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Nth Moment of Discrete Random Variable 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%
✖Pixel Intensity Level refer to the range of possible intensity values that can be assigned to pixels in an image. This concept is particularly relevant in grayscale images.ⓘ Pixel Intensity Level [r_i]			+10% -10%
✖Mean of Intensity Level represents the mean of the intensity levels, which is essentially the average intensity value across the entire image.ⓘ Mean of Intensity Level [m]			+10% -10%
✖Order of Moment denotes the order of the moment, which determines the weighting applied to each intensity level.ⓘ Order of Moment [n]			+10% -10%

✖Nth Moment of Discrete Random Variable represents the nth moment of the random variable r, which typically refers to the intensity level of a pixel in the image.ⓘ Nth Moment of Discrete Random Variable [μ_n]

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Nth Moment of Discrete Random Variable Solution

STEP 0: Pre-Calculation Summary

Formula Used

Nth Moment of Discrete Random Variable = sum(x,0,Number of Intensity Levels-1,Probability of Intensity Ri*(Pixel Intensity Level-Mean of Intensity Level)^Order of Moment)
μ_n = sum(x,0,L-1,p_ri*(r_i-m)^n)
This formula uses 1 Functions, 6 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

Nth Moment of Discrete Random Variable - (Measured in Watt per Square Meter) - Nth Moment of Discrete Random Variable represents the nth moment of the random variable r, which typically refers to the intensity level of a pixel in the image.
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.
Pixel Intensity Level - (Measured in Watt per Square Meter) - Pixel Intensity Level refer to the range of possible intensity values that can be assigned to pixels in an image. This concept is particularly relevant in grayscale images.
Mean of Intensity Level - Mean of Intensity Level represents the mean of the intensity levels, which is essentially the average intensity value across the entire image.
Order of Moment - Order of Moment denotes the order of the moment, which determines the weighting applied to each intensity level.

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
Pixel Intensity Level: 15 Watt per Square Meter --> 15 Watt per Square Meter No Conversion Required
Mean of Intensity Level: 7 --> No Conversion Required
Order of Moment: 4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

μ_n = sum(x,0,L-1,p_ri*(r_i-m)^n) --> sum(x,0,4-1,0.2*(15-7)^4)

Evaluating ... ...

μ_n = 3276.8

STEP 3: Convert Result to Output's Unit

3276.8 Watt per Square Meter --> No Conversion Required

FINAL ANSWER

3276.8 Watt per Square Meter <-- Nth Moment of Discrete Random Variable

(Calculation completed in 00.011 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

Nth Moment of Discrete Random Variable Formula

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What is Nth Moment of a Discrete Random Variable in Digital Image Processing ?

The nth moment of a discrete random variable, in the context of digital image processing, characterizes the statistical properties of the intensity distribution in an image.
Statistical Properties: Different moments capture different aspects of the distribution, such as:
Mean (n = 1): Average intensity level (overall brightness).
Variance (n = 2): Spread of intensity values around the mean (high variance indicates high contrast).
Skewness (n = 3): Asymmetry of the distribution (positive skew suggests more bright pixels).
Kurtosis (n = 4): "Peakedness" of the distribution compared to a normal distribution.

What are the Applications of Nth Moments ?

Image Segmentation: Identifying regions with similar intensity characteristics, which can be helpful in segmenting objects from the background.
Feature Extraction: Extracting quantitative features from images based on moments, such as texture analysis or shape recognition.
Image Quality Assessment: Analyzing the distribution of intensity levels to assess factors like contrast or noise levels in an image.

How to Calculate Nth Moment of Discrete Random Variable?

Nth Moment of Discrete Random Variable calculator uses Nth Moment of Discrete Random Variable = sum(x,0,Number of Intensity Levels-1,Probability of Intensity Ri*(Pixel Intensity Level-Mean of Intensity Level)^Order of Moment) to calculate the Nth Moment of Discrete Random Variable, The Nth Moment of Discrete Random Variable formula characterizes the average behavior of pixel intensity (r) raised to the power of n in a digital image. Nth Moment of Discrete Random Variable is denoted by μ_n symbol.

How to calculate Nth Moment of Discrete Random Variable using this online calculator? To use this online calculator for Nth Moment of Discrete Random Variable, enter Number of Intensity Levels (L), Probability of Intensity Ri (p_ri), Pixel Intensity Level (r_i), Mean of Intensity Level (m) & Order of Moment (n) and hit the calculate button. Here is how the Nth Moment of Discrete Random Variable calculation can be explained with given input values -> 3276.8 = sum(x,0,4-1,0.2*(15-7)^4).

FAQ

What is Nth Moment of Discrete Random Variable?

The Nth Moment of Discrete Random Variable formula characterizes the average behavior of pixel intensity (r) raised to the power of n in a digital image and is represented as μ_n = sum(x,0,L-1,p_ri*(r_i-m)^n) or Nth Moment of Discrete Random Variable = sum(x,0,Number of Intensity Levels-1,Probability of Intensity Ri*(Pixel Intensity Level-Mean of Intensity Level)^Order of Moment). 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, Pixel Intensity Level refer to the range of possible intensity values that can be assigned to pixels in an image. This concept is particularly relevant in grayscale images, Mean of Intensity Level represents the mean of the intensity levels, which is essentially the average intensity value across the entire image & Order of Moment denotes the order of the moment, which determines the weighting applied to each intensity level.

How to calculate Nth Moment of Discrete Random Variable?

The Nth Moment of Discrete Random Variable formula characterizes the average behavior of pixel intensity (r) raised to the power of n in a digital image is calculated using Nth Moment of Discrete Random Variable = sum(x,0,Number of Intensity Levels-1,Probability of Intensity Ri*(Pixel Intensity Level-Mean of Intensity Level)^Order of Moment). To calculate Nth Moment of Discrete Random Variable, you need Number of Intensity Levels (L), Probability of Intensity Ri (p_ri), Pixel Intensity Level (r_i), Mean of Intensity Level (m) & Order of Moment (n). With our tool, you need to enter the respective value for Number of Intensity Levels, Probability of Intensity Ri, Pixel Intensity Level, Mean of Intensity Level & Order of Moment 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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