## Histogram Equalization Transformation Solution

STEP 0: Pre-Calculation Summary
Formula Used
Transformation of Continuous intensities = (Number of Intensity Levels-1)*int(Probability Density Function*x,x,0,Continuous Intensity)
Tr = (L-1)*int(Pr*x,x,0,r)
This formula uses 1 Functions, 4 Variables
Functions Used
int - The definite integral can be used to calculate net signed area, which is the area above the x -axis minus the area below the x -axis., int(expr, arg, from, to)
Variables Used
Transformation of Continuous intensities - Transformation of Continuous intensities can be obtained once probability density function has been estimated from the input image.
Number of Intensity Levels - Number of Intensity Levels is the total number of distinct intensity values an image can represent, determined by its bit depth.
Probability Density Function - Probability Density Function is the density function of continuous random variable of an input image.
Continuous Intensity - Continuous Intensity is the continuous random variable of an input image.
STEP 1: Convert Input(s) to Base Unit
Number of Intensity Levels: 4 --> No Conversion Required
Probability Density Function: 0.2 --> No Conversion Required
Continuous Intensity: 64 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Tr = (L-1)*int(Pr*x,x,0,r) --> (4-1)*int(0.2*x,x,0,64)
Evaluating ... ...
Tr = 1228.8
STEP 3: Convert Result to Output's Unit
1228.8 --> No Conversion Required
1228.8 <-- Transformation of Continuous intensities
(Calculation completed in 00.004 seconds)
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## Credits

Created by Zaheer Sheik
Seshadri Rao Gudlavalleru Engineering College (SRGEC), Gudlavalleru
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Verified by Dipanjona Mallick
Heritage Insitute of technology (HITK), Kolkata
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## < 14 Intensity Transformation Calculators

Histogram Linearization
Discrete Form of Transformation = ((Number of Intensity Levels-1)/(Digital Image Row*Digital Image Column)*sum(x,0,Number of Intensity Levels-1,Number of Pixels with Intensity Ri))
Nth Moment of Discrete Random Variable
Nth Moment of Discrete Random Variable = sum(x,0,Number of Intensity Levels-1,Probability of Intensity Ri*(Intensity Level of Ith Pixel-Mean of Intensity Level)^Order of Moment)
Variance of Pixels in Subimage
Variance of Pixels in Subimage = sum(x,0,Number of Intensity Levels-1,Probability of Occurrence of Rith in Subimage*(Intensity Level of Ith Pixel-Subimage Pixel Mean Intensity Level)^2)
Mean Value of Pixels in Neighborhood
Global Mean Pixel Intensity level of Subimage = sum(x,0,Number of Intensity Levels-1,Intensity Level of Ith Pixel*Probability of Occurrence of Rith in Subimage)
Mean Value of Pixels in Subimage
Mean Value of Pixels in Subimage = sum(x,0,Number of Intensity Levels-1,Intensity Level of ith Pixel in Subimage*Probability of Zi in Subimage)
Histogram Equalization Transformation
Transformation of Continuous intensities = (Number of Intensity Levels-1)*int(Probability Density Function*x,x,0,Continuous Intensity)
Transformation Function
Transformation Function = (Number of Intensity Levels-1)*sum(x,0,(Number of Intensity Levels-1),Probability of Intensity Ri)
Average Intensity of Pixels in Image
Average Intensity of Image = sum(x,0,(Intensity Value-1),(Intensity Level*Normalized Histogram Component))
Characteristic Response of Linear Filtering
Characteristic Response of Linear Filtering = sum(x,1,9,Filter Coefficients*Corresponding Image Intensities of Filter)
Bits Required to Store Digitized Image
Bits in Digitized Image = Digital Image Row*Digital Image Column*Number of Bits
Bits Required to Store Square Image
Bits in Digitized Square Image = (Digital Image Column)^2*Number of Bits
Energy of Components of EM Spectrum
Energy of Component = [hP]/Frequency of Light
Wavelength of Light
Wavelength of Light = [c]/Frequency of Light
Number of Intensity Levels
Number of Intensity Level = 2^Number of Bits

## Histogram Equalization Transformation Formula

Transformation of Continuous intensities = (Number of Intensity Levels-1)*int(Probability Density Function*x,x,0,Continuous Intensity)
Tr = (L-1)*int(Pr*x,x,0,r)

## What is Histogram Equalization?

Histogram equalization is a technique used in image processing to enhance the contrast of an image by redistributing the intensity values. The basic idea is to spread out the intensity values so that they cover the entire dynamic range more evenly.

## How to Calculate Histogram Equalization Transformation?

Histogram Equalization Transformation calculator uses Transformation of Continuous intensities = (Number of Intensity Levels-1)*int(Probability Density Function*x,x,0,Continuous Intensity) to calculate the Transformation of Continuous intensities, The Histogram Equalization Transformation formula is defined as the technique used in image processing to enhance the contrast of an image by redistributing the intensity values. Transformation of Continuous intensities is denoted by Tr symbol.

How to calculate Histogram Equalization Transformation using this online calculator? To use this online calculator for Histogram Equalization Transformation, enter Number of Intensity Levels (L), Probability Density Function (Pr) & Continuous Intensity (r) and hit the calculate button. Here is how the Histogram Equalization Transformation calculation can be explained with given input values -> 1228.8 = (4-1)*int(0.2*x,x,0,64).

### FAQ

What is Histogram Equalization Transformation?
The Histogram Equalization Transformation formula is defined as the technique used in image processing to enhance the contrast of an image by redistributing the intensity values and is represented as Tr = (L-1)*int(Pr*x,x,0,r) or Transformation of Continuous intensities = (Number of Intensity Levels-1)*int(Probability Density Function*x,x,0,Continuous Intensity). Number of Intensity Levels is the total number of distinct intensity values an image can represent, determined by its bit depth, Probability Density Function is the density function of continuous random variable of an input image & Continuous Intensity is the continuous random variable of an input image.
How to calculate Histogram Equalization Transformation?
The Histogram Equalization Transformation formula is defined as the technique used in image processing to enhance the contrast of an image by redistributing the intensity values is calculated using Transformation of Continuous intensities = (Number of Intensity Levels-1)*int(Probability Density Function*x,x,0,Continuous Intensity). To calculate Histogram Equalization Transformation, you need Number of Intensity Levels (L), Probability Density Function (Pr) & Continuous Intensity (r). With our tool, you need to enter the respective value for Number of Intensity Levels, Probability Density Function & Continuous Intensity and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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