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

# Measurement statistics of fibers

This image analysis example came from a representative of a biotech company. He was interested in figuring out how Pixcavator can help them to automatically carry out a function that they currently do manually. They were looking for a method to automatically measure, document, and summarize characteristics of a certain kind of fibers in digital photos. Specifically, they needed: length and width, along with some very basic statistical data (size, length, width, ratio length to width, etc.), and graphical representations of the data (histograms). The image is below.

Capturing fibers wasn’t hard. Some of the irrelevant features are also captured by Pixcavator but they were easy to filter out. The results would be better with better images: uniform dark background, less reflection etc. Separating fibers from each other would be a challenge; fortunately, the fibers were to be measured as "clumps" if they are attached to each other.

Averages are computed automatically but to have the answer in inches I had to calibrate the image. For that I used the ruler in the image (all the computations in the spreadsheet [1]). I just found the coordinates of the end points of the one inch part of the ruler: (193,235) and (196,44). This gives the distance between them:

SQRT( (196-193) * (196-193) + (235-44) * (235-44) ) = 191 pixels.

So,

1 inch = 191 pixels.

Then I recomputed the averages in inches. The result:

Average width: 0.02, average length: 0.52 inches.

This does not seem too far off. There may be a discrepancy in the way people understand width and length though. Basically, we consider the area and the perimeter of the object, then find the rectangle with these measurements, then take its width and length (see Thickness and length).

The rest of the required output is easily acquired after some Excel work. The histogram of sizes (in pixels) of fibers is below.