Geometric calibration of a camera - Revision history

imported>Student221: /* Conclusions */

2019-12-12T23:17:12Z

Conclusions

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	== Conclusions ==		== Conclusions ==
	In summary, by using the MATLAB camera calibrator, both standard and fisheye mode images were calibrated. The measurements of real planner objects show high accuracy without distortion. The future work will concentrate on the calibration of ~~dual or multiple~~ cameras ~~to measure~~ the ~~depth and movement~~ of ~~object in the 3D space~~.		In summary, by using the MATLAB camera calibrator, both standard and fisheye mode images were calibrated. The measurements of real planner objects show high accuracy without distortion. The future work will concentrate on the development of calibration software without checkerboard pattern or the calibration of nanoscale imaging cameras like the camera of scan electron microscope (SEM), transmission electron microscope (TEM), etc.

	== References==		== References==

imported>Student221: /* Conclusions */

2019-12-12T23:14:29Z

Conclusions

← Older revision		Revision as of 23:14, 12 December 2019
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	== Conclusions ==		== Conclusions ==
	In summary, by using the MATLAB camera calibrator, both standard and fisheye mode ~~image are~~ calibrated. The measurements of real planner objects show high accuracy without distortion. The future work ~~may~~ concentrate on the calibration of dual ~~camera model~~ to measure the depth and movement of object in 3D space.		In summary, by using the MATLAB camera calibrator, both standard and fisheye mode images were calibrated. The measurements of real planner objects show high accuracy without distortion. The future work will concentrate on the calibration of dual or multiple cameras to measure the depth and movement of object in the 3D space.

	== References==		== References==

imported>Student221: /* Methods and Results */

2019-12-12T23:13:01Z

Methods and Results

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	[[File:yecunfig6.png\|600px\|center\|thumb\|'''Figure 6''': Measurement of a planner object. (a)Original image. (b)Undistorted image. (c)Coins segmentation. (d)Coins detection.]]		[[File:yecunfig6.png\|600px\|center\|thumb\|'''Figure 6''': Measurement of a planner object. (a)Original image. (b)Undistorted image. (c)Coins segmentation. (d)Coins detection.]]

	The image was then transformed into 3D world coordinate to measure the size of the penny. The ~~diameter~~ of the four pennies were shown in table 1 with a mean value of 19.19 mm and variance of 0.02. The actual size of a penny should be 19.05 mm, the test results give an error of 0.7%, indicating the high accuracy of the measurement.		The image was then transformed into the 3D world coordinate to measure the size of the penny. The diameters of the four pennies were shown in table 1 with a mean value of 19.19 mm and a variance of 0.02. The actual size of a penny should be 19.05 mm, the test results give an error of 0.7%, indicating the high accuracy of the measurement.

	[ # Diameter (mm) ]		[ # Diameter (mm) ]
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	[ 3 19.12 ]		[ 3 19.12 ]
	[ 4 18.95 ]		[ 4 18.95 ]

	Fisheye mode calibration		Fisheye mode calibration

	The fisheye lens is an extremely wide-angle lens that the angle of view of is between 100 and 180 degrees. However, to achieve the ultra-wide-angle, the lines of perspective in the images are distorted. The pinhole camera model is no longer suitable for the fisheye lens because the alignment coefficients of the intrinsic parameters are related to the relative position of the sensor plane and the pixel plane.		The fisheye lens is an extremely wide-angle lens that the angle of view of is between 100 and 180 degrees. However, to achieve the ultra-wide-angle, the lines of perspective in the images are distorted. The pinhole camera model is no longer suitable for the fisheye lens because the alignment coefficients of the intrinsic parameters are related to the relative position of the sensor plane and the pixel plane.
	In this project, instead of using a fisheye lens, the fish eye image were taken from a software embedded in the Samsung Galaxy A20 camera as shown in figure 7.		In this project, instead of using a fisheye lens, the fish eye image were taken from a software embedded in the Samsung Galaxy A20 camera as shown in figure 7.

imported>Student221: /* Methods and Results */

2019-12-12T23:11:53Z

Methods and Results

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	Measurement of objects		Measurement of objects
	We then took the parameters of the camera to measure the size of a penny. Four coins were put on top of the checkerboard as shown in figure 6a, and the ~~image were~~ taken about 50 cm away from the checkerboard. The undistorted image can be obtained by using the parameters of the calibrated camera as P=[R\|t]K, which is demonstrated in figure 6b. Since the penny is shiny and colorful than the background, so it is possible to detect it from the coins in by using the saturation component of the HSV representation of the image. The image was first converted to HSV color space, and then threshold the image to black and white as shown in figure 6c. The coins can be detected as the image in figure 6d.
			We then took the parameters of the camera to measure the size of a penny. Four coins were put on top of the checkerboard as shown in figure 6a, and the images was taken about 30 cm away from the checkerboard. The undistorted image can be obtained by using the parameters of the calibrated camera as P=[R\|t]K, which is demonstrated in figure 6b. Since the penny is shiny and colorful than the background, so it is possible to detect it from the coins in by using the saturation component of the HSV representation of the image. The image was first converted to HSV color space, and then threshold the image to black and white as shown in figure 6c. The coins can be detected as the image in figure 6d.

