Neighborhood pixels

DIGITAL IMAGE PROCESSING

IMAGE ENHANCEMENTNeighborhood Pixels Processing

by Paresh Kamble

Neighborhood Pixels Processing

• It is also spatial domain technique in image enhancement.

• Here, we consider one pixel at a time & modify it accordingly.

• Its neighboring pixels are also taken in consideration.

• So, we change pixel value based on 8 neighbors.

• Along with 3x3 neighborhood, 5x5 & 7x7 can also be used.

• A lot of things can be achieved by neighborhood processing not possible by point processing.

Neighborhood Pixels Processing• 3 x 3 Neighborhood / Mask / Window / Template:

(y - 1) y (y + 1) Y

W1 W2 W3(x - 1) g(x-1, y-1) g(x-1, y) g(x-1, y+1)

W4 W5 W6x g(x, y-1) g(x, y) g(x, y+1)

W7 W8 W9(x + 1) g(x+1, y-1) g(x+1, y) g(x+1, y+1)

X


• To achieve neighborhood processing:

• Place the mask on the image.• Multiply each mask component with the pixel component.• Add them, place value at center. Similar to CONVOLUTION.• Only here we need not flip the mask as it is symmetric.

• If g is original image & f is modified image, then:

f( x, y) = g(x-1,y-1).w1 + g(x-1,y).w2 + g(x-1,y+1).w3+ g(x,y-1).w4 + g( x, y).w5 + g(x,y+1).w6

+ g(x+1,y-1).w7 + g(x+1,y).w8 + g(x+1,y+1).w9


• Once f( x, y) is calculated, shift mask by 1 step to right.• Now, W5 coincide with g(x, y+1).• Application of neighborhood processing : Image Filtering.• E.g. LPF, HPF, BPF, BRF• In 1D signals, if 2 signals represent voltage then,• How fast the signal changes is indication of frequency.

• Same concept is applied to images where we have gray levels instead.

• If gray scale change slowly over a region then LF area. E.g. Background

• If gray scale change abruptly over a region then HF area.E.g. Edges, Boundaries.


Low Pass Filtering (Smoothing):• Removes HF content from image.• Used to remove noise (HF component) from image.

• Noise:• Noise creeps in during image acquisition & transmission.

• Noises are classified as:• i) Gaussian Noise• ii) Salt & Pepper Noise• iii) Rayleigh Noise• iv) Gamma Noise• v) Exponential Noise• vi) Uniform Noise


Low Pass Averaging filter:

Generally used for removal of Gaussian noise from images.

It uses a mask that gives LPF operation.

Important thing: All the coefficients are positive.

Standard LPF Averaging masks:

1 1 1 1 ----- 1 1 19 1 1 1

3 x 3 Averaging Mask


1 1 1 1 11 1 1 1 1 1--- 1 1 1 1 125 1 1 1 1 1

1 1 1 1 1

5 x 5 Averaging Mask


Ex. 1) 8x8 Pseudo image with a single edge (High Frequency) of 10 & 50. Remove using a 3x3 size averaging mask.

10 10 10 10 10 10 10 1010 10 10 10 10 10 10 1010 10 10 10 10 10 10 1010 10 10 10 10 10 10 1050 50 50 50 50 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 50

8x8 Image


10 10 10 10 10 10 10 1010 10 10 10 10 10 10 1010 10 10 10 10 10 10 1010 10 10 10 10 10 10 1050 50 50 50 50 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 50

1 1 1 1----- 1 1 1

9 1 1 1


0 0 00 10 10 10 10 10 10 10 100 10 10 10 10 10 10 10 10

10 10 10 10 10 10 10 1010 10 10 10 10 10 10 1050 50 50 50 50 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 50

1 1 1 1----- 1 1 1

9 1 1 1


0 0 00 4.44 10 10 10 10 10 10 100 10 10 10 10 10 10 10 10

10 10 10 10 10 10 10 1010 10 10 10 10 10 10 1050 50 50 50 50 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 50

1 0 0 0----- 0 10 10

9 0 10 10


0 0 0 00 4.44 6.66 10 10 10 10 10 100 10 10 10 10 10 10 10 10

10 10 10 10 10 10 10 1010 10 10 10 10 10 10 1050 50 50 50 50 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 50

1 0 0 0----- 10 10 10

9 10 10 10


0 0 0 0 00 4.44 6.66 6.66 10 10 10 10 100 10 10 10 10 10 10 10 10

10 10 10 10 10 10 10 1010 10 10 10 10 10 10 1050 50 50 50 50 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 50

