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Transformation Function Formula

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Transformation Function represents the transformation function.It typically maps the intensity values of pixels in an image to new intensity values to create a more evenly distributed histogram. Check FAQs

Tr k = (L - 1) \cdot \sum (x, 0, (L - 1), p ri)

Tr_k - Transformation Function?L - Number of Intensity Levels?p_ri - Probability of Intensity Ri?

Transformation Function Example

With values

With units

Only example

Here is how the Transformation Function equation looks like with Values.

Here is how the Transformation Function equation looks like with Units.

Here is how the Transformation Function equation looks like.

2.4 = (4 - 1) \cdot \sum (x, 0, (4 - 1), 0.2)

2.4 = (4 - 1) \cdot \sum (x, 0, (4 - 1), 0.2)

2.4 = (4 - 1) \cdot \sum (x, 0, (4 - 1), 0.2)

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Transformation Function Solution

Follow our step by step solution on how to calculate Transformation Function?

FIRST Step Consider the formula

Tr k = (L - 1) \cdot \sum (x, 0, (L - 1), p ri)

Next Step Substitute values of Variables

∴

Tr k = (4 - 1) \cdot \sum (x, 0, (4 - 1), 0.2)

Next Step Prepare to Evaluate

∴

Tr k = (4 - 1) \cdot \sum (x, 0, (4 - 1), 0.2)

LAST Step Evaluate

∴

Tr k = 2.4

Transformation Function Formula Elements

Variables

Functions

Transformation Function

Transformation Function represents the transformation function.It typically maps the intensity values of pixels in an image to new intensity values to create a more evenly distributed histogram.

Symbol: Tr_k

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Transformation Function

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 of Intensity Ri

Probability of Intensity Ri represents the probability of occurrence of the intensity level r_i. It indicates the likelihood of encountering a pixel with that specific intensity value in the image.

Symbol: p_ri

Measurement: NAUnit: Unitless

Note: Value should be less than 1.1.

Formulas to find Probability of 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 Transformation Function?

Transformation Function evaluator uses Transformation Function = (Number of Intensity Levels-1)*sum(x,0,(Number of Intensity Levels-1),Probability of Intensity Ri) to evaluate the Transformation Function, The Transformation Function formula represents the transformation function itself. In histogram equalization, this function typically maps the intensity values of pixels in an image to new intensity values to create a more evenly distributed histogram. Transformation Function is denoted by Tr_k symbol.

How to evaluate Transformation Function using this online evaluator? To use this online evaluator for Transformation Function, enter Number of Intensity Levels (L) & Probability of Intensity Ri (p_ri) and hit the calculate button.

FAQs on Transformation Function

What is the formula to find Transformation Function?

The formula of Transformation Function is expressed as Transformation Function = (Number of Intensity Levels-1)*sum(x,0,(Number of Intensity Levels-1),Probability of Intensity Ri). Here is an example- 2.4 = (4-1)*sum(x,0,(4-1),0.2).

How to calculate Transformation Function?

With Number of Intensity Levels (L) & Probability of Intensity Ri (p_ri) we can find Transformation Function using the formula - Transformation Function = (Number of Intensity Levels-1)*sum(x,0,(Number of Intensity Levels-1),Probability of Intensity Ri). This formula also uses Summation Notation (sum) function(s).

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Transformation Function Formula

Transformation Function Example

Transformation Function Solution

Transformation Function Formula Elements

Other formulas in Intensity Transformation category

How to Evaluate Transformation Function?

FAQs on Transformation Function

Variable Name