Geometric Calibration Of A Stereo Camera - Revision history

imported>Student2017: /* Appendix I */

2017-12-17T00:39:04Z

Appendix I

← Older revision		Revision as of 00:39, 17 December 2017
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	== Appendix I==		== Appendix I==
	The Matlab script for JEDEYE calibration and rectification: [[file~~:PSYCH221JEDEYECalibration~~.~~zip]]~~		The Matlab script for JEDEYE calibration and rectification: https://drive.google.com/open?id=1T0dQ4HWxzLDTTUTDbHyhRNvG8_MAtTFF (The uploaded file is not complete, and updating with new versions have failed.)

	Our code is available at github (https://github.com/VitaminAJ/Simulation-of-stereo-camera-calibration-parameters.git). To run the code, you need to install docker container, iset (add path of iset) and pbrt-v2.		Our code is available at github (https://github.com/VitaminAJ/Simulation-of-stereo-camera-calibration-parameters.git). To run the code, you need to install docker container, iset (add path of iset) and pbrt-v2.

imported>Student2017: /* Appendix I */

2017-12-16T06:56:22Z

Appendix I

← Older revision		Revision as of 06:56, 16 December 2017
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	== Appendix I==		== Appendix I==
			The Matlab script for JEDEYE calibration and rectification: [[file:PSYCH221JEDEYECalibration.zip]]

	Our code is available at github (https://github.com/VitaminAJ/Simulation-of-stereo-camera-calibration-parameters.git). To run the code, you need to install docker container, iset (add path of iset) and pbrt-v2.		Our code is available at github (https://github.com/VitaminAJ/Simulation-of-stereo-camera-calibration-parameters.git). To run the code, you need to install docker container, iset (add path of iset) and pbrt-v2.

imported>Student2017: /* Methods */

2017-12-16T00:40:11Z

Methods

← Older revision		Revision as of 00:40, 16 December 2017
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	* Compute the following;		* Compute the following;
	** <math>L = \frac{p - C}{\|\|p - C\|\|}, s = \frac{L \times u}{\|\|L \times u\|\|}, u^' = s \times L</math>		** <math>L = \frac{p - C}{\|\|p - C\|\|}, s = \frac{L \times u}{\|\|L \times u\|\|}, u^' = s \times L</math>
	** The rotation matrix is <math> R = \begin{bmatrix} - & s^T & - \\ - & u^'^T & - \\ - & -L^T & - \end{bmatrix} \in \mathbb{R}^{3 \times 3} </math>		** The rotation matrix is <math> R = \begin{bmatrix} - & s^T & - \\ - & u^{'^T} & - \\ - & -L^T & - \end{bmatrix} \in \mathbb{R}^{3 \times 3} </math>
	** The translation vector is obtained as <math>t= -RC \in \mathbb{R}^{3 x 1}</math>		** The translation vector is obtained as <math>t= -RC \in \mathbb{R}^{3 x 1}</math>
	** The extrinsic matrix is the block matrix given by <math>\begin{bmatrix} R & t \\ 0 & 1 \end{bmatrix} \in \mathbb{R}^{4 \times 4}</math>		** The extrinsic matrix is the block matrix given by <math>\begin{bmatrix} R & t \\ 0 & 1 \end{bmatrix} \in \mathbb{R}^{4 \times 4}</math>

imported>Student2017: /* Methods */

2017-12-16T00:39:23Z

Methods

← Older revision		Revision as of 00:39, 16 December 2017
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	To recall, extrinsic parameters describe the mapping from the 3D world coordinates to the 3D camera coordinates. It is composed of the rotation matrix and the translation vector. In our setting, we know the location of the object and the camera in world coordinates and the orientation of the camera in terms of the ‘up’ vector. Using these, the Extrinsic matrix is computed as follows;		To recall, extrinsic parameters describe the mapping from the 3D world coordinates to the 3D camera coordinates. It is composed of the rotation matrix and the translation vector. In our setting, we know the location of the object and the camera in world coordinates and the orientation of the camera in terms of the ‘up’ vector. Using these, the Extrinsic matrix is computed as follows;

