This site is devoted to mathematics and its applications. Created and run by Peter Saveliev.

Measuring holes in a gasket

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Gasket.jpg

Given an image of a gasket. Its resolution is 300 dpi.

Next Pixcavator analyzes the image under a magnification of 13x. The shrunk image is on the right.

The analysis yields perimeters of the 4 large holes as 952, 957, 964, & 953 pixels (average = 956). When one "physically" measures these openings, the result is that the diameter is 3.452 in. = 87.68 mm. This would correspond to a circle with circumference (length) of 10.845 in. = 275.46 mm. Question: what scaling factor is appropriate to generate correct results for the area and the circumference?

To get the correct measurement for the area one shouldn't multiply by 13. This number refers to each of the dimensions of the image in pixels, i.e., the length (e.g., 100x100 turns into 1300x1300). As a result while the the lengths and perimeters go down by 13, the areas of objects go down by 13*13 = 169. Using this scaling factor produces a result that is close to the actual measurement: 956x3.6/300 = 11.472 inches.

One thing to keep in mind is that the accuracy of computation of lengths is limited (see Lengths of curves) regardless of the resolution. Assuming that the hole is known to be a circle and if you are interested in the diameter, you are better off getting it from the area of the hole instead of the perimeter - you get 3.4 inches. Similar for squares.

This is an example of calibration.

Run this analysis with Pixcavator SI.

Other image analysis examples