Image Segmentation - Bezier and Splines in Image Processing and Machine Vision - page 44

M N

K = c ij . (2.20)

i =1 j =1

The contrast c ij , at the pixel position ( i, j ) is written using the concept of
psycho-visual perception as [73]

c ij = |

B−B ij |

,

B

(2.21)

= | B

|

,

B

where B is the immediate surrounding luminance of the ( i, j )th pixel with
intensity B ij . Equations (2.20) and (2.21) reveal that the contrast of pixels in
a perfectly homogeneous region is zero everywhere except near the boundary
points. The contribution to K of the image, therefore, comes mainly from its
noisy pixels and contrast regions (edge points). Thus the image quality index
or the average contrast per pixel is defined as

K
n k ,

IQI = (2.22)

where n k = MN n h , n k = total number of significant contrast points,

n h = total number of significant homogeneous points, and MN = number
of pixels in the image. Note that the average is taken over only those pixels
that mainly contribute to the contrast measure, K; the pixels of homogeneous
regions, being least contributory, have been discarded.
To find out n h we define the homogeneity, h ij of the ( i, j ) th pixel as

−

8

exp −| B ij − B r |

r =1

h ij = , (2.23)

8

where B r indicates the intensity of a background pixel in the 3 3 neigh-

borhood, N 3 ( i, j ), of ( i, j ). From equation (2.23), it is seen that when each
background pixel is equal to the central pixel, the tiny region around the
central pixel is perfectly homogeneous, and the homogeneity measure at the
central pixel is equal to unity. For other cases, homogeneity value of a pixel
exponentially drops with its difference from the background intensity.
Therefore, if we compute total homogeneity of an image as

×

M N

H = h ij , (2.24)

i =1 j =1

then the major contribution to H comes only from the pixels that lie in per-
fectly homogeneous regions. Thus, H will be a good approximation to n h .
Therefore,