	* Let <math>C</math> be the camera center, <math>p</math> – object location, <math>u</math> – camera ‘up’ vector.		* Let <math>C \in \mathbb{R}^{3 \times 1}</math> be the camera center, <math>p \in \mathbb{R}^{3 \times 1}</math> – object location, <math>u \in \mathbb{R}^{3 \times 1}</math> – camera ‘up’ vector.
	* Compute the following;		* Compute the following;
	** <math>L = \frac{p - C}{\|\|p - C\|\|}, s = \frac{L \times u}{\|\|L \times u\|\|}, u^' = s \times L</math>		** <math>L = \frac{p - C}{\|\|p - C\|\|}, s = \frac{L \times u}{\|\|L \times u\|\|}, u^' = s \times L</math>
	** The rotation matrix is <math> R = \begin{bmatrix} - & s & - \\ - & u^' & - \\ - & -L & - \end{bmatrix} \in \mathbb{R}^{3 \times 3} </math>		** The rotation matrix is <math> R = \begin{bmatrix} - & s^T & - \\ - & u^'^T & - \\ - & -L^T & - \end{bmatrix} \in \mathbb{R}^{3 \times 3} </math>
	** The translation vector is obtained as <math>t= -RC \in \mathbb{R}^{3 x 1}</math>		** The translation vector is obtained as <math>t= -RC \in \mathbb{R}^{3 x 1}</math>
	** The extrinsic matrix is the block matrix given by <math>\begin{bmatrix} R & t \\ 0 & 1 \end{bmatrix} \in \mathbb{R}^{4 \times 4}</math>		** The extrinsic matrix is the block matrix given by <math>\begin{bmatrix} R & t \\ 0 & 1 \end{bmatrix} \in \mathbb{R}^{4 \times 4}</math>

imported>Student2017 at 17:08, 15 December 2017

2017-12-15T17:08:55Z

← Older revision		Revision as of 17:08, 15 December 2017
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	<math>P = \begin{bmatrix} R & \| & t \end{bmatrix} K</math>		<math>P = \begin{bmatrix} R & \| & t \end{bmatrix} K</math>

	[R \| t] is the extrinsic matrix, it describes the 3D spatial relationship between the filming object and the camera. It is a 3x3 rotation matrix (R) concatenating with a 3x1 translation vector (t), making a 3x4 matrix. This operation is translation from ~~the~~ Euclidean ~~coordinates~~ to homogeneous ~~coordinates~~ which is a standard procedure in computer graphics. This matrix represents the location of the camera in the 3D scene, as well as the direction it is looking at. It provides rigid transformation from the 3D real world coordinates to the 3D camera’s coordinates.		[R \| t] is the extrinsic matrix, it describes the 3D spatial relationship between the filming object and the camera. It is a 3x3 rotation matrix (R) concatenating with a 3x1 translation vector (t), making a 3x4 matrix. This operation is a translation from Euclidean coordinate to homogeneous coordinate, which is a standard procedure in computer graphics. This matrix represents the location of the camera in the 3D scene, as well as the direction it is looking at. It provides rigid transformation from the 3D real world coordinates to the 3D camera’s coordinates.
	The Intrinsic parameters K characterizes the geometric parameters of the camera including focal length, optical center, and skew coefficient. This matrix then projects the 3D camera coordinates into the image 2D coordinates. The complete image capturing process has two transformation steps, as illustrated in Fig. 1.		The Intrinsic parameters K characterizes the geometric parameters of the camera including focal length, optical center, and skew coefficient. This matrix then projects the 3D camera coordinates into the image 2D coordinates. The complete image capturing process has two transformation steps, as illustrated in Fig. 1.

imported>Student2017 at 17:07, 15 December 2017

2017-12-15T17:07:46Z

← Older revision		Revision as of 17:07, 15 December 2017
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	<math>P = \begin{bmatrix} R & \| & t \end{bmatrix} K</math>		<math>P = \begin{bmatrix} R & \| & t \end{bmatrix} K</math>

	[R \| t] is the extrinsic matrix, it describes the 3D spatial relationship between the filming object and the camera. It is a 3x3 rotation matrix (R) concatenating with a 3x1 translation vector (t), making a 3x4 matrix. This matrix represents the location of the camera in the 3D scene, as well as the direction it is looking at. It provides rigid transformation from the 3D real world coordinates to the 3D camera’s coordinates.		[R \| t] is the extrinsic matrix, it describes the 3D spatial relationship between the filming object and the camera. It is a 3x3 rotation matrix (R) concatenating with a 3x1 translation vector (t), making a 3x4 matrix. This operation is translation from the Euclidean coordinates to homogeneous coordinates which is a standard procedure in computer graphics. This matrix represents the location of the camera in the 3D scene, as well as the direction it is looking at. It provides rigid transformation from the 3D real world coordinates to the 3D camera’s coordinates.
	The Intrinsic parameters K characterizes the geometric parameters of the camera including focal length, optical center, and skew coefficient. This matrix then projects the 3D camera coordinates into the image 2D coordinates. The complete image capturing process has two transformation steps, as illustrated in Fig. 1.		The Intrinsic parameters K characterizes the geometric parameters of the camera including focal length, optical center, and skew coefficient. This matrix then projects the 3D camera coordinates into the image 2D coordinates. The complete image capturing process has two transformation steps, as illustrated in Fig. 1.

imported>Student2017: /* Appendix I */

2017-12-15T16:17:13Z

Appendix I

← Older revision		Revision as of 16:17, 15 December 2017
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	== Appendix I==		== Appendix I==
	Our code is available at github (https://github.com/VitaminAJ/Simulation-of-stereo-camera-calibration-parameters.git). To run the code, you need to install docker container, iset (add path of iset) and pbrt-v2.		Our code is available at github (https://github.com/VitaminAJ/Simulation-of-stereo-camera-calibration-parameters.git). To run the code, you need to install docker container, iset (add path of iset) and pbrt-v2.


