Image Filtering

Purpose:

–Image Enhancement

–Noise Removal

–Edge Enhancement/Detection

• An image is a matrix of points called pixels

• Resolution

– 640 X 480 ( 0.3 MegaPixels)

– 1600 X 1200 ( 2 MegaPixels)

– 3872 X 2592 (10 MegaPixels)

• Grayscale: generally 8 bits per pixel Intensities in range

[0…255]

• RGB color: 3 of 8-bit color planes: IR , IG , IB

Images

Example of a grayscale image intensity I(x,y)

(0 = black, 255 = white)

255 255 255 255 255 255 255 255 255 255 255 255

255 255 255 255 255 255 255 255 255 255 255 255

255 255 255 20 0 255 255 255 255 255 255 255

255 255 255 75 75 75 255 255 255 255 255 255

255 255 75 95 95 75 255 255 255 255 255 255

255 255 96 127 145 175 255 255 255 255 255 255

255 255 127 145 175 175 175 255 255 255 255 255

255 255 127 145 200 200 175 175 95 255 255 255

255 255 127 145 200 200 175 175 95 47 255 255

255 255 127 145 145 175 127 127 95 47 255 255

255 255 74 127 127 127 95 95 95 47 255 255

255 255 255 74 74 74 74 74 74 255 255 255

255 255 255 255 255 255 255 255 255 255 255 255

255 255 255 255 255 255 255 255 255 255 255 255

Images

=

x

y

r s t

u v w

x y z

Origin x

y Image I (x, y)

eprocessed = v*e + r*a + s*b + t*c + u*d + w*f + x*g + y*h + z*i

Filter Simple 3*3

Neighbourhood e

3*3 Filter

a b c

d e f

g h i

Original Image

Pixels

*

This process is called convolution and is repeated for every pixel in the original image to get the filtered image

Image Spatial Filtering

Simply average all of the pixels in a neighbourhood around a central value

1/9 1/9 1/9

1/9 1/9

1/9

1/9 1/9

1/9

Mean Smoothing Filters

sum of filter values = 1

Example

8 5 8 8 5 8

8 5 8 8 5 8

8 5 8 8 5 8

1

9

1 1 1

1 1 1

1 1 1

7 7 7 7 7 7

7 7 7 7 7 7

7 7 7 7 7 7

Mean Smoothing Filters

Image smoothed with mean filters

Original 33 99

Mean Smoothing Filters

Pixels closer to the central pixel are more important

1/16 2/16

1/16

2/16 4/16

2/16

1/16 2/16

1/16

Gaussian Weighted Filter

Weighted Smoothing Filters

sum of filter values = 1

Gaussian

Original image

Mean

Weighted Smoothing Filters

Example

6 7

3 7 8

2 3

4 6 7

2, 3, 3, 4, 6, 7, 7, 7, 8

Median Smoothing Filters

Noisy image 5x5 median filter 5x5 mean filter

Median Smoothing Filters

1 1 1 1 1 1 1 1 1

0 0 0 0 2 0 0 0 0

-

Edge Enhancement (Sharpening)

sum of filter values = 1

• Convert a 2D image into a set of curves

• Extracts salient features of the scene

Edge Detection

• Directional Edge Detection

• Simple mask for:

– horizontal edges

– vertical edges

-1 1

-1

1

Edge Detection

sum of filter values = 0

Sobel Filter is a combination of 2 filters:

the combined image will show edges from both directions

-1 0 1

-2 0 2

-1 0 1

-1 -2 -1

0 0 0

1 2 1

Sobel Edge Detection

xI yI

2 2

x yI I

Sobel Edge Detection

xI yI 2 2

x yI I

x

y Image I(x, y)

e

At the borders of an image we are missing pixels to form a neighbourhood

• Truncate the image

• Replicate border pixels

• Pad the image (with either

all white or all black pixels)

Dealing with Borders