How many pixels does it take to find a flaw?

Here’s an interesting machine vision application, hot off the pages of Vision-Systems.com. This describes a PPT-based system that inspects O-rings. Part way through we are told that two cameras with “a per-pixel resolution of approximately 0.11 mm” can “detect cracks as small as 0.22 × 0.33 mm.”

In other words, the minimum crack that can be detected is 2 pixels by 3 pixels.

Further down the page we are then told about a third camera, “With a resolution of 0.28 mm per pixel, [which] can detect cracks and flashes as large as 0.84 × 0.84 mm.” So an area 3 pixels square is needed, according to the system developers anyway.

Now I’d like to hear what you think about this, because in my view these minimum defect sizes are pretty optimistic. Yes, it may be possible, given enough contrast, but doesn’t it rather depend on the orientation of the defect with regard to the pixels in the camera?

My rule of thumb, (you may call it the Grey Heuristic if you wish,) is that 3 by 3 pixels is the absolute minimum needed to detect anything, and I’d be much more comfortable with 5 by 5. Of course, what we should do is factor in a “probability of detection” to come up with a guideline for how many pixels are needed to reliably find a blob, edge, crack or chip.

Interesting enough, this is pretty much what the Johnson Criteria seeks to do.

John Johnson was working with night vision equipment back in the 1950’s when he developed a set of criteria for detection, orientation, recognition and identification. Now he was working with interlaced displays, so his criteria are defined in terms of line pairs, but I think that can be extrapolated to pixels, leading to the guidelines given on this web site.

So far, so good, but isn’t it time this was all updated for modern digital imaging. I think it would be useful to have some guidelines relating probability of detection, flaw or feature size, and contrast. Who wants to volunteer to do the work?