High Speed Vision System and Object Tracking - Revision history

ClaraSmart: /* For Tracking Objects in 2D */

2010-06-05T21:48:28Z

For Tracking Objects in 2D

← Older revision		Revision as of 16:48, 5 June 2010
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	==For Tracking Objects in 2D==		==For Tracking Objects in 2D==
	To calibrate the camera to track objects in a plane, first create a calibration grid. The Calibration Toolbox includes a calibration template of black and white squares of side length = ~~3cm~~. Print it off and mount it on a sheet of aluminum, foam core board or PVC to create a stiff backing. This grid must be as flat and uniform as possible to obtain an accurate calibration.		To calibrate the camera to track objects in a plane, first create a calibration grid. The Calibration Toolbox includes a calibration template of black and white squares of side length = 30mm. Print it off and mount it on a sheet of aluminum, foam core board or PVC to create a stiff backing. This grid must be as flat and uniform as possible to obtain an accurate calibration.

	===Intrinsic Parameters===		===Intrinsic Parameters===

ClaraSmart: /* Example Intrinsic Parameters (LIMS Lab, Winter 2010) */

2010-06-05T21:46:54Z

Example Intrinsic Parameters (LIMS Lab, Winter 2010)

← Older revision		Revision as of 16:46, 5 June 2010
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	Focal Length: fc = [ 1219.49486 1227.09415 ] ± [ 1.98092 1.95916 ]		Focal Length: fc = [ 1219.49486 1227.09415 ] ± [ 1.98092 1.95916 ]

	Principal point: cc = [ 502.28854 524.25824 ] ± [ 1.26522 1.07298 ]		Principal point: cc = [ 502.28854 524.25824 ] ± [ 1.26522 1.07298 ]

	Skew: alpha_c = [ 0.00000 ] ± [ 0.00000 ] => angle of pixel axes = 90.00000 ± 0.00000 degrees		Skew: alpha_c = [ 0.00000 ] ± [ 0.00000 ] => angle of pixel axes = 90.00000 ± 0.00000 degrees

	Distortion: kc = [ -0.39504 0.36943 -0.00018 -0.00105 0.00000 ] ± [ 0.00307 0.01033 0.00016 0.00021 0.00000 ]		Distortion: kc = [ -0.39504 0.36943 -0.00018 -0.00105 0.00000 ] ± [ 0.00307 0.01033 0.00016 0.00021 0.00000 ]

	Pixel error: err = [ 0.27578 0.25400 ]		Pixel error: err = [ 0.27578 0.25400 ]

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	[[Image:CalibImages.jpg\|thumb\|200px\|Mosaic of Calibration Images\|left]]		[[Image:CalibImages.jpg\|thumb\|200px\|Mosaic of Calibration Images\|left]]
	[[Image:ErrorPlot.jpg\|thumb\|~~200px~~\|Error Plot following optimization\|~~right~~]]		[[Image:ErrorPlot.jpg\|thumb\|400px\|Error Plot following optimization\|center]]

ClaraSmart: /* Example Intrinsic Parameters (LIMS Lab, Winter 2010) */

2010-06-05T21:45:28Z

Example Intrinsic Parameters (LIMS Lab, Winter 2010)

← Older revision		Revision as of 16:45, 5 June 2010
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	Note: The numerical errors are approximately three times the standard deviations (for reference).		Note: The numerical errors are approximately three times the standard deviations (for reference).

	[[~~image~~:~~2D_imaging~~.jpg\|thumb\|~~500px~~\|~~'''Figure 3:''' Projection~~ of ~~calibration~~ ~~grid onto the image plane.~~\|~~center~~]]		[[Image:CalibImages.jpg\|thumb\|200px\|Mosaic of Calibration Images\|left]]
	[[Image:~~CalibImages~~.jpg\|thumb\|~~500px~~\|~~Mosaic~~ of ~~Calibration~~ ~~Images~~\|~~left~~]]		[[Image:ErrorPlot.jpg\|thumb\|200px\|Error Plot following optimization\|right]]
	[[Image:ErrorPlot.jpgthumb\|500px\|Error Plot following optimization\|right]]

ClaraSmart: /* Example Intrinsic Parameters (LIMS Lab, Winter 2010) */

2010-06-05T21:44:26Z

Example Intrinsic Parameters (LIMS Lab, Winter 2010)

← Older revision		Revision as of 16:44, 5 June 2010
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	Note: The numerical errors are approximately three times the standard deviations (for reference).		Note: The numerical errors are approximately three times the standard deviations (for reference).

