OpenCV canny edge detection is not working properly on ideal square

Question

I am using this binary square image of 15*15 pixels.

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 1 1 1 1 1 1 1 1 1 0 0
0 0 0 1 1 1 1 1 1 1 1 1 1 0 0
0 0 0 1 1 1 1 1 1 1 1 1 1 0 0
0 0 0 1 1 1 1 1 1 1 1 1 1 0 0
0 0 0 1 1 1 1 1 1 1 1 1 1 0 0
0 0 0 1 1 1 1 1 1 1 1 1 1 0 0
0 0 0 1 1 1 1 1 1 1 1 1 1 0 0
0 0 0 1 1 1 1 1 1 1 1 1 1 0 0
0 0 0 1 1 1 1 1 1 1 1 1 1 0 0
0 0 0 1 1 1 1 1 1 1 1 1 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

I am applying canny edge detection provided by openCV (version 2.7) for object size measurement. My expected output should look like,

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 1 1 1 1 1 1 1 1 1 0 0
0 0 0 1 0 0 0 0 0 0 0 0 1 0 0
0 0 0 1 0 0 0 0 0 0 0 0 1 0 0
0 0 0 1 0 0 0 0 0 0 0 0 1 0 0
0 0 0 1 0 0 0 0 0 0 0 0 1 0 0
0 0 0 1 0 0 0 0 0 0 0 0 1 0 0
0 0 0 1 0 0 0 0 0 0 0 0 1 0 0
0 0 0 1 0 0 0 0 0 0 0 0 1 0 0
0 0 0 1 0 0 0 0 0 0 0 0 1 0 0
0 0 0 1 1 1 1 1 1 1 1 1 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

But two edges (top and left edge) are always getting shifted by one pixel. The output of canny edge detection is,
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 1 1 1 1 1 1 1 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 1 0 0
0 0 1 0 0 0 0 0 0 0 0 0 1 0 0
0 0 1 0 0 0 0 0 0 0 0 0 1 0 0
0 0 1 0 0 0 0 0 0 0 0 0 1 0 0
0 0 1 0 0 0 0 0 0 0 0 0 1 0 0
0 0 1 0 0 0 0 0 0 0 0 0 1 0 0
0 0 1 0 0 0 0 0 0 0 0 0 1 0 0
0 0 1 0 0 0 0 0 0 0 0 0 1 0 0
0 0 1 0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 1 1 1 1 1 1 1 1 1 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Why is this pixel shift happening?
Is there any way I can avoid this. (I cannot manually adjust pixel shift after output, as I have to use edge detection on irregular shapes) The same shift happens irrespective of odd / even pixels.

Answer 1

At first glance, I was quite surprised when I came across this question. Moreover I did not believe that Canny edge detection would be so deceiving. So I took a similar image and applied Canny edge to it. To my surprise I encountered the same problem you are facing. Why is it so?

After digging in to the documentation I came across many operations that were occurring under the hood.

The documentation claims that Gaussian filtering is done to reduce noise. Well, it is true. But this blurs out the existing edges present in the image as well. So when you blur a perfect square/rectangle, it tends to have curved corners.

After Gaussian filtering, the next step is finding edge gradient. As said, by now the perfect edge of the square/rectangle is gone due to blurring (Gaussian filtering). What is left are rounded/curved edges. Finding the intensity of gradients on rounded/curved edges will never yield a perfect square/rectangle -like edge. I might be wrong, but I guess this the main reason as to why we do not get perfect edges while performing Canny edge detection.

If you want a perfect edge my suggestion would be to try finding contours(as suggested by Micka) and draw a bounding rectangle.