What edges look like

Yesterday, under the heading of “Better measurements from a worse image?” I shared the before and after images from my look into the benefits of low pass filtering. To this a commenter kindly suggested that perhaps I was confusing the effect of softening the image with the number of pixels needed to find the edge.

I respectfully disagree. What I was driving at is the effect of image noise on repeated measurements. If you look closely at a live image you’ll see how the pixel values jump around – 55, 57, 54, 57, and so on. Thus when one acquires an image and applies edge tools the software has to perform the differentiation over a set of numbers that bounce around. What a low pass filter does is to smooth out that random noise, so making the measurement more stable.

To see this for yourself take a look at the graph below.

 

This shows the gray values across the black to white transition in the images I shared yesterday. The blue line is from the raw image while the pink shows how the pixels values changed after smoothing.

Now I’m not delving into the math behind all this, but it seems pretty clear to me that smoothing will reduce the influence of noise in an image, and so yield more repeatable edge detection.