Digital Image ProcessingDigital Image Processing

Image Enhancement in Spatial DomainImage Enhancement in Spatial Domain

Dr. Abdul Basit Siddiqui

Image Sampling and Quantization

• To create a digital image, we need to convert the continuous sensed data into digital form --> this involves sampling and quantization

• Digitizing the coordinate values is called sampling

• Digitizing the amplitude values is called quantization

---> see Fig. 2.16 in the textbook

• In practice, the method of sampling is determined by the sensor

arrangement used to generate the image

• The quality of a digital image is determined by the number of samples

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Spatial resolution and intensity resolution

• Sampling is the principal factor defining the spatial resolution of an image, and quantization is the principal factor defining the intensity resolution

• Spatial resolution - number of rows and columns for example: 128 x128, 256 by 256, etc.; -->see Figs. 2.19 and 2.20

• Intensity resolution - number of gray levels for example: 8 bits, 16 bits, etc.; --->see Fig. 2.21

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Image Enhancement

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Image Enhancement

Process an image to make the result more suitable than theoriginal 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

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

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Image Enhancement

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Basic Concepts

Spatial domain enhancement methods can be generalized asg(x,y)=T[f(x,y)]

f(x,y): input imageg(x,y): processed (output) imageT[*]: 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)

Point Processes

• Point processes are the simplest of basic image processing operations.

• A point operation takes a single input image into a single output image in such a way that each output pixel's gray level depends only upon the gray level of the corresponding input pixel.

• Thus, a point operation cannot modify the spatial relationships within an image.

• Point operations transform the gray scale of an image.

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Point Processes

• Linear and nonlinear point operations• Examples:

– Contrast Stretching

– Image Negatives

– Intensity-level Slicing

– Bit-plane Slicing

– Other Intensity Transformations

– Histogram Equalization

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Basic Concepts

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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 functionLet 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 filteringMasks (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

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Common Pixel Operations

Image Negatives Log Transformations Power-Law

Transformations

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Image Negatives

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

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

Image Negatives

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Image Scaling

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

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Log Transformations

Function of s = cLog(1+r)

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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”

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Log Transformations

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Power-Law Transformation

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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 power law and need to be corrected

Gamma (γ) correction The process used to correct the power-law response

phenomena

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Power-Law Transformation

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Gamma Correction

Histogram• Gray level histogram of an image - a function showing

for each gray level the number of

• pixels in the image that have that gray level; it is simply a bar graph of the pixel intensities

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Histogram• Histogram gives us a convenient, easy-to-read

representation of concentration of pixels versus intensity in an image

• Dynamic range - an range of intensity values that occur in an image

• Contrast stretching - if image has low-dynamic range; low-dynamic range can result from poor illumination, lack of dynamic range in imaging sensor, wrong setting of the sensor parameters, etc.

• Compression of dynamic range - if the dynamic range of the image far exceeds the capability of the display device

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Histogram calculation

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Examples of several types of image histograms:

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Histogram Equalization• Images with poor intensity distributions can often be

enhanced with histogram equalization <-- point process

• The goal is to obtain a uniform histogram

• • Histogram equalization will not flatten a histogram; if a histogram has peaks and valleys it will still have them after equalization - they will be shifted and spread over the entire range of image intensities

• Works best on images with fine details in darker regions

• Use it carefully - good images can be often degraded by histogram equalization

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Histogram of the equalized image

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Histogram Equalization-Example

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