Camera Calibration PhaseOne 80mm Lens A & B For Jamie Heath Terrasaurus Aerial Photography Ltd.
Page 2 PhaseOne with 80mm lens
PhaseOne with 80mm lens Table of Contents Executive Summary 5 Camera Calibration Results 6 Results table from MSAT 7 Comparing the Two Calibrations 8 Results from CAST Error! Bookmark not defined. The Measurement Process 8 The Wall 8 Taut String Method 8 Camera Positions 9 Second Set of Readings Error! Bookmark not defined. Computer Processing 11 Resample 11 MSAT 11 Checking Results Error! Bookmark not defined. Camera Calibration Report 80mm 13 Conclusions 19 List of Figures & Tables Figure 1: BCIT Camera Calibration Wall... 10 Figure 2: Taut String Method... 10 Figure 3: Camera Positions... 10 Figure 4: Resample Auto Measuring System... 12 Figure 5: Resample measures line strings... 12 Figure 6: Manual Edit and Renumbering... 12 Table 1 : Camera Calibration Summary... 8 Page 4
Camera Calibration Executive Summary On September 3 rd, 2012 a camera calibration was performed at BCIT by Eric Saczuk, Ph.D. on the camera PhaseOne owned by Terrasaurus Aerial Photography Ltd. Two lenses were provided, both with a focal length of 80mm. This camera calibration was successful and the results are shown in the section Camera Calibration Results. The main values that would be used in creating a virtual camera for photogrammetric measurement are listed in italics at the top of page 4. The next section describes the measurement process. The calibration wall is described along with the system of using taut strings to define lines that may be used to determine lens distortion. The camera positions and the number of exposures required are discussed. In the Computation Process section the strings and control points are measured by a program called Resample. This requires a manual edit step to ensure that false readings are removed and that all the lines and points have consistent numbering. Finally, the bundle adjustment is performed by a program called MSAT which calibrates the lens/camera. The results are tested using the program CAST which compares the results of different calibrations to see if there are any changes to the geometry of the camera over time. The lens is removed and replaced and this might have consequences on the calibration. In the case of this camera and lenses, the results of CAST show that this camera is consistent between calibrations. In conclusion the camera calibration of the PhaseOne supplied by Terrasaurus Aerial Photography was successful. Page 5
PhaseOne with 80mm lens Camera Calibration Results PhaseOne with Lens A distortions removed: 80mm Lens Xp = 0.058mm Principal Point Yp = -0.126mm Principal Point C = 80.542mm Focal Length (average) K1 = 5.3133 x 10-7 Lens distortion (average) Dim = 8984 X 6732 Sensor Dimensions 53.904 X 40.392mm Pixel = 0.006 X 0.006 Pixel Size PhaseOne with Lens B distortions removed: 80mm Lens Xp = 0.092mm Principal Point Yp = -0.104mm Principal Point C = 80.478mm Focal Length (average) K1 = 5.3252 x 10-7 Lens distortion (average) Dim = 8984 X 6732 Sensor Dimensions 53.904 X 40.392mm Pixel = 0.006 X 0.006 Pixel Size PhaseOne with Lens A distortions retained: 80mm Lens Xp = 0.054mm Principal Point Yp = -0.120mm Principal Point C = 80.559mm Focal Length (average) K1 = -7.0591 x 10-6 Lens distortion (average) Dim = 8984 X 6732 Sensor Dimensions 53.904 X 40.392mm Pixel = 0.006 X 0.006 Pixel Size PhaseOne with Lens B distortions retained: 80mm Lens Xp = 0.101mm Principal Point Yp = -0.116mm Principal Point C = 80.562mm Focal Length (average) K1 = -6.8510 x 10-6 Lens distortion (average) Dim = 8984 X 6732 Sensor Dimensions 53.904 X 40.392mm Pixel = 0.006 X 0.006 Pixel Size Page 6
