Camera matrix calibration using circular control points 

Get Complete Project Material File(s) Now! »

Camera matrix extraction

Considering the global calibration method by [ZHANG 2000], theoretically one can claim that camera calibration is a closed topic. At the same time, when calibrating a camera, the major difficulty lies in optical distortion; its correction is a necessary step for high precision results. The mentioned global calibration approach mixes the distortion parameters with other camera parameters and their calculation is held by simultaneous minimization. However, this could potentially lead to residual error compensation of distortion parameters and other camera parameters that would decrease the calibration stability, since the physics of distortion field would not be captured correctly. Moreover, the error compensation cannot be eliminated in the framework of global methods, and therefore, the distortion compensation must be  held separately, as a preliminary step to any further calibration. The recently developed method relying on the calibration harp by [TANG 2011] allows calculating a distortion field separately from other parameters. Its main
idea is based on straightness measure of tightly stretched strings, pictures of which must be taken in different orientations. In that respect, it lies in the category of plumb-line methdods. While it requires using an additional calibration pattern, the trade-off is that we are able to control the residual distortion error magnitude in addition to having distortion detached from other camera parameters. This separation should also allow producing more reliable results since it solves the problem of residual error compensation. Another questions we address, given distortion compensated calibration image, is how to eliminate a perspective bias. Since we deal with circular patterns and ellipse centers as keypoints (as it is more precise than using square patterns), the detected control points can potentially be corrupted by perspective bias. It can be described by fact that image of the ellipse center does not correspond to the center of the ellipse image. Therefore, we try to compensate for the perspectivebias by taking into account rather circle-ellipse affine transformation than point transformation and then use correspondence of detected keypoints with pattern keypoints given the affine conic transform.

Chromatic aberration correction accuracy with reflex cameras

To evaluate the correction method three types of images are used: calibration pattern, test pattern and real images. Two types of calibration patterns are considered in order to show the importance of having precise keypoints: with circles where each keypoint is a center, and with noise where keypoints are detected using SIFT algorithm. The circled pattern is printed on A3 format paper and there, 37×26 = 962 black disks are drawn of the radius 0.4cm and separation of 1.1cm between consecutive disks. The picture of calibration pattern is taken with chosen fixed settings, after that a test image is taken of the same pattern. After the calibration is complete, the correction method is applied to the test image to evaluate precision there; after, some outdoor images were taken under the same camera settings as before in order to demonstrate the image quality improvement.

Calibration matrix stability for synthetic data

Pattern and camera views synthesis The image resolution is set to 1296×864 pixels. The number of circles is 10×14, each of radius 1cm, and consecutive circles have 3cm separation between each other. The pattern has resolution 42cm×30cm. The synthetic camera has following parameters: = 1250, = 1250, = 1.09083, u0 = 648, v0 = 432. For the high quality images, we firstly generate high resolution pattern image and then subject it to the geometric displacement (all distortion is eliminated), Gaussian blurring and then down-sampling to the image resolution. Geometric image re-sampling is carried out by mapping from the transformed image to the original pattern. This involves calculating for every pixel in the transformed image, the corresponding pixel coordinate in the original image, which requires an inverse mapping. The transformed image intensity is then calculated based on the standard linear interpolation around the corresponding coordinate of the original pattern. Pattern positioning In order to test calibration matrix stability, we generated 5 sets of images, each set included 5 images (different views on the pattern). This allows to extract 5 calibration matrices so that to see stability of its parameters along the sets. The generated image views are simulated by using pseudo-randomly generated homographies which consist of 3D rotation and translation whose values are drawn randomly from a specific range. This range limit ensures that the transformed image lies roughly within an image window. Meanwhile, there is always variance of rotations and translation along the sets. The roation angles always lie whithin the range [15,−45]. For the re-sampling of the transformed image, an inverse of homography matrices is used.

READ  Topology Design of Hybrid Satellite - MANET 

Table of contents :

1 Introduction – version française 
1.1 Correction de l’aberration chromatique
1.2 Extraction de caméra matrice
1.3 Les chapitres de la thèse
1.4 Les contributions principales
2 Introduction 
2.1 Chromatic aberration correction
2.2 Camera matrix extraction
2.3 The thesis chapter by chapter
2.4 Main contributions
3 Robust and precise feature detection of a pattern plane 
3.1 Introduction
3.2 Sub-pixel keypoint detection
3.2.1 Geometrical model
3.2.2 Intensity model
3.2.3 Parametric model estimation through minimization
3.3 Keypoint ordering
3.4 Sub-pixel ellipse center detection accuracy
3.5 Conclusion
4 High-precision correction of lateral chromatic aberration in digital images 
4.1 Introduction
4.2 Calibration and correction
4.3 Experiments
4.3.1 Chromatic aberration correction accuracy with reflex cameras
4.3.2 Visual improvement for real scenes
4.3.3 Experiments with compact digital cameras
4.4 Conclusion
5 Camera matrix calibration using circular control points 
5.1 Introduction
5.1.1 Camera calibration workflow
5.1.2 Camera calibration basic steps and equations
5.2 Incorporation of conic transform into homography estimation as perspective bias compensation
5.2.1 Center of conic’s image vs. image of conic’s center
5.2.2 Recovering homography by conic transform cost function
5.3 Experiments
5.3.1 Homography estimation precision
5.3.2 Calibration matrix stability for synthetic data
5.3.3 Calibration matrix stability for real data
5.4 Conclusion
6 Thesis conclusions 
A High-precision lens distortion correction using calibration harp 
A.1 Introduction
A.2 The harp calibration method
A.2.1 Main equations
A.2.2 A solution for the line angle
A.2.3 Simplified minimization for obtaining the polynomial coefficients
A.3 Experiments
A.3.1 Choice of polynomial degree
A.3.2 Real data experiments
A.3.3 Measuring distortion correction of global calibration method
A.4 Conclusion
Bibliography

GET THE COMPLETE PROJECT

Related Posts