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Transformation Function Calculator

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Intensity Transformation Basics of Image Processing

✖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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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

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< Intensity Transformation Calculators

Bits Required to Store Digitized Image

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

Bits Required to Store Square Image

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

Wavelength of Light

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

Number of Intensity Levels

LaTeX Go Number of Intensity Levels = 2^Number of Bits

Transformation Function Formula

LaTeX Go

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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