1 0 0 0----- 10 10 10

9 10 10 10


0 0 0 0 0 00 4.44 6.66 6.66 6.66 10 10 10 100 10 10 10 10 10 10 10 10

10 10 10 10 10 10 10 1010 10 10 10 10 10 10 1050 50 50 50 50 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 50

1 0 0 0----- 10 10 10

9 10 10 10


0 0 0 0 0 0 0 0 00 4.44 6.66 6.66 6.66 6.66 6.66 6.66 4.44 00 6.66 10 10 10 10 10 10 10 0

10 10 10 10 10 10 10 1010 10 10 10 10 10 10 1050 50 50 50 50 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 50

1 10 10 10----- 10 10 10

9 10 10 10


0 0 0 0 0 0 0 0 0 0 4.44 6.66 6.66 6.66 6.66 6.66 6.66 4.44 0 0 6.66 10 10 10 10 10 10 6.66 00 6.66 10 10 10 10 10 10 6.66 00 15.55 10 10 10 10 10 10 10 00 50 50 50 50 50 50 50 50 0

50 50 50 50 50 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 50

1 0 10 10----- 0 10 10

9 0 50 50


0 0 0 0 0 0 0 0 0 0 4.44 6.66 6.66 6.66 6.66 6.66 6.66 4.44 0 0 6.66 10 10 10 10 10 10 6.66 00 6.66 10 10 10 10 10 10 6.66 00 15.55 23.33 10 10 10 10 10 10 00 50 50 50 50 50 50 50 50 0

50 50 50 50 50 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 50

1 10 10 10----- 10 10 10

9 50 50 50


0 0 0 0 0 0 0 0 0 0 4.44 6.66 6.66 6.66 6.66 6.66 6.66 4.44 0 0 6.66 10 10 10 10 10 10 6.66 00 6.66 10 10 10 10 10 10 6.66 00 15.55 23.3323.3323.33 23.33 23.33 23.33 15.55 00 24.44 36.66 50 50 50 50 50 50 0

50 50 50 50 50 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 50

1 10 10 10----- 50 50 50

9 50 50 50


0 0 0 0 0 0 0 0 0 0 4.44 6.66 6.66 6.66 6.66 6.66 6.66 4.44 0 0 6.66 10 10 10 10 10 10 6.66 00 6.66 10 10 10 10 10 10 6.66 00 15.55 23.3323.3323.33 23.33 23.33 23.33 15.55 00 24.44 36.6636.66 36.66 36.66 36.66 36.66 24.44 00 33.33 50 50 50 50 50 50 50

50 50 50 50 50 50 50 5050 50 50 50 50 50 50 50

1 50 50 50----- 50 50 50

9 50 50 50


0 0 0 0 0 0 0 0 0 0 4.44 6.66 6.66 6.66 6.66 6.66 6.66 4.44 0 0 6.66 10 10 10 10 10 10 6.66 00 6.66 10 10 10 10 10 10 6.66 00 15.55 23.3323.3323.33 23.33 23.33 23.33 15.55 00 24.44 36.6636.66 36.66 36.66 36.66 36.66 24.44 00 33.33 50 50 50 50 50 50 33.33 00 33.33 50 50 50 50 50 50 33.33 00 22.22 33.33 33.33 33.33 33.3333.33 33.33 22.22 0

0 0 0 0 0 0 0 0 01 50 50 0

----- 50 50 09 0 0 0


10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 23.33 23.3323.33 23.33 23.33 23.33 1050 36.66 36.66 36.66 36.66 36.66 36.66 5050 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50

50 50 50 50 50 50 50 50

1 1 1 1----- 1 1 1

9 1 1 1


In the resultant image the Low frequency region has remained unchanged.

Sharp transition between 10 & 50 has changed from 10 to 23.33 to 36.66 and finally to 50.

Thus, Sharp edges has become blurred. Best result when used over image corrupted by Gaussian

noise. Other types of low pass averaging mask are:

1 0 1 0 1 1 1 1---- 1 2 1 ---- 1 2 16 0 1 0 10 1 1 1


Low Pass Median Filtering: Averaging Filter removes the noise by blurring till it is no

longer seen. It blurs the edges too. Bigger the averaging mass more the blurring. Sometimes the image contains ‘salt & pepper noise’. If averaging filter is used then it will remove the noise at the

cost of ruined edges. Thus a nonlinear filter Median filter is required. They are also called as order statistics filter since their

response is based on ordering or ranking of pixels contained within the mask.