			[[image:2D_imaging.jpg\|thumb\|500px\|'''Figure 3:''' Projection of calibration grid onto the image plane.\|center]]
	[[Image:CalibImages.jpg]]
			[[Image:CalibImages.jpg\|thumb\|500px\|Mosaic of Calibration Images\|left]]
	[[Image:ErrorPlot.jpg]]
			[[Image:ErrorPlot.jpgthumb\|500px\|Error Plot following optimization\|right]]

ClaraSmart: /* Example Intrinsic Parameters (LIMS Lab, Winter 2010) */

2010-06-05T21:38:13Z

Example Intrinsic Parameters (LIMS Lab, Winter 2010)

← Older revision		Revision as of 16:38, 5 June 2010
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	Number of Images = 15		Number of Images = 15

			Error optimization completed by adjusting the values of winty and wintx for various images.

			Calibration results after optimization (with uncertainties):

			Focal Length: fc = [ 1219.49486 1227.09415 ] ± [ 1.98092 1.95916 ]
			Principal point: cc = [ 502.28854 524.25824 ] ± [ 1.26522 1.07298 ]
			Skew: alpha_c = [ 0.00000 ] ± [ 0.00000 ] => angle of pixel axes = 90.00000 ± 0.00000 degrees
			Distortion: kc = [ -0.39504 0.36943 -0.00018 -0.00105 0.00000 ] ± [ 0.00307 0.01033 0.00016 0.00021 0.00000 ]
			Pixel error: err = [ 0.27578 0.25400 ]

			Note: The numerical errors are approximately three times the standard deviations (for reference).

			[[Image:CalibImages.jpg]]
			[[Image:ErrorPlot.jpg]]

ClaraSmart: /* Calibrating the High Speed Camera */

2010-06-05T21:30:21Z

Calibrating the High Speed Camera

← Older revision		Revision as of 16:30, 5 June 2010
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	In order to calibrate the camera, download the [http://www.vision.caltech.edu/bouguetj/calib_doc/ Camera Calibration Toolbox for Matlab]. This resource includes detailed descriptions of how to use the various features of the toolbox as well as descriptions of the calibration parameters.		In order to calibrate the camera, download the [http://www.vision.caltech.edu/bouguetj/calib_doc/ Camera Calibration Toolbox for Matlab]. This resource includes detailed descriptions of how to use the various features of the toolbox as well as descriptions of the calibration parameters.

			Once downloaded, to open the gui in matlab, go to the toolbox directory then type 'calib_gui' in the command window. (Then select standard memory).

	==For Tracking Objects in 2D==		==For Tracking Objects in 2D==
	To calibrate the camera to track objects in a plane, first create a calibration grid. The Calibration Toolbox includes a calibration template of black and white squares of side length = 3cm. Print it off and mount it on a sheet of aluminum, foam core board or PVC to create a stiff backing. This grid must be as flat and uniform as possible to obtain an accurate calibration.		To calibrate the camera to track objects in a plane, first create a calibration grid. The Calibration Toolbox includes a calibration template of black and white squares of side length = 3cm. Print it off and mount it on a sheet of aluminum, foam core board or PVC to create a stiff backing. This grid must be as flat and uniform as possible to obtain an accurate calibration.

ClaraSmart: /* Example Intrinsic Parameters (LIMS Lab, Winter 2010) */

2010-06-05T21:14:06Z

Example Intrinsic Parameters (LIMS Lab, Winter 2010)

← Older revision		Revision as of 16:14, 5 June 2010
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	The below example was completed for the high speed vision system in the LIMS lab during Winter Quarter 2010.		The below example was completed for the high speed vision system in the LIMS lab during Winter Quarter 2010.

