estimating camera measures

You will likely run into cases where you cannot use the given fiducial markers and/or the calibration report in order to resample the images. This might be because:

• the fiducial markers are obscured or otherwise cut off in the scans;

• the fiducial markers are ambiguous;

• the calibration report has been lost to time, or you otherwise do not have a calibration report.

In these cases, you can use a combination of spymicmac.matching, spymicmac.micmac.batch_saisie_fids() and spymicmac.micmac.estimate_measures_camera() to generate a MeasuresCamera.xml file with the fiducial marker locations.

identifying fiducial markers

Important

When you are inputting fiducial marker locations using spymicmac.micmac.batch_saisie_fids(), make sure your image orientation is consistent!

Scans will sometimes have the images rotated, but not consistently. For example, this image, which has the data strip on the right side, whereas most of the others have the data strip on the left:

Most calibration reports will give the fiducial marker locations with the assumption that the data strip is on the left-hand side of the image, but be sure to check!

Create MeasuresIm files for a number of images - you don’t necessarily need to use all of the images that you have (but at the same time, you’ll need to do this step anyway), but you should come up with a sufficient sample size to be able to smooth over any differences due to difficulty identifying marks, or issues with film development or scanning.

worked example

To illustrate how this works, we’re going to use an example for a set of images that does have a calibration certificate:

The calibration certificate for these images can be downloaded from the USGS Camera Calibration Reports Database - this is Report Number RT-R/403:

Translating the coordinates from the report using spymicmac.micmac.create_measures_xml(), we have the following locations for our fiducial markers:

name	x	y
P1	8.710	217.292
P2	217.278	8.706
P3	8.693	8.704
P4	217.290	217.292
P5	0.0	112.992
P6	225.969	112.989
P7	112.998	0.0
P8	113.001	225.991

To be able to use spymicmac.micmac.estimate_measures_camera(), we need the following information, detailed/illustrated in the next sections:

• approx: a DataFrame of approximate fiducial marker locations, or a dict of fiducial marker names and their angle with respect to the principal point;

• pairs: a list of pairs of co-linear fiducial markers;

We also need to know the scanning resolution of the image in meters, to be able to convert from pixels to camera geometry - for example, if the images are scanned at 25 microns (25 µm per pixel), the value of scan_res should be 2.5e-5 (\(2.5 \times 10^{-5}\) m per pixel).

approximate measures

The following code will create a DataFrame with the approximate fiducial marker locations for the camera illustrated above:

Note

Note the convention here, with the y (i) axis starting with 0 at the top of the image, increasing to 1 at the bottom of the image.

approx = pd.DataFrame(data={'name': ['P1', 'P2', 'P3', 'P4', 'P5', 'P6', 'P7', 'P8'],
                            'j': [0, 1, 0, 1, 0, 1, 0.5, 0.5],
                            'i': [1, 0, 0, 1, 0.5, 0.5, 0, 1]}).set_index('name')

name	x	y
P1	0	1
P2	1	0
P3	0	0
P4	1	1
P5	0	0.5
P6	1	0.5
P7	0.5	0
P8	0.5	0

Note

These values don’t need to be exact - this is primarily used to align the locations measured for each image. Values of 0, 1 for corner fiducials and 0, 0.5, or 1 for mid-side fiducials should be sufficient.

Alternatively, we can pass a dict of name/value pairs with the fiducial marker names and the angle they make with respect to the principal point and the x-axis.

Here, we’re imagining that the principal point is the origin of a coordinate axis, with the x-axis increasing toward the right, and the y-axis increasing towards the top of the image:

Using the examples above, P1 makes an angle of 225° (or \(5\pi / 4\)); P2 makes an angle of 45° (or \(\pi\)/4), P3 makes an angle of 135° (or \(3\pi / 4\)), and so on:

angles = {'P1': 225, 'P2': 45, 'P3': 135, 'P4': 315,
          'P5': 180, 'P6': 0, 'P7': 90, 'P8': 270}

Note

Angle values can be either given in degrees or radians.

collinear pairs

Finally, we need a list of the collinear pairs - that is, the pairs of fiducial markers that are co-linear with the principal point:

In the example above, P1 and P2 are collinear, as the line connecting them passes through the principal point. A list of each of the pairs of collinear markers would then be:

pairs = [('P1', 'P2'), ('P3', 'P4'),
         ('P5', 'P6'), ('P7', 'P8')]

scanning resolution

The last piece of information that we need is the scanning resolution, in m. If you happen to know this value (for example, you know that the images were scanned at 25 micron resolution), then you can use this directly.

However, it is worth noting that the nominal/reported value is not necessarily the true value, and it is perhaps worth calculating the distance between a pair of collinear markers (or several pairs). Using calibration reports for similar cameras, you can then estimate the scanning resolution by dividing the expected distance in mm by the measured distance in pixels.

checking the results

With these pieces in place, we can run estimate_measures_camera. This will read all of the MeasuresIm files in the given ori directory (e.g., InterneScan for Ori-InterneScan), rotate the coordinates to match with the values given by approx, and scale them with the value given by scan_res:

import pandas as pd
from spymicmac import micmac


approx = pd.DataFrame(data={'name': ['P1', 'P2', 'P3', 'P4', 'P5', 'P6', 'P7', 'P8'],
                            'j': [0, 1, 0, 1, 0, 1, 0.5, 0.5],
                            'i': [1, 0, 0, 1, 0.5, 0.5, 0, 1]}).set_index('name')

pairs = [('P1', 'P2'), ('P3', 'P4'),
         ('P5', 'P6'), ('P7', 'P8')]

micmac.estimate_measures_camera(
    approx,
    pairs,
    ori='InterneScan',
    scan_res=2.5e-5,
    how='mean', # choose between mean, median
    write_xml=True # if True, creates Ori-{ori}/MeasuresCamera.xml
    inverted=True # y-axis used for approx is inverted
)

This will create two .csv files in the current directory:

• AverageMeasures.csv, containing the average location calculated from each MeasuresIm file;

• AllMeasures.csv, containing the (rotated) locations for each MeasuresIm file.

If write_xml is True, this will also create Ori-{ori}/MeasuresCamera.xml, which can be read by, for example, mm3d ReSamFid.

To see how we’ve done, let’s compare the results from this set of images with the calibration report:

This looks rather good - on our diagram, the locations all align reasonably well. If we take the difference between the values from the report, and the values estimated by estimate_measures_camera, we can see that the locations agree to better than 0.04 mm:

name	\(\Delta x\)	\(\Delta y\)
P1	0.0191	-0.0312
P2	0.0247	-0.0198
P3	-0.0086	-0.0200
P4	-0.0117	-0.0152
P5	-0.0192	0.0064
P6	0.0163	0.0046
P7	0.0025	0.0041
P8	-0.0064	0.0305

While this doesn’t replace the value of having a contemporary calibration report for a particular camera, this hopefully provides a reasonable approximation to the correct camera geometry - especially for cases where the original fiducial markers are either ambiguous or cut out of the scan.