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Histogram Equalization Transformation Formula

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Transformation of Continuous intensities can be obtained once probability density function has been estimated from the input image. Check FAQs

T r = (L - 1) \cdot \int (P r \cdot x, x, 0, r)

T_r - Transformation of Continuous intensities?L - Number of Intensity Levels?P_r - Probability Density Function?r - Continuous Intensity?

Histogram Equalization Transformation Example

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With units

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Here is how the Histogram Equalization Transformation equation looks like with Values.

Here is how the Histogram Equalization Transformation equation looks like with Units.

Here is how the Histogram Equalization Transformation equation looks like.

1228.8 = (4 - 1) \cdot \int (0.2 \cdot x, x, 0, 64)

1228.8 = (4 - 1) \cdot \int (0.2 \cdot x, x, 0, 64)

1228.8 = (4 - 1) \cdot \int (0.2 \cdot x, x, 0, 64)

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Histogram Equalization Transformation Solution

Follow our step by step solution on how to calculate Histogram Equalization Transformation?

FIRST Step Consider the formula

T r = (L - 1) \cdot \int (P r \cdot x, x, 0, r)

Next Step Substitute values of Variables

∴

T r = (4 - 1) \cdot \int (0.2 \cdot x, x, 0, 64)

Next Step Prepare to Evaluate

∴

T r = (4 - 1) \cdot \int (0.2 \cdot x, x, 0, 64)

LAST Step Evaluate

∴

T r = 1228.8

Histogram Equalization Transformation Formula Elements

Variables

Functions

Transformation of Continuous intensities

Transformation of Continuous intensities can be obtained once probability density function has been estimated from the input image.

Symbol: T_r

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Transformation of Continuous intensities

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.

Symbol: L

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Intensity Levels

Probability Density Function

Probability Density Function is the density function of continuous random variable of an input image.

Symbol: P_r

Measurement: NAUnit: Unitless

Note: Value should be less than 1.1.

Formulas to find Probability Density Function

Continuous Intensity

Continuous Intensity is the continuous random variable of an input image.

Symbol: r

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Continuous Intensity

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.

Syntax: int(expr, arg, from, to)

Other formulas in Intensity Transformation category

Go Wavelength of Light

W = \frac{[c]}{v}

Go Number of Intensity Levels

L = 2^{n b}

Go Bits Required to Store Digitized Image

n id = M \cdot N \cdot n b

Go Bits Required to Store Square Image

b s = {(N)}^{2} \cdot n b

How to Evaluate Histogram Equalization Transformation?

Histogram Equalization Transformation evaluator uses Transformation of Continuous intensities = (Number of Intensity Levels-1)*int(Probability Density Function*x,x,0,Continuous Intensity) to evaluate 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 T_r symbol.

How to evaluate Histogram Equalization Transformation using this online evaluator? To use this online evaluator for Histogram Equalization Transformation, enter Number of Intensity Levels (L), Probability Density Function (P_r) & Continuous Intensity (r) and hit the calculate button.

FAQs on Histogram Equalization Transformation

What is the formula to find Histogram Equalization Transformation?

The formula of Histogram Equalization Transformation is expressed as Transformation of Continuous intensities = (Number of Intensity Levels-1)*int(Probability Density Function*x,x,0,Continuous Intensity). Here is an example- 1228.8 = (4-1)*int(0.2*x,x,0,64).

How to calculate Histogram Equalization Transformation?

With Number of Intensity Levels (L), Probability Density Function (P_r) & Continuous Intensity (r) we can find Histogram Equalization Transformation using the formula - Transformation of Continuous intensities = (Number of Intensity Levels-1)*int(Probability Density Function*x,x,0,Continuous Intensity). This formula also uses Definite Integral (int) function(s).

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Histogram Equalization Transformation Formula

Histogram Equalization Transformation Example

Histogram Equalization Transformation Solution

Histogram Equalization Transformation Formula Elements

Other formulas in Intensity Transformation category

How to Evaluate Histogram Equalization Transformation?

FAQs on Histogram Equalization Transformation

Variable Name