			Number of Images = 15

ClaraSmart: /* Error Minimization of Calibration Coefficients */

2010-06-05T21:02:55Z

Error Minimization of Calibration Coefficients

← Older revision		Revision as of 16:02, 5 June 2010
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	Further information and examples can be found at [http://www.vision.caltech.edu/bouguetj/calib_doc/htmls/example.html, the first calibration example].		Further information and examples can be found at [http://www.vision.caltech.edu/bouguetj/calib_doc/htmls/example.html, the first calibration example].

			==Example Intrinsic Parameters (LIMS Lab, Winter 2010) ==

			The below example was completed for the high speed vision system in the LIMS lab during Winter Quarter 2010.

ClaraSmart: /* Error Minimization of Calibration Coefficients */

2010-06-05T21:01:34Z

Error Minimization of Calibration Coefficients

← Older revision		Revision as of 16:01, 5 June 2010
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	==Error Minimization of Calibration Coefficients ==		==Error Minimization of Calibration Coefficients ==

			Following the computation of the intrinsic parameters, the relative error can be analyzed using the calibration toolbox. To see the error in a graphical form click 'Analyze Error' in the main gui. This plot will show the error in pixel units. The different point colors represent different images used for calibration. To begin to optimize this error, click on an outlier point. The image number and point of this point will be displayed in the matlab command window. Click outliers of the same color, is there a specific image that has many errors?

			You can also view the projected calibration points on a specific image by clicking 'Reproject on Image' and at the prompt enter the number of the error prone image. This will allow you to see the points which are creating the most error. If the calibration points are significantly off the corners of the grid, it may be a good idea to use 'Add/Suppress Images' to remove then recalibrate the image. (You can also click all corners manually)

			However, if the entire image is not error prone, it is possible to minimize the error by changing the dimensions of the "search box" for which the calibration algorithm looks for a corner. This is accomplished by changing the values of wintx and winty, the default values during calibration are set at 5. To do this click 'Recomp Corners' in the calibration gui, then at the prompt for wintx and winty enter a different (typically larger value, ie 8). Then at the prompt for the numbers of the images for which to recompute the corners, enter the numbers of the images with the error outliers as determined above.

			Repeat this process until the error is within reason. (Typically 3-4 pixels, but dependent on resolution, distance from object, pixel size and application)

			Further information and examples can be found at [http://www.vision.caltech.edu/bouguetj/calib_doc/htmls/example.html, the first calibration example].

ClaraSmart: /* Calculating the Position of an Object on a Plane: Using Matlab */

2010-06-05T20:43:04Z

Calculating the Position of an Object on a Plane: Using Matlab

← Older revision		Revision as of 15:43, 5 June 2010
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	(It is assumed the Z value is a plane and is a constant known parameter)		(It is assumed the Z value is a plane and is a constant known parameter)

	[World_x, World_y] = Transpose(Rc_ext) * (~~zdist~~ *(normalize([pix_x, pix_y], fc, cc, kc, alpha_a), 1) - Tc_ext)		[World_x, World_y] = Transpose(Rc_ext) * (zdist_pix *(normalize([pix_x, pix_y], fc, cc, kc, alpha_a), 1) - Tc_ext)

	Where:		Where:
	Rc_Ext and Tc_ext are parameters from the extrinsic calibration		Rc_Ext and Tc_ext are parameters from the extrinsic calibration
	~~zdist~~ is the distance from the focal point to the object in ~~world units~~. (measure distance from camera to object using meter stick ~~etc~~)		zdist_pix is the distance from the focal point to the object in pixels. (measure distance from camera to object using meter stick then convert to pixels by determining the number of pixels per cm in calibration image at that distance)
	pix_x and pix_y are the camera pixel coordinates corresponding to the desired world point		pix_x and pix_y are the camera pixel coordinates corresponding to the desired world point
	fc, cc, kc and alpha_a are parameters from the intrinsic camera calibration		fc, cc, kc and alpha_a are parameters from the intrinsic camera calibration