SCCS 476 1

Point Processing• Basic Image Processing Operations

• Arithmetic Operations

• Histograms

SCCS 476 2

Basic Image Processing Operations

• Transforms

– process entire image as one large block

• Neighborhood processing

– process the pixel in a small neighborhood of pixels around the given pixel.

• Point operations

– process according to the pixel’s value alone (single pixel).

Image-Processing operations may be divided into 3 classes based on information required to perform the transformation.

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Schema of Image Processing

ImageTransformed

Image

Transform

OutputImage

Inverse TransformProcessed

Transformed Image

Image-processing operation

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Arithmetic Operations

• Addition

• Subtraction

• Multiplication

• Division

• Complement

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Arithmetic Operations (cont)

• Addition: y = x + c

• Subtraction: y = x - c

• Multiplication: y = cx

• Division: y = x/c

• Complement: y= 255 - x

Let x is the old gray value, y is the new gray value, c is a positive constant.

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Arithmetic Operations (cont)• Addition: y = x + c

• Subtraction: y = x - c

• Multiplication: y = cx

• Division: y = x/c

• Complement: y= 255 - x

To ensure that the results are integers in the range [0, 255], the following operations should be performed

• Rounding the result to obtain an integer• Clipping the result by setting

• y = 255 if y > 255• y = 0 if y < 0

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Arithmetic Operations (cont)

• MATLAB functions– Addition: imadd(x,y)

• Add two images or add constant to image

– Subtraction: imsubstract(x,y)• Subtract two images or subtract constant to image

– Multiplication: immultiply(x,y)• Multiply two images or multiply image by constant

– Division: imdivide(x,y)• Divide two images or divide image by constant

– Complement: imcomplement(x)

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Addition & Subtraction• Lighten/darken the image• Some details may be lost• MATLAB:

– commands: • x = imread(‘filename.ext’);• y = uint8(double(x) + c); or• y = uint8(double(x) - c);

– function: • x = imread(‘filename.ext’);• y = imadd(x, c); or• y = imsubtract(x, c);

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Ex: Addition & Subtraction

Added by 128

Subtracted by 128

Draw graphs of the transformation functions !!!

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Multiplication & Division

• Lighten/darken the image

• Some details may be lost (but less than addition/subtraction)

• MATLAB:

– commands: • x = imread(‘filename.ext’);• y = uint8(double(x)*c); or• y = uint8(double(x)/c);

– functions: • x = imread(‘filename.ext’);• y = immultiply(x, c); or• y = imdivide(x, c);

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Ex: Multiplication & Division

Multiplied by 2

Divided by 2

Draw graphs of the transformation functions !!!

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Comparison: Addition VS Multiplication

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Comparison: Subtraction VS Division

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Complement

• Create the negative image

• MATLAB:– commands:

• x = imread(‘filename.ext’);• y = uint8(255 - double(x));

– function: • x = imread(‘filename.ext’);• y = imcomplement(x);

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Ex: Complement

Draw a graph of the transformation function !!!

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Histogram

• Graph showing the number of pixels for each intensity

• Normalized histogram: histogram where the number of pixel is divided by the total number of pixel so the range is [0,1]

• Cumulative histogram: histogram which shows the number of pixels whose intensity is less or equal to each intensity.

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Histogram Example

>> p = imread(‘pout.tif’)>> inshow(p)

>> figure;imhist(p)

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What Histogram Describes?• Brightness

– dark image has gray levels (histogram) clutered at the lower end.

– bright image has gray levels (histogram) clutered at the higher end.

• Contrast– well contrasted image has gray levels (histogram)

spread out over much of the range.– low contrasted image has gray levels (histogram)

clutered in the center.

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Contrast Enhancement by Spreading Out Histogram

• Histogram Stretching

(Contrast Stretching)

• Histogram Equalization

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1. Histogram Stretching

0 maxI I

#pixel #pixel

Imin Imax

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Steps of Histogram/Contrast Stretching• Create the histogram of the image

Gray level ( i ) No. of gray value ( ni )

0…………………………………………….15

1…………………………………………….. 0 2…………………………………………….. 0 3……………………………………………. .0 4…………………………………………….. 0 5…………………………………………….70 6……………………………………………110 7…………………………………………….45 8…………………………………………… 70 9…………………………………………….35 10………………………………………..... . 0 11………………………………………….. 0 12…………………………………………... 0 13…………………………………………… 0 14…………………………………………… 0 15………………………………………….. 15

Draw the histogram.

