Consider the three binary images shown in the following figure. The image on the left is c...

Consider the three binary images shown in the following figure. The image on the left is composed of squares of sizes 1, 3, 5, 7, 9, and 15 pixels on the side. The image in the middle was generated by eroding the image on the left with a square structuring element of 1s, of size 13 × 13 pixels, with the objective of eliminating all the squares, except the largest ones. Finally, the image on the right is the result of dilating the image in the center with the same structuring element, with the objective of restoring the largest squares. You know that erosion followed by dilation is the opening of an image, and you know also that opening generally does not restore objects to their original form. Explain why full reconstruction of the large squares was possible in this case.