Camera Calibration Results table from MSAT The values above were extracted from the results file created by the MSAT bundle adjustment program. In the case of the PhaseOne camera the results from MSAT are very encouraging. Table 1 shows three columns with results from the first set of calibration pictures, Set 1, the results of the last set of calibration pictures, Set 2 and the difference between the two calibrations. The first 3 parameters are the X and Y coordinate of the perspective centre and the focal length, C. These are very similar in value from Set 1 to Set 2 in the order or 1/100 of a mm. The lens distortion value K1 has no measurable difference from Set 1 to Set 2. Page 7
PhaseOne with 80mm lens Comparing the Two Calibrations Two calibrations were performed on the lens. The lens was removed between each calibration to verify that the mounting mechanism is consistent. The two calibrations produce slightly different results. The differences could be caused by minor changes in the lens position and minor differences in the readings of the control points and strings. The program CAST is needed to determine whether two sets of Interior Orientation Parameters are equivalent to one another. Table 1: Camera Calibration Summary 80mm Lens A distortions removed Lens B distortions removed Difference xp 0.058 0.092 0.034mm yp -0.126-0.104 0.022mm C 80.542 80.478 0.064mm K1 5.3133 x 10-7 5.3252 x 10-7 1.1951E-09 80mm Lens A distortions retained Lens B distortions retained Difference xp 0.054 0.101 0.047mm yp -0.120-0.116 0.004mm C 80.559 80.562 0.003mm K1-7.0591 x 10-6 -6.8510 x 10-6 2.08077E-07 The Measurement Process The Wall The BCIT calibration wall consists of two components, the control targets and the frame. There are 16 control targets that have been cemented to the wall. These are made of non fading signpost material. Their positions have been measured using survey quality total stations to sub mm accuracy. The frame is a wooden structure that can be assembled on the spot. The frame is stored when not in use. The frame is approximately 5 meters by 4 meters. Once the frame has been assembled, strings are threaded through islets around the edges and pulled tight. The tension on the strings is maintained by bungee cords. Taut String Method This system of calibrating medium format non-metric cameras has been developed by Ayman Habib at the University of Calgary. The system works by taking a series of photographs of the wall. The focal length and perspective centres are calculated by using the control points. The radial lens distortion is calculated using the strings. The strings are assumed to be straight lines and so any deviation from this must be caused by lens distortion which can be measured and calculated. Page 8
Camera Calibration Camera Positions Six camera positions are used for taking the photographs; left, middle, right, and both top and bottom. The distance from the wall is determined by the focal length of the lens. The bottom pictures are taken from a tripod set low on the ground. For the top pictures the camera tripod was set on top of a set of moveable metal stairs. In each position one landscape (horizontal) and one portrait (vertical) picture is taken. This produces 12 pictures per set calibration. They are renumbered as LBH, LBV, MBH, MBV, RBH, RBV, LTH, LTV, MTH, MTV, RTH, and RTV where L= Left, M=Middle, R=Right, B= Bottom, T=Top, H=Horizontal, V=Vertical. Page 9
PhaseOne with 80mm lens Figure 1: BCIT Camera Calibration Wall Sixteen fixed surveyed targets are attached to the wall. The wooded frame is assembled for the calibration. Figure 2: Taut String Method Strings are threaded through hooks along the wooden frame. These strings are pulled tight to produce straight lines. These lines are used by the software to determine lens distortion. Figure 3: Camera Positions 12 Photographs are taken of the wall from six positions. At each position the camera is rotated so that one photo is landscape and the other is portrait orientation. Page 10