Here we use a blank mask.


Steps to perform median filtering: Assume a 3x3 empty mask.

Place the empty mask at the Left Hand corner.

Arrange the 9 pixels in ascending or descending order.

Choose the median from these 9 values.

Place the median at the centre.

Move the mask in same manner as averaging filter.


Apply 3x3 median filter to find a new image.

3 4 2 3

1 7 3 2 4 5 3 8

2 3 1 7 3x3 blank mask

Noisy Image S & P noise



3 4 2 3 3 4 2 3

1 7 3 2 1 3 24 5 3 8 4 8

2 3 1 7 2 3 1 7

1) 1 2 3 3 3 4 4 5 7



3 4 2 3 3 4 2 3

1 7 3 2 1 3 3 24 5 3 8 4 8

2 3 1 7 2 3 1 7

1) 1 2 3 3 3 4 4 5 72) 2 2 3 3 3 4 5 7 8



3 4 2 3 3 4 2 3

1 7 3 2 1 3 3 24 5 3 8 4 3 8

2 3 1 7 2 3 1 7

1) 1 2 3 3 3 4 4 5 72) 2 2 3 3 3 4 5 7 83) 1 1 2 3 3 3 4 5 7



3 4 2 3 3 4 2 3

1 7 3 2 1 3 3 24 5 3 8 4 3 3 8

2 3 1 7 2 3 1 7

1) 1 2 3 3 3 4 4 5 72) 2 2 3 3 3 4 5 7 83) 1 1 2 3 3 3 4 5 74) 1 2 3 3 3 5 7 7 8


Ex. 2) 8x8 Pseudo image with a single edge (High Frequency) of 10 & 50. Remove using a 3x3 size median filter mask.

10 10 10 10 10 10 10 1010 10 10 10 10 10 10 1010 250 10 10 10 10 10 1010 10 10 10 10 10 10 1050 50 50 50 250 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 50

8x8 Image


10 10 10 10 10 10 10 1010 10 10 10 10 10 10 1010 250 10 10 10 10 10 1010 10 10 10 10 10 10 1050 50 50 50 250 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 50

8x8 Image with blank mask


10 10 10 10 10 10 10 1010 10 10 10 10 10 10 1010 250 10 10 10 10 10 1010 10 10 10 10 10 10 1050 50 50 50 250 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 50



10 10 10 10 10 10 10 1010 10 10 10 10 10 10 1010 10 10 10 10 10 10 1010 10 10 10 10 10 10 1050 50 50 50 250 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 50



10 10 10 10 10 10 10 1010 10 10 10 10 10 10 1010 10 10 10 10 10 10 1010 10 10 10 10 10 10 1050 50 50 50 250 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 50



10 10 10 10 10 10 10 1010 10 10 10 10 10 10 1010 10 10 10 10 10 10 1010 10 10 10 10 10 10 1050 50 50 50 250 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 50



10 10 10 10 10 10 10 1010 10 10 10 10 10 10 1010 10 10 10 10 10 10 1010 10 10 10 10 10 10 1050 50 50 50 50 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 5050 50 50 50 50 50 50 50



Ex. 3) If x = {2 3 4 3 4 5 6} & w = {-1 0 1}, perform median filtering.

Size of mask is 1x3. Term ‘0’ indicates the position from where filtering starts.

Soln: 2 3 4 3 4 5 6

-1 0 1 Border value: 2

2 3 4 3 4 5 6-1 0 1 Median value {2 3 4}: 3

2 3 4 3 4 5 6-1 0 1 Median value {3 3 4}: 3


2 3 4 3 4 5 6-1 0 1 Median value {3 4 4}: 4

2 3 4 3 4 5 6-1 0 1 Median value {3 4 5}: 4

2 3 4 3 4 5 6-1 0 1 Median value {4 5 6}: 5

2 3 4 3 4 5 6-1 0 1 Border value: 6

Result: {2 3 3 4 4 5 6}


Ex 4). Find the median filtered image by 3x3 mask for the given image.

2 4 15 0

3 5 2 611 0 2 10

6 16 0 2


High Pass Filtering: Retains HF component while eliminates LF components.

High passed image will have no background(Low freq region).

It will have enhanced edges.

Used to sharpen blurred images.

