## Histogram Linearization Solution

STEP 0: Pre-Calculation Summary
Formula Used
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))
sk = ((L-1)/(M*N)*sum(x,0,L-1,nj))
This formula uses 1 Functions, 5 Variables
Functions Used
sum - Summation or sigma (∑) notation is a method used to write out a long sum in a concise way., sum(i, from, to, expr)
Variables Used
Discrete Form of Transformation - Discrete Form of Transformation is The transformation (mapping) in this equation is called a histogram equalization or histogram linearization transformation.
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.
Digital Image Row - Digital Image Row is the row or small pixel that is present at the x-axis storing image information.
Digital Image Column - Digital Image Column is the column or small pixel that is present at the y-axis.
Number of Pixels with Intensity Ri - Number of Pixels with Intensity Ri is the number of pixels that have intensity Ri.
STEP 1: Convert Input(s) to Base Unit
Number of Intensity Levels: 4 --> No Conversion Required
Digital Image Row: 9 --> No Conversion Required
Digital Image Column: 1.5 --> No Conversion Required
Number of Pixels with Intensity Ri: 2 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
sk = ((L-1)/(M*N)*sum(x,0,L-1,nj)) --> ((4-1)/(9*1.5)*sum(x,0,4-1,2))
Evaluating ... ...
sk = 1.77777777777778
STEP 3: Convert Result to Output's Unit
1.77777777777778 --> No Conversion Required
1.77777777777778 1.777778 <-- Discrete Form of Transformation
(Calculation completed in 00.004 seconds)
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## Credits

Created by Zaheer Sheik
Seshadri Rao Gudlavalleru Engineering College (SRGEC), Gudlavalleru
Zaheer Sheik has created this Calculator and 10+ more calculators!
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 Linearization Formula

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))
sk = ((L-1)/(M*N)*sum(x,0,L-1,nj))

## What is Histogram Linearization?

Histogram linearization involves transforming the distribution of pixel values in an image's histogram into a more uniform or evenly spread out distribution. This process improves image contrast and brightness by redistributing pixel values. Techniques like histogram equalization or stretching are commonly used for histogram linearization, enhancing the overall appearance of the image.

## How to Calculate Histogram Linearization?

Histogram Linearization calculator uses 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)) to calculate the Discrete Form of Transformation, The Histogram Linearization formula is a process of transforming a histogram, which represents the distribution of pixel values in an image, into a linear distribution. Discrete Form of Transformation is denoted by sk symbol.

How to calculate Histogram Linearization using this online calculator? To use this online calculator for Histogram Linearization, enter Number of Intensity Levels (L), Digital Image Row (M), Digital Image Column (N) & Number of Pixels with Intensity Ri (nj) and hit the calculate button. Here is how the Histogram Linearization calculation can be explained with given input values -> 1.777778 = ((4-1)/(9*1.5)*sum(x,0,4-1,2)).

### FAQ

What is Histogram Linearization?
The Histogram Linearization formula is a process of transforming a histogram, which represents the distribution of pixel values in an image, into a linear distribution and is represented as sk = ((L-1)/(M*N)*sum(x,0,L-1,nj)) or 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)). Number of Intensity Levels is the total number of distinct intensity values an image can represent, determined by its bit depth, Digital Image Row is the row or small pixel that is present at the x-axis storing image information, Digital Image Column is the column or small pixel that is present at the y-axis & Number of Pixels with Intensity Ri is the number of pixels that have intensity Ri.
How to calculate Histogram Linearization?
The Histogram Linearization formula is a process of transforming a histogram, which represents the distribution of pixel values in an image, into a linear distribution is calculated using 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)). To calculate Histogram Linearization, you need Number of Intensity Levels (L), Digital Image Row (M), Digital Image Column (N) & Number of Pixels with Intensity Ri (nj). With our tool, you need to enter the respective value for Number of Intensity Levels, Digital Image Row, Digital Image Column & Number of Pixels with Intensity Ri 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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