	~~You can include images as follows (you will need to upload the image first using the toolbox on the left bar.):~~
	~~[[File:Screen_Shot_2016-11-29_at_7.05.37_PM.png\|200px]]~~

	==Appendix II==		==Appendix II==
	Work breakdown		Work breakdown
	The JEDEYE calibration was lead by Bryce, and Anqi and Varsha also contributed in the initial calibration steps and image capturing. For the simulation of stereo camera parameters, Anqi created the simulation environment. Varsha created the scripts for calculation of intrinsic and extrinsic parameters. Anqi and Varsha tuned the parameters of the settings and calibrated the images together.		The JEDEYE calibration was lead by Bryce, and Anqi and Varsha also contributed in the initial calibration steps and image capturing. For the simulation of stereo camera parameters, Anqi created the simulation environment. Varsha created the scripts for calculation of intrinsic and extrinsic parameters. Anqi and Varsha tuned the parameters of the settings and calibrated the images together.

imported>Student2017: /* Part II Simulation */

2017-12-15T16:12:49Z

Part II Simulation

← Older revision		Revision as of 16:12, 15 December 2017
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	==Part II Simulation==		==Part II Simulation==
	~~'''~~Goal~~'''~~		===Goal===

	1. Simulate stereo camera images in any given 3D scene.		1. Simulate stereo camera images in any given 3D scene.
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	~~'''~~Methods~~'''~~		===Methods===

	'''1. Simulation environment setup:'''		'''1. Simulation environment setup:'''

imported>Student2017: /* Appendix I */

2017-12-15T12:00:59Z

Appendix I

← Older revision		Revision as of 12:00, 15 December 2017
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	You can include images as follows (you will need to upload the image first using the toolbox on the left bar.):		You can include images as follows (you will need to upload the image first using the toolbox on the left bar.):
	[[File:Screen_Shot_2016-11-29_at_7.05.37_PM.png\|200px]]		[[File:Screen_Shot_2016-11-29_at_7.05.37_PM.png\|200px]]

	~~[[File:Transform_math.png\|300px]]~~

	==Appendix II==		==Appendix II==
	Work breakdown		Work breakdown
	The JEDEYE calibration was lead by Bryce, and Anqi and Varsha also contributed in the initial calibration steps and image capturing. For the simulation of stereo camera parameters, Anqi created the simulation environment. Varsha created the scripts for calculation of intrinsic and extrinsic parameters. Anqi and Varsha tuned the parameters of the settings and calibrated the images together.		The JEDEYE calibration was lead by Bryce, and Anqi and Varsha also contributed in the initial calibration steps and image capturing. For the simulation of stereo camera parameters, Anqi created the simulation environment. Varsha created the scripts for calculation of intrinsic and extrinsic parameters. Anqi and Varsha tuned the parameters of the settings and calibrated the images together.

imported>Student2017: /* Appendix I */

2017-12-15T12:00:22Z

Appendix I

← Older revision		Revision as of 12:00, 15 December 2017
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	[[File:Screen_Shot_2016-11-29_at_7.05.37_PM.png\|200px]]		[[File:Screen_Shot_2016-11-29_at_7.05.37_PM.png\|200px]]

	~~http~~:~~//scarlet.stanford.edu/teach/images/8/85/~~Transform_math.png		[[File:Transform_math.png\|300px]]

	==Appendix II==		==Appendix II==
	Work breakdown		Work breakdown
	The JEDEYE calibration was lead by Bryce, and Anqi and Varsha also contributed in the initial calibration steps and image capturing. For the simulation of stereo camera parameters, Anqi created the simulation environment. Varsha created the scripts for calculation of intrinsic and extrinsic parameters. Anqi and Varsha tuned the parameters of the settings and calibrated the images together.		The JEDEYE calibration was lead by Bryce, and Anqi and Varsha also contributed in the initial calibration steps and image capturing. For the simulation of stereo camera parameters, Anqi created the simulation environment. Varsha created the scripts for calculation of intrinsic and extrinsic parameters. Anqi and Varsha tuned the parameters of the settings and calibrated the images together.