Process of mask moving on image is same only the mask coefficients change.

Mask coefficients should have positive value at centre and negative values elsewhere.

Sum of coefficients must be zero.

Since, it should give Zero after being placed on LP region.


High Pass Masks: 3x3 High pass masks

-1 -1 -1

-1 8 -1

-1 -1 -1

0 -1 0 -1 -2 -1

-1 4 -1 -2 12 -2

0 -1 0 -1 -2 -1


Ex 5) 8x8 Pseudo image with a single edge (High Frequency) of 10 & 100. Remove LP using a 3x3 size High pass filter mask.

10 10 10 10 10 10 10 1010 10 10 10 10 10 10 1010 10 10 10 10 10 10 1010 10 10 10 10 10 10 10

100 100 100 100 100 100 100 100100 100 100 100 100 100 100 100100 100 100 100 100 100 100 100100 100 100 100 100 100 100 100


10 10 10 10 10 10 10 1010 10 10 10 10 10 10 1010 10 10 10 10 10 10 1010 10 10 10 10 10 10 10

100 100 100 100 100 100 100 100100 100 100 100 100 100 100 100100 100 100 100 100 100 100 100100 100 100 100 100 100 100 100

-1 -1 -1 -10-10-10-10-10-10-10-10+80 = 0

-1 8 -1

-1 -1 -1


10 10 10 10 10 10 10 1010 10 10 10 10 10 10 1010 10 10 10 10 10 10 1010 10 10 10 10 10 10 10

100 100 100 100 100 100 100 100100 100 100 100 100 100 100 100100 100 100 100 100 100 100 100100 100 100 100 100 100 100 100

-1 -1 -1 -10-10-10-10-10-10-10-10+80 = 0

-1 8 -1

-1 -1 -1


10 10 10 10 10 10 10 1010 10 10 10 10 10 10 1010 10 10 10 10 10 10 1010 10 10 10 10 10 10 10

100 100 100 100 100 100 100 100100 100 100 100 100 100 100 100100 100 100 100 100 100 100 100100 100 100 100 100 100 100 100

-1 -1 -1 -10-10-10-10-10-100-100-100+80 = -270

-1 8 -1

-1 -1 -1


10 10 10 10 10 10 10 1010 10 10 10 10 10 10 1010 10 10 10 10 10 10 1010 10 10 10 10 10 10 10

100 100 100 100 100 100 100 100100 100 100 100 100 100 100 100100 100 100 100 100 100 100 100100 100 100 100 100 100 100 100

-1 -1 -1 -10-10-10-100-100-100-100-100+800 = +270

-1 8 -1

-1 -1 -1


10 10 10 10 10 10 10 1010 10 10 10 10 10 10 1010 10 10 10 10 10 10 1010 10 10 10 10 10 10 10

100 100 100 100 100 100 100 100100 100 100 100 100 100 100 100100 100 100 100 100 100 100 100100 100 100 100 100 100 100 100

-1 -1 -1 -100-100-100-100-100-100-100-100+800 = 0

-1 8 -1

-1 -1 -1


0 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0

-270 -270 -270 -270 -270 -270 -270 -270270 270 270 270 270 270 270 270

0 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0

Note: -270 is replaced by 0.

Neighborhood Pixels ProcessingEx. 6) Obtain the digital negative of the following 8 bits per pixel

image of fig.1.

121 205 217 156 151 2 1 2 2 1139 127 157 117 125 2 3 4 5 2252 117 236 138 142 6 2 7 6 0227 182 178 197 242 2 6 6 5 1 201 106 119 251 240 0 3 2 2 1

fig. 1 fig. 2

Ex. 7) Perform intensity level (gray level) slicing on a 3 bpp image of fig. 2 . Let r1 = 3 & r2 = 5. Draw the modified image using with background & without background transformation.

Neighborhood Pixels ProcessingEx. 8) The image shown below has 8 different gray levels. Plot

this image using only 4 gray levels.

0 1 1 1 1 41 1 2 3 2 21 1 2 2 3 31 2 4 6 2 31 2 4 2 4 41 2 3 7 2 5

Neighborhood Pixels Processing8 gray levels:

0 01 0 02 23 2 14 45 4 26 6 0 0 0 0 0 47 6 3 0 0 2 2 2 2

0 0 2 2 2 20 2 4 6 2 20 2 4 2 4 40 2 2 6 2 4

Education

Neighborhood pixels