	[[File:yecunfig6.png\|600px\|center\|thumb\|'''Figure 6''': Measurement of a planner object. (a)Original image. (b)Undistorted image. (c)Coins segmentation. (d)Coins detection.]]		[[File:yecunfig6.png\|600px\|center\|thumb\|'''Figure 6''': Measurement of a planner object. (a)Original image. (b)Undistorted image. (c)Coins segmentation. (d)Coins detection.]]

imported>Student221: /* Methods and Results */

2019-12-12T23:10:08Z

Methods and Results

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	Calibration		Calibration
	After the identification of the checkerboard, the standard mode with two coefficients ~~were~~ first tested. The mean reprojection error is shown in figure 3. While the three coefficients give a lower error (mean value 1.39 pixels), nevertheless, the two ~~coefficient~~ is sufficient for the standard pictures. The extrinsic parameters (the relative orientation of the checkerboard with respect to the camera) are then shown in the 3D diagram in figure 4. Figure 4a demonstrates a camera-centric schematic, while figure 4b is a pattern-centric view.
			After the identification of the checkerboard, the standard mode with two coefficients was first tested. The mean reprojection error is shown in figure 3. While the three coefficients give a lower error (mean value 1.39 pixels), nevertheless, the two coefficients is sufficient for the standard pictures. The extrinsic parameters (the relative orientation of the checkerboard with respect to the camera) are then shown in the 3D diagram in figure 4. Figure 4a demonstrates a camera-centric schematic, while figure 4b is a pattern-centric view.

	[[File:yecunfig3.png\|600px\|center\|thumb\|'''Figure 3''': Mean reprojection error per image.]]		[[File:yecunfig3.png\|600px\|center\|thumb\|'''Figure 3''': Mean reprojection error per image.]]
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	The intrinsic and extrinsic parameters were exported as:		The intrinsic and extrinsic parameters were exported as:

	Intrinsics		Intrinsics

	----------		----------
	Focal length (pixels): [ 3310.3793 +/- 10.4656 3309.6850 +/- 10.4052 ]		Focal length (pixels): [ 3310.3793 +/- 10.4656 3309.6850 +/- 10.4052 ]
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	Extrinsics		Extrinsics

	----------		----------
	Rotation vectors:		Rotation vectors:

imported>Student221: /* Methods and Results */

2019-12-12T23:08:57Z

Methods and Results

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	== Methods and Results ==		== Methods and Results ==
	Pattern for calibration		Pattern for calibration
	The checkerboard pattern is used for MATLAB Camera Calibrator. The pattern was printed on a letter size paper and stick on a hard board to prevent curvature on the pattern. The grid size of the checkerboard pattern is 21.2×21.~~2mm~~. The pattern was ~~hold~~ ~50 cm from the camera and was ~~focus by~~ the camera. The camera was not in ~~auto focus~~ mode and the zoom ~~keep~~ constant in the process. Totally 15 images were taken with different ~~orientation~~ relative to the camera. These pictures were shown in figure 2.
			The checkerboard pattern is used for MATLAB Camera Calibrator. The pattern was printed on a letter-size paper and stick on a hard board to prevent curvature on the pattern. The grid size of the checkerboard pattern is 21.2×21.2 mm. The pattern was held ~50 cm from the camera and was focused on the camera. The camera was not in autofocus mode and the zoom kept constant in the process. Totally, 15 images were taken with different orientations relative to the camera. These pictures were shown in figure 2.

	[[File:yecunfigure2.png\|600px\|center\|thumb\|'''Figure 2''': Checkerboard patterns for calibration.]]		[[File:yecunfigure2.png\|600px\|center\|thumb\|'''Figure 2''': Checkerboard patterns for calibration.]]

imported>Student221: /* Background */

2019-12-12T23:06:25Z

Background

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	The camera can be modeled as a pinhole crema as shown in figure 2. Hence, the intrinsic transformation is to transform from a 3D camera coordinate to 2D image plane coordinate, which can be modeled as K = [fx 0 0\|s fy 0\|cx cy 1], where fx and fy is the normalized focal length, cx and cy is the optical center of the image, and s is Skew coefficient for non-perpendicular axes case.		The camera can be modeled as a pinhole crema as shown in figure 2. Hence, the intrinsic transformation is to transform from a 3D camera coordinate to 2D image plane coordinate, which can be modeled as K = [fx 0 0\|s fy 0\|cx cy 1], where fx and fy is the normalized focal length, cx and cy is the optical center of the image, and s is Skew coefficient for non-perpendicular axes case.