Camera Calibration Computer Processing Resample Resample is part of the University of Calgary package for camera calibration. Its task is the automatic measurement of lines and points on the 12 photographs taken for the calibration. The program also allows the operator to edit the measurement. Extra or incorrect lines or points may be deleted. Missing lines or points may be measured. Existing lines may be edited, for example one bad point on a line may be removed. Lines and points can also be renumbered. The automatic measurement of lines and points is quite computer intensive. In this calibration session two camera lenses were calibrated Lens A and Lens B, both 80mm. The first image on the opposite page, Figure 4, shows one of the stages of the resample program as it tries to isolate line strings and points from the other background objects in the image. The second image, Figure 5, shows lines that have been measured. The strings of coloured crosses indicate measurements. On this particular image many of the shadows are also measured and will have to be removed. Resample is fairly good at distinguishing shadows from the real line especially if the two are very close together. The bottom image, Figure 6, shows the file after manual editing. The incorrect lines have been removed and the points measured and numbered. The manual editing can be time consuming as all the lines and all the points must be numbered in the same way for all pictures. MSAT Once the measuring stage is completed the measured files, one for lines and one for control points are translated into a different format. The program MSAT uses the lines and points files to run a bundle adjustment and calculate the camera parameters. This program is very sensitive to any mistakes in point numbering or line numbering. It also requires series of input files that contain the control coordinates and the approximate orientations of the cameras. Diligence is critical to make sure the values are correct and in the correct format within the files for the successful execution of the program. The final results file shows all the computations and different iterations that took place through the adjustment. There is a summary of the parameters near the end of the file and these will be used by other processes when using the camera to perform photogrammetry. Page 11
PhaseOne with 80mm lens Figure 4: Resample Auto Measuring System Resample uses specific image processing techniques to identify stings and control points within the image. Figure 5: Resample measures line strings The strings are measured and numbered. Sometimes shadows or other lines on the wall are also measured. Figure 6: Manual Edit and Renumbering Unwanted lines and points are removed and lines and points are renumbered in each photo. Page 12
Camera Calibration Camera Calibration Report 80mm For Camera: PhaseOne 80mm Lens A distortions removed Date: September 3 rd, 2012 Pixel size: 6.0μm Sigma 2.2336965970 x 10-3 xp : 5.7758900024e-002 yp : -1.2589458809e-001 C: 8.0542399410e+001 stdev_xp: 3.3343528083e-003 stdev_yp: 3.2838406413e-003 stdev_c : 1.1266557713e-002 Dispersion: 1.1117908650e-005-3.0258344500e-007 6.5927008567e-007-3.0258344500e-007 1.0783609357e-005-1.3281358449e-006 6.5927008567e-007-1.3281358449e-006 1.2693532271e-004 Correlation: 1.1117908650e-005-2.7634495409e-002 1.7549331338e-002-2.7634495409e-002 1.0783609357e-005-3.5897911190e-002 1.7549331338e-002-3.5897911190e-002 1.2693532271e-004 Distortion: 5.3133145916e-007 stdev_k1: 2.9047043491e-008 stdev_k2: 2.2336965970e-007 stdev_p1: 2.2336965970e-007 stdev_p2: 2.2336965970e-007 stdev_a1: 2.2336965970e-005 stdev_a2: 2.2336965970e-005 Dispersion: 8.4373073558e-008 4.9894004873e-006 4.9894004873e-006 4.9894004873e-006 Page 13
