object

space Gamal H. Seedahmed and Ayman F. Habib

This paper presents a new closed form solution to a single photo-resection in a

planar object space based on homogenous coordinate representation and matrix

factorization. Homogenous coordinate representation offers a direct matrix

correspondence between the parameters of the 2-D projective transformation

and the collinearity model. This correspondence lends itself to a direct matrix

factorization to solve the photo-resection problem. The matrix factorization

starts by recovering the elements of the rotation matrix and then solving for the

camera position. It will be shown that an incomplete representation of the

rotation matrix is captured by the 2-D projective parameters but the actual

physical parameters of the rotation matrix still can be recovered explicitly and

without any ambiguity. These elements were used to build a complete rotation

matrix, which in turn facilitates the correct solution of the camera position. The

developed solution can serve as a complementary companion to the classical

DLT model. In this paper, a detailed derivation of the proposed solution will be

presented, accommodated with two simulated examples to demonstrate its

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validity. The first example simulates aerial photography and the second one

simulates close range photogrammetric application.

10. Nonparametric, Model-Based Radial Lens Distortion Correction Using

Tilted Camera Assumption Janez Pers, Stanislav Kovacic

Radial lens distortion prohibits use of simple pinhole camera models in

computer vision applications, especially when using wide-angle lenses, which

result in barrel type distortion. Usual approach to radial distortion is by the

means of polynomial approximation, which introduces distortion-specific

parameters into the camera model and requires iterative methods for their

calculation. Based on the properties of distorted images, an alternative

approach is proposed in this paper. The basic assumption is that distortion

occurs due to transformation of the observed differential of radius and is locally

dependent of the angle of principal rays. The geometric relations which result

from this assumption are complemented with the equations of the perspective

radial lens projection function to derive model of radial distortion with single

parameter - focal length. Experiments were conducted to illustrate the validity

and performance of this approach.

11. Direct Recovery of the Camera Internal Parameters Using Known Angles

Marina Kolesnik

In this paper a pen-size laser crosshair projector is used to generate a reference

pattern whose angular features are known. Each known angle between a pair of

optical rays imposes one angular constraint on the internal camera parameters.

Several constraints form a system of equations, which is solved for the internal

parameters. Because the angular constraints are given in the standard

coordinate system of the camera, the internal parameters are recovered directly,

that is without referring to any world coordinate system. An advantage that

follows, is that calibration does not require precise measurements of 3-D

coordinates of reference points. The final calibration parameters as well as the

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first order radial distortion parameter are computed by nonlinear optimization.

We analyze an accuracy of angular values between optical rays and present

experimental results of camera calibration. Angular calibration is fast, robust

and easy to implement method, which is suitable for quick off lab calibration

of cameras.

12. A camera calibration technique using targets of circular features

Gines Garcia Mateos

Accurate camera calibration is essential in many computer vision applications,

where quantitative information is extracted from the images. This paper deals

with the problems of sub pixel feature location on the calibration target and its

automatic matching with the corresponding 3-D world points, as the first part

of an unsupervised calibration process. In the proposed method a grid of

circular features is used as target. Feature detection and location is carried out

using a very simple and efficient connected component labeling algorithm,

which incrementally calculates an ellipsoidal description of the regions. This

description is a robust and accurate model of the projected circular features,

since the perspective projection of a circle is always an ellipse. Some heuristics

are presented for selecting those regions corresponding to circles in the target.

From these ellipses, feature points are extracted, considering the effect of

perspective. Experimental results have shown high robustness of the method

against random noise and defocusing. Sub pixel accuracy is achieved and

computational complexity is linear with the number of pixels.

13. Lens Distortion Calibration Using Point Correspondences

G. P. Stein

This paper describes a new method for lens distortion calibration using only point

correspondences in multiple views, without the need to know either the 3D location

of the points or the camera locations. The standard lens distortion model is a model

of the deviations of a real camera from the ideal pinhole or projective camera

model. Given multiple views of a set of corresponding points taken by ideal pinhole

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cameras there exist epipolar and trilinear constraints among pairs and triplets of

these views. In practice, due to noise in the feature detection and due to lens

distortion these constraints do not hold exactly and we get some error. The

calibration is a search for the lens distortion parameters that minimize this error.

Using simulation and experimental results with real images we explore the

properties of this method. We describe the use of this method with the standard lens

distortion model, radial and decentering, but it could also be used with any other

parametric distortion models. Finally we demonstrate that lens distortion calibration

improves the accuracy of 3D reconstruction. Due to lack of space this paper will

focus on the 3 image method.

14. Straight lines have to be straight, Automatic calibration and removal of

distortion from scenes of structured environments

Frederic Devernay, Olivier Faugeras

Most algorithms in 3D computer vision rely on the pinhole camera model because

of its simplicity, whereas video optics, especially low-cost wide-angle or fish-eye

lenses, generate a lot of non-linear distortion which can be critical. To find the

distortion parameters of a camera, we use the following fundamental property: a

camera follows the pinhole model if and only if the projection of every line in space

onto the camera is a line. Consequently, if we find the transformation on the video

image so that every line in space is viewed in the transformed image as a line, then

we know how to remove the distortion from the image. The algorithm consists of

first doing edge extraction on a possibly distorted video sequence, then doing

polygonal approximation with a large tolerance on these edges to extract possible

lines from the sequence, and then finding the parameters of our distortion model

that best transform these edges to segments. Results are presented on real video

images, compared with distortion calibration obtained by a full camera calibration

method, which uses a calibration grid.

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DIGITAL CAMERA GEOMETRIC CALIBRATION WITH MODIFIED DLT (DIRECT LINEER

TRANSFORMATION) METHOD COMPARING Fevzi KARSLI1[1]

Eminnur AYHAN2[2

Nowadays, digital cameras are widely taking place especially in the point of basic data source of terrestrial

photogrammetry applications. Digital cameras have found wide spread of application area opportunity from measuringarchitectural monuments to measuring industrial elements. You have to know the geometric performances of the camera

to get the real measurements. Geometric accuracy can only get by finding some parameters like camera constant,principal point coordinates, distortion etc. In the calibration of digital cameras generally methods of DLT (Direct Linear

Transformation), which based on collinearity condition and bundle adjustment (ray bundle with additional parameters)are being used. In this paper, the calibration of digital camera has done with modified DLT method, which simplifies

mathematical model and facilitates the solution by using 3D test field network. With this method, the solution has doneby considering a few photographs and control points and the efficiency of the obtained calibration parameters on

position sensitivity has been investigated. All calculations and evaluations are done in the Matlab 5.0 software.

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