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Steps of Histogram/Contrast Stretching (cont)

• From the histogram, stretch out the gray levels in the center of the range by applying the piecewise linear function – Ex: [5,9] [2,14]– y = [(14 – 2)/(9 – 5)](x – 5) + 2, Draw a graph of transformation

• Gray levels outside this range are either left as original values or transforming according to the linear function at the ends of the graph.

x y5 26 57 88 119 14

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Steps of Histogram/Contrast Stretching (cont)

• Change the old gray values to the new gray values by using the piecewise linear function from the previous step as a mapping function.

• Create the histogram from the new image

SCCS 476 24

Histogram Stretching: Example

original output

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Histogram before/after Adjustment

Before After

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Histogram Mapping: Piecewise Linear

I

#pixel

Imin Imax I

#pixel

Imin Imax

Mapping function:

21;1)12()12(

)1(2or 1 ;

IxIIxIyIyIyIxIx

IxIIxIIxII

Ix1 Ix2 Iy1 Iy2

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MATLAB: Histogram/Contrast Stretching

• Command: imadjust

• Syntax: imadjust(x, [a,b], [c,d]);

imadjust(x, [a,b], [c,d], );– convert intensity x a to c

– convert intensity x b to d

– values of a,b,c,d must be between 0 and 1 : positive constant (describe the shape of the function,

< 1 concave downward, > 1 concave upward)

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Transformation Function with Gamma (Power –Law Transformation)

Brighten image Linear mapping Darken image

ccdab

ainputoutput

)(

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Example of Adjusting by the Power-Law Transformation

Original Adjust by usingGamma = 0.5

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MATLAB: Piecewise Linear

• A MATLAB function for applying a piecewise linear-stretching function (see Figure 4.15)

• Command: find• Syntax: find(condition)• Ex

pix = find(im >= a(i) & im < a(i+1));

pix holds the index for members in im having intensity between a(i) and a(i+1) include a(i).

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2. Histogram Equalization

• The trouble with the methods of histogram stretching is that they require user input.

• Histogram equalization is an entirely automatic procedure.

• Idea: Each gray level in the image occurs with the same frequency.

• Give the output image with uniform intensity distribution.

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Histogram Equalization (cont)

• Mapping function:

where p(i) is the PDF of the intensity level i,

obtained from cumulative histogram.

,)()(0

inputf

iinputoutput ipfg

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Histogram Equalization: Procedure

Example: Suppose a 4-bit grayscale image has the histogram associated with a table of the numbers ni of gray values. (page 78)

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Histogram Equalization: Example

BEFORE AFTER

http://www.mathworks.com/access/helpdesk/help/toolbox/images/histeq.html

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MATLAB: Histogram Equalization

• Command: histeq• Syntax: histeq(image, target_hist) histeq(image, #bin)

histeq(indexed_im, #bin, target_hist) histeq(indexed_im, map, #bin)

• Default: #bin = 64• Output: output_im, [output_im, transform],

new_map, [new_map, transform]

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Lookup Tables

• Improve the performance of point processing

• Why?– one intensity is always mapped to the same value– reduce the computing time

• Lookup table: array

Input intensity: index in the array

Output intensity: value of the member

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Ex: Lookup Table (1)

• Function: output = input/2;

• MATLAB

>> T = uint8(floor(0:255)/2);

>> output = T(input);

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Ex: Lookup Table in MATLAB (2)

• Function:

• MATLAB>> T1 = 0.6667*[0:95];>> T2 = 2*[96:160] – 128;

>> T3 = 0.6632*[161:255] + 85.8947;>> T = uint8(floor([T1 T2 T3]));

inputinput

inputinput

inputinput

output

161;8947.856632.0

16196 ;1282

96 ;6667.0