Transformation Function Calculator

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Intensity Transformation

Digital Image Fundamentals

✖Number of Intensity Levels is the total number of distinct intensity values an image can represent, determined by its bit depth.ⓘ Number of Intensity Levels [L]			+10% -10%
✖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.ⓘ Probability of Intensity Ri [p_ri]			+10% -10%

✖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.ⓘ Transformation Function [Tr_k]

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Formula

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Transformation Function

Formula

`"Tr"_{"k"} = ("L"-1)*sum(x,0,("L"-1),"p"_{"ri"})`

Example

`"2.4"=("4"-1)*sum(x,0,("4"-1),"0.2")`

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Transformation Function Solution

STEP 0: Pre-Calculation Summary

Formula Used

Transformation Function = (Number of Intensity Levels-1)*sum(x,0,(Number of Intensity Levels-1),Probability of Intensity Ri)
Tr_k = (L-1)*sum(x,0,(L-1),p_ri)
This formula uses 1 Functions, 3 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

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.
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 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.

STEP 1: Convert Input(s) to Base Unit

Number of Intensity Levels: 4 --> No Conversion Required
Probability of Intensity Ri: 0.2 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Tr_k = (L-1)*sum(x,0,(L-1),p_ri) --> (4-1)*sum(x,0,(4-1),0.2)

Evaluating ... ...

Tr_k = 2.4

STEP 3: Convert Result to Output's Unit

2.4 --> No Conversion Required

FINAL ANSWER

2.4 <-- Transformation Function

(Calculation completed in 00.004 seconds)

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Created by Vignesh Naidu

Vellore Institute of Technology (VIT), Vellore,Tamil Nadu

Vignesh Naidu has created this Calculator and 25+ more calculators!

Verified by Dipanjona Mallick

Heritage Insitute of technology (HITK), Kolkata

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< 14 Intensity Transformation Calculators

Histogram Linearization

Go 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

Go 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

Go 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

Go 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

Go 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

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

Transformation Function

Go 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

Go Average Intensity of Image = sum(x,0,(Intensity Value-1),(Intensity Level*Normalized Histogram Component))

Characteristic Response of Linear Filtering

Go Characteristic Response of Linear Filtering = sum(x,1,9,Filter Coefficients*Corresponding Image Intensities of Filter)

Bits Required to Store Digitized Image

Go Bits in Digitized Image = Digital Image Row*Digital Image Column*Number of Bits

Bits Required to Store Square Image

Go Bits in Digitized Square Image = (Digital Image Column)^2*Number of Bits

Energy of Components of EM Spectrum

Go Energy of Component = [hP]/Frequency of Light

Wavelength of Light

Go Wavelength of Light = [c]/Frequency of Light

Number of Intensity Levels

Go Number of Intensity Level = 2^Number of Bits

Transformation Function Formula

Transformation Function = (Number of Intensity Levels-1)*sum(x,0,(Number of Intensity Levels-1),Probability of Intensity Ri)
Tr_k = (L-1)*sum(x,0,(L-1),p_ri)

What are the Applications of Transformation Function ?

Image Processing:
Histogram Equalization: As discussed previously, transformation functions are crucial for histogram equalization, a technique used to improve image contrast by redistributing pixel intensities.

Image Enhancement: Transformations can be used for various image enhancement tasks like adjusting brightness, contrast, and color balance. Different functions can be applied to manipulate pixel values and achieve desired visual effects.

How to Calculate Transformation Function?

Transformation Function calculator uses Transformation Function = (Number of Intensity Levels-1)*sum(x,0,(Number of Intensity Levels-1),Probability of Intensity Ri) to calculate 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 calculate Transformation Function using this online calculator? To use this online calculator for Transformation Function, enter Number of Intensity Levels (L) & Probability of Intensity Ri (p_ri) and hit the calculate button. Here is how the Transformation Function calculation can be explained with given input values -> 2.4 = (4-1)*sum(x,0,(4-1),0.2).

FAQ

What is 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 and is represented as Tr_k = (L-1)*sum(x,0,(L-1),p_ri) or Transformation Function = (Number of Intensity Levels-1)*sum(x,0,(Number of Intensity Levels-1),Probability of Intensity Ri). Number of Intensity Levels is the total number of distinct intensity values an image can represent, determined by its bit depth & 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.

How to calculate 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 is calculated using Transformation Function = (Number of Intensity Levels-1)*sum(x,0,(Number of Intensity Levels-1),Probability of Intensity Ri). To calculate Transformation Function, you need Number of Intensity Levels (L) & Probability of Intensity Ri (p_ri). With our tool, you need to enter the respective value for Number of Intensity Levels & Probability of 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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