Distortions and Error Using Engauge Digitizer
Objective:
Determine sources of error that are inherent to measurements taken with Engauge Digitizer.
Description:
A rotary cutting mat with a 23inx35in grid was bolted onto ply wood. The bolts were placed to prevent
mat flexure from distorting the grid lines. The ply wood was then mounted to a pre-threaded steel base.
The grid was photographed with 6 ft. between the gridded surface and the camera. The camera was
aligned at the 0,0 mark on the gridded mat. The image was imported into Engauge Digitizer to
determine what error would exist in measurements. The points that were defined in Engauge Digitizer
are shown in Fig. 1.
Fig. 1: Measurement Grid with User Defined Points
Values were recorded along the lines shown in Fig. 2 to determine the extent of inaccuracies.
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Fig. 2: Lines Used to Determine Error
Results:
The first source of error discovered was in point placement. At 6ft distance between the target and
camera, the smallest observable increment in point location is .026. Fig. 3 demonstrates where this
value is displayed.
Fig.3: Point Placement Increment
Another source of error is a mismatch between the reference grid generated within Engauge Digitizer
and the grid that is observed in the images. This mismatch is caused by visual perspective and can be
seen in Fig. 4.
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Fig. 4: Comparison of Generated Grid and Photographically Observed Grid
Between the user-defined axis reference points the deviation of digitally measured values follows the
trend shown in Fig. 5.
Fig. 5: Discrepancy of Measured Values Between Defined Points
Difference of Y Values for Line
X=0
Difference (in.)
0.15
0.1
0.05
0
-0.05
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0
5
10
15
Marked Distance on Grid (in.)
3
20
The deviation of digitally measured values away from a defined point can be seen in Fig. 6.
Fig. 6: Discrepancy of Measured Values Away From Defined Point
Difference of X Values for Line Y=0
0.8
Difference (in.)
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
5
10
15
Marked Distance on Grid (in.)
20
Attempts to use obtain simple polynomial functions to map digitally measured values to the physical
dimensions have proven unsuccessful.
Recommendations:
If accurate correction of photographic distortion is desired, more detailed care will be required to
properly align the camera with the measurement grid. This could be aided using a laser such as those
typically found in inexpensive keychain-type laser pointers. An apparatus could be created with
computer aided design and/or computer aided manufacturing to mount the pointer to a typical camera
tripod. Fig. 7 shows an example of such a mount that could be set between the camera and a typical
tripod.
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Fig. 7: Possible Alignment Assisting Apparatus
Such an apparatus would ensure that the laser itself is aligned with the viewing vector of the camera.
The offset of the pointer lens from the camera lens could then be measured. This offset could then be
used to accurately place the camera relative to the grid. The shape of the laser on the grid could then
assist in reducing or eliminating angular eccentricity. With eccentricities minimized or eliminated, the
image could be closely measured to determine rates of change (partial derivatives) to quantify
perspective distortion. With photographs taken at multiple distances, one could solve for the rate of
change due to distance from target. A program could be written that could correct for parallax
distortion as well as perspective distortion. Input parameters would likely include alignment point on
the physical grid, measured rates of change, distance from camera to target, and distance from target to
measurement grid. An inexpensive rangefinder can be used to assist distance measurements. One such
rangefinder with accuracy to within .25 in. can be purchased at http://www.opticsplanet.net/soninlaser-targeting-rangefinder.html
Relevant Files and Documents:
E:\Results and Reports, End of Summer\Distortions and Error in Engauge Digitizer\Distance Distortions
with Grid.xlsx
E:\Results and Reports, End of Summer\Distortions and Error in Engauge Digitizer\SolidWorks Files
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