Question

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Problem 2 (12 points) An 8x8 image is given below: 1 1 1 0 0 1 1 1 1 1 1 0 0 1 0 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 1 0 1 0 0 1 0 1 0 0 1 0 1 1 1 1 1 0 1 1 a) If 8-connectivity is assumed, how many connected components are there in the binary image? Mark them on the binary image. You don't have to apply the algorithm if you can determine the number by visual inspection. b) What is the area of each of the connected components? c) Create a smaller image by cutting out a chunk of the binary image with corners at the pixels (2, 5), (2, 8), (5, 5) and (5,8). Assume that the spatial coordinates of the upper left corner pixel are (1, 1). Show the image. d) Apply the dilation operator on the smaller image to remove the black hole within the white object. How many passes of the dilation operator are necessary? [Show the filtered image after every pass. Assume small image is padded with 1s and that structuring element is a 3x3 box filter

Answer 1

a)

There are 4 connected components of the binary image.

They as marked as follows:

1 111 Jo o o o | 1 1 | o o o | 1 1 1 | 1 1 o o | 11 | |1 | oo oo | 1 | o o 1 oo oo | 1 1 1 1 | 1 1 1 o o o o o 1 [0] 1 | o o o 1 1 | 1 1 1 | | 1 1 1 1 |

b)

The area of the component is number of pixels in the component.

Area of connected component I = 8

Area of connected component II = 8

Area of connected component III = 12

Area of connected component IV = 6

c)

The binary image is as follows

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