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Digital Image Processing
EEE415
Lecture 3

Image Enhancement in Spatial Domain

Pixel Operations and Histogram Processing

Image Enhancement

Process an image to make the result more suitable than the original image for a specific application
Image enhancement is subjective (problem/application oriented)
Image enhancement methods
Spatial domain: Direct manipulation of pixel in an image (on the image plane)
Frequency domain: Processing the image based on modifying the Fourier transform of an image

Some techniques are based on various combinations of methods from these two categories

Image Enhancement

No general theory

Viewer is ultimate judge

Highly subjective process

Easier in machine perception

Types of image enhancement operations - Pixel point processing

Pixel point processing is a form of image enhancement based only on the intensity of single pixels. No consideration what-so-ever is taken of neighbouring pixels, or the spatial arrangement of groups of pixels, or of the position of the pixel within the digital image.

Pixel point processing is a simple but important type of image enhancement technique. All pixels are processed individually.

Pixel Point Processing

The general equation for a point process is given by:

g(x,y) = M[f(x,y)]

Where g(x,y) is the output digital image, f(x,y) is the input digital image, and M is the mapping function.

M maps or converts input pixel brightness to an output pixel brightness.

The mapping function can be non-linear.

Types of image enhancement operations: Block processing

Local operations The output value at (x,y) is dependent on the input values in the neighborhood of (x,y)

Global operations The output value at (x,y) is dependent on all the values in the input image

Basic concepts

Spatial domain enhancement methods can be generalized as

g(x,y)=T[f(x,y)]

f(x,y) : input image

g(x,y): processed (output) image

T[*] : an operator on f (or a set of input images), defined over neighborhood of (x,y)

Neighborhood about (x,y): a square or rectangular sub- image area centered at (x,y)

Basic Concepts

3x3 neighborhood about (x,y)

Basic concepts

g(x,y) = T [f(x,y)]

Pixel/point operation:

Neighborhood of size 1x1: g depends only on f at (x,y)

T: a gray-level/intensity transformation/mapping function

Let r = f(x,y) s = g(x,y)

r and s represent gray levels of f and g at (x,y)

Then s = T(r)

Local operations:

g depends on the predefined number of neighbors of f at (x,y)

Implemented by using mask processing or filtering

Masks (filters, windows, kernels, templates) :

a small (e.g. 3×3) 2-D array, in which the values of the coefficients determine the nature of the process

Common pixel operations

Image negatives

Log transformations

Power-law transformations

Pixel Operations: Image negatives

Reverses the gray level order
For L gray levels the transformation function is

s =T(r) = (L-1)-r

Input image (X-ray image) Output image (negative)

Application: To enhance the visibility for images with more dark portion

Pixel Operations: Contrast Scaling

s =T(r) = a.r (a is a constant)

Pixel Operations: Log transformations

Function of s = c Log(1+r)

Pixel Operations: Log transformations

Properties of log transformations

For lower amplitudes of input image the range of gray levels is expanded
For higher amplitudes of input image the range of gray levels is compressed

Application:

This transformation is suitable for the case when the dynamic range of a processed image far exceeds the capability of the display device (e.g. display of the Fourier spectrum of an image)
Also called “dynamic-range compression / expansion”

Pixel Operations: Log transformations

Fourier spectrum with values of range 0 to 1.5 x 106 scaled linearly

The result applying log transformation, c = 1

Pixel Operations: Power-law Transformation

Basic form:

s = crg ,

where c & g

are positive

Plots of equation s = crg, For various values of g (c = 1)

Pixel Operations: Power-law Transformation

For γ < 1: Expands values of dark pixels, compress values of brighter pixels

For γ > 1: Compresses values of dark pixels, expand values of brighter pixels

If γ=1 & c=1: Identity transformation (s = r)

A variety of devices (image capture, printing, display) respond according to a power law and need to be corrected;

Gamma (γ) correction

The process used to correct the power-law response phenomena

Pixel Operations: Power-law Transformation

Example of gamma correction

To linearize the CRT response a pre-distortion circuit is needed s = cr1/g

Pixel Operations: Gamma correction

Linear wedge gray scale image

Response of CRT to Linear wedge

Gamma corrected wedge

Output of monitor

Pixel Operations: Power-law Transformation

MRI image of fractured human spine