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Histogram Linearization Formula

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Discrete Form of Transformation is The transformation (mapping) in this equation is called a histogram equalization or histogram linearization transformation. Check FAQs

s k = (\frac{L - 1}{M \cdot N} \cdot \sum (x, 0, L - 1, n j))

s_k - Discrete Form of Transformation?L - Number of Intensity Levels?M - Digital Image Row?N - Digital Image Column?n_j - Number of Pixels with Intensity Ri?

Histogram Linearization Example

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With units

Only example

Here is how the Histogram Linearization equation looks like with Values.

Here is how the Histogram Linearization equation looks like with Units.

Here is how the Histogram Linearization equation looks like.

43.7158 = (\frac{4 - 1}{9 \cdot 0.061} \cdot \sum (x, 0, 4 - 1, 2))

43.7158 = (\frac{4 - 1}{9 \cdot 0.061} \cdot \sum (x, 0, 4 - 1, 2))

43.7158 = (\frac{4 - 1}{9 \cdot 0.061} \cdot \sum (x, 0, 4 - 1, 2))

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Histogram Linearization Solution

Follow our step by step solution on how to calculate Histogram Linearization?

FIRST Step Consider the formula

s k = (\frac{L - 1}{M \cdot N} \cdot \sum (x, 0, L - 1, n j))

Next Step Substitute values of Variables

∴

s k = (\frac{4 - 1}{9 \cdot 0.061} \cdot \sum (x, 0, 4 - 1, 2))

Next Step Prepare to Evaluate

∴

s k = (\frac{4 - 1}{9 \cdot 0.061} \cdot \sum (x, 0, 4 - 1, 2))

Next Step Evaluate

∴

s k = 43.7158469945355

LAST Step Rounding Answer

∴

s k = 43.7158

Histogram Linearization Formula Elements

Variables

Functions

Discrete Form of Transformation

Discrete Form of Transformation is The transformation (mapping) in this equation is called a histogram equalization or histogram linearization transformation.

Symbol: s_k

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Discrete Form of 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.

Symbol: L

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Intensity Levels

Digital Image Row

Digital Image Row is the row or small pixel that is present at the x-axis storing image information.

Symbol: M

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Digital Image Row

Digital Image Column

Digital Image Column is the column or small pixel that is present at the y-axis.

Symbol: N

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Digital Image Column

Number of Pixels with Intensity Ri

Number of Pixels with Intensity Ri is the number of pixels that have intensity Ri.

Symbol: n_j

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Number of Pixels with Intensity Ri

sum

Summation or sigma (∑) notation is a method used to write out a long sum in a concise way.

Syntax: sum(i, from, to, expr)

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 Linearization?

Histogram Linearization evaluator 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 evaluate 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 s_k symbol.

How to evaluate Histogram Linearization using this online evaluator? To use this online evaluator for Histogram Linearization, enter Number of Intensity Levels (L), Digital Image Row (M), Digital Image Column (N) & Number of Pixels with Intensity Ri (n_j) and hit the calculate button.

FAQs on Histogram Linearization

What is the formula to find Histogram Linearization?

The formula of Histogram Linearization is expressed as 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)). Here is an example- 43.71585 = ((4-1)/(9*0.061)*sum(x,0,4-1,2)).

How to calculate Histogram Linearization?

With Number of Intensity Levels (L), Digital Image Row (M), Digital Image Column (N) & Number of Pixels with Intensity Ri (n_j) we can find Histogram Linearization using the 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)). This formula also uses Summation Notation Function function(s).

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Histogram Linearization Formula

Histogram Linearization Example

Histogram Linearization Solution

Histogram Linearization Formula Elements

Other formulas in Intensity Transformation category

How to Evaluate Histogram Linearization?

FAQs on Histogram Linearization

Variable Name