PhaseOne with 80mm lens 4.9894004873e-006 4.9894004873e-006 Correlation: 8.4373073558e-008 4.9894004873e-006 4.9894004873e-006 4.9894004873e-006 4.9894004873e-006 4.9894004873e-006 For Camera: PhaseOne 80mm Lens B distortions removed Date: September 3 rd, 2012 Pixel size: 6.0μm Sigma 2.0717253384 x 10-3 xp : 9.2052825243e-002 yp : -1.0413614704e-001 C: 8.0477569544e+001 stdev_xp: 2.9667199926e-003 stdev_yp: 2.9320095353e-003 stdev_c : 9.0285480839e-003 Dispersion: 8.8014275147e-006-3.5299159857e-007 3.8228097080e-007-3.5299159857e-007 8.5966799154e-006 4.5171307025e-007 3.8228097080e-007 4.5171307025e-007 8.1514680503e-005 Correlation: 8.8014275147e-006-4.0580970808e-002 1.4272110732e-002-4.0580970808e-002 8.5966799154e-006 1.7063941882e-002 1.4272110732e-002 1.7063941882e-002 8.1514680503e-005 Distortion: 5.3252661089e-007 Page 14
Camera Calibration stdev_k1: 2.5377611516e-008 stdev_k2: 2.0717253384e-007 stdev_p1: 2.0717253384e-007 stdev_p2: 2.0717253384e-007 stdev_a1: 2.0717253384e-005 stdev_a2: 2.0717253384e-005 Dispersion: 6.4402316625e-008 4.2920458779e-006 4.2920458779e-006 4.2920458779e-006 4.2920458779e-006 4.2920458779e-006 Correlation: 6.4402316625e-008 4.2920458779e-006 4.2920458779e-006 4.2920458779e-006 4.2920458779e-006 4.2920458779e-006 Page 15
PhaseOne with 80mm lens For Camera: PhaseOne 80mm Lens A distortions retained Date: September 3 rd, 2012 Pixel size: 6.0μm Sigma 3.7125100554e-003 xp : 5.3951233865e-002 yp : -1.2007042997e-001 C: 8.0559193298e+001 stdev_xp: 5.4196261059e-003 stdev_yp: 5.3528876148e-003 stdev_c : 1.6085505200e-002 Dispersion: 2.9372347128e-005-5.4848648291e-007 1.7865349606e-006-5.4848648291e-007 2.8653405817e-005-1.6351494386e-006 1.7865349606e-006-1.6351494386e-006 2.5874347753e-004 Correlation: 2.9372347128e-005-1.8906384143e-002 2.0493091910e-002-1.8906384143e-002 2.8653405817e-005-1.8990422141e-002 2.0493091910e-002-1.8990422141e-002 2.5874347753e-004 Distortion: -7.0590949413e-006 stdev_k1: 4.1432450366e-008 stdev_k2: 3.7125100554e-007 stdev_p1: 3.7125100554e-007 stdev_p2: 3.7125100554e-007 stdev_a1: 3.7125100554e-005 stdev_a2: 3.7125100554e-005 Dispersion: 1.7166479434e-007 1.3782730912e-005 1.3782730912e-005 1.3782730912e-005 1.3782730912e-005 Page 16
Camera Calibration 1.3782730912e-005 Correlation: 1.7166479434e-007 1.3782730912e-005 1.3782730912e-005 1.3782730912e-005 1.3782730912e-005 1.3782730912e-005 For Camera: PhaseOne 80mm Lens B distortions retained Date: September 3 rd, 2012 Pixel size: 6.0μm Sigma 2.1863513935e-003 xp : 1.0097525345e-001 yp : -1.1641889779e-001 C: 8.0562413924e+001 stdev_xp: 3.0742116026e-003 stdev_yp: 3.0361842740e-003 stdev_c : 9.0062797712e-003 Dispersion: 9.4507769773e-006-3.2167562095e-007 8.1160261992e-007-3.2167562095e-007 9.2184149457e-006-2.2305109575e-007 8.1160261992e-007-2.2305109575e-007 8.1113075317e-005 Correlation: 9.4507769773e-006-3.4463252673e-002 2.9313268715e-002-3.4463252673e-002 9.2184149457e-006-8.1570063579e-003 2.9313268715e-002-8.1570063579e-003 8.1113075317e-005 Distortion: -6.8510181373e-006 stdev_k1: 2.4635280900e-008 Page 17
PhaseOne with 80mm lens stdev_k2: 2.1863513935e-007 stdev_p1: 2.1863513935e-007 stdev_p2: 2.1863513935e-007 stdev_a1: 2.1863513935e-005 stdev_a2: 2.1863513935e-005 Dispersion: 6.0689706502e-008 4.7801324160e-006 4.7801324160e-006 4.7801324160e-006 4.7801324160e-006 4.7801324160e-006 Correlation: 6.0689706502e-008 4.7801324160e-006 4.7801324160e-006 4.7801324160e-006 4.7801324160e-006 4.7801324160e-006 Page 18
Camera Calibration Conclusions This PhaseOne camera has been calibrated. The results have been tested and reveal that that camera is consistent. This camera may be used under the guidelines outlined by the: BC Government Ministry of Agriculture and Lands Integrated Land Management Bureau (ILMB) Base Mapping and Geomatic Services Branch SMALL & MEDIUM FORMAT DIGITAL CAMERA SPECIFICATIONS Integrated Land Management Bureau (ILMB) BASE MAPPING AND GEOMATIC SERVICES March 19, 2007 VERSION 0.11 Eric Saczuk, Ph.D. Instructor in Geomatics British Columbia Institute of Technology 3700 Willingdon Ave, Burnaby, BC V5G 3H2 Eric_Saczuk@bcit.ca 604 451 7197 Page 19