	Therefore, the calibration process can be mathematically described as: P = [R\|t]K.		Therefore, the calibration process can be mathematically described as: P = [R\|t]K.

imported>Student221: /* Background */

2019-12-12T23:06:09Z

Background

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	The extrinsic parameter is a 3D to 3D transformation, it describes the rotation (R) and translation (t) of the relative position of crema and 3D object.		The extrinsic parameter is a 3D to 3D transformation, it describes the rotation (R) and translation (t) of the relative position of crema and 3D object.

	Intrinsic parameter		Intrinsic parameter

imported>Student221: /* Background */

2019-12-12T23:05:54Z

Background

← Older revision		Revision as of 23:05, 12 December 2019
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	Extrinsic parameter		Extrinsic parameter

	The extrinsic parameter is a 3D to 3D transformation, it describes the rotation (R) and translation (t) of the relative position of crema and 3D object.		The extrinsic parameter is a 3D to 3D transformation, it describes the rotation (R) and translation (t) of the relative position of crema and 3D object.
	Intrinsic parameter		Intrinsic parameter

	The camera can be modeled as a pinhole crema as shown in figure 2. Hence, the intrinsic transformation is to transform from a 3D camera coordinate to 2D image plane coordinate, which can be modeled as K = [fx 0 0\|s fy 0\|cx cy 1], where fx and fy is the normalized focal length, cx and cy is the optical center of the image, and s is Skew coefficient for non-perpendicular axes case.		The camera can be modeled as a pinhole crema as shown in figure 2. Hence, the intrinsic transformation is to transform from a 3D camera coordinate to 2D image plane coordinate, which can be modeled as K = [fx 0 0\|s fy 0\|cx cy 1], where fx and fy is the normalized focal length, cx and cy is the optical center of the image, and s is Skew coefficient for non-perpendicular axes case.

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	Distortion		Distortion
	The lens distortion ~~in camera~~ contains radical and tangential distortion, which cannot be described by the pinhole camera model. For the radical distortion, the further from the center, the larger the distortion we have, which can be corrected by using Taylor series expansion: xdistorted = x(1 + k1r2 + k2r4 + k3r6); ydistorted= y(1 + k1r2 + k2r4 + k3r6)
			The lens distortion contains radical and tangential distortion, which cannot be described by the pinhole camera model. For the radical distortion, the further from the center, the larger the distortion we have, which can be corrected by using Taylor series expansion: xdistorted = x(1 + k1r2 + k2r4 + k3r6); ydistorted= y(1 + k1r2 + k2r4 + k3r6)
	On the other hand, the tangential distortion origins from the unparallel of the lens and camera sensor plane, which can be corrected by xdistorted = x + [2 * p1 * x * y + p2 * (r2 + 2 * x2)] and ydistorted = y + [p1 * (r2 + 2 y2) + 2 p2 * x * y].		On the other hand, the tangential distortion origins from the unparallel of the lens and camera sensor plane, which can be corrected by xdistorted = x + [2 * p1 * x * y + p2 * (r2 + 2 * x2)] and ydistorted = y + [p1 * (r2 + 2 y2) + 2 p2 * x * y].


	== Methods and Results ==		== Methods and Results ==

imported>Student221: /* Introduction */

2019-12-12T23:04:50Z

Introduction

← Older revision		Revision as of 23:04, 12 December 2019
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	== Introduction ==		== Introduction ==
	By calibrating the parameters of the lens and image sensors, the distortion of an image can be calibrated to reconstruct the relative position of a camera and objects in the three-dimensional world. It has been widely used in the areas of remote sensing, measurement, etc. The MATLAB provides calibration tool based on the calibration method proposed by Zhang et al. In this project, the crema of a Samsung Galaxy A20 was calibrated by using MATLAB toolbox. The results showed high accuracy in both standard mode and fisheye mode.		By calibrating the parameters of the lens and image sensors, the distortion of an image can be calibrated to reconstruct the relative position of a camera and objects in the three-dimensional world. It has been widely used in the areas of remote sensing, measurement, etc. The MATLAB provides a calibration tool based on the calibration method proposed by Zhang et al. In this project, the crema of a Samsung Galaxy A20 was calibrated by using MATLAB toolbox. The results showed high accuracy in both standard mode and fisheye mode.

	== Background ==		== Background ==