Variance of Pixels in Subimage 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 Occurrence of Rith in Subimage represents the probability of occurrence of the intensity level r_i within the subimage S_xy.ⓘ Probability of Occurrence of Rith in Subimage [p_{Sxy_ri}]			+10% -10%
✖Intensity Level of Ith Pixel represents the i-th possible intensity level in the image.ⓘ Intensity Level of Ith Pixel [r_i]			+10% -10%
✖Subimage Pixel Mean Intensity Level represents the mean intensity level of pixels in the subimage S_xy.ⓘ Subimage Pixel Mean Intensity Level [m_Sxy]			+10% -10%

✖Variance of Pixels in Subimage represents the variance of pixel intensities in the subimage S_xy. The unit of variance is the square of the unit of the intensity levels.ⓘ Variance of Pixels in Subimage [σ²Sxy]

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Formula

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Variance of Pixels in Subimage

Formula

`("σ"^{"2"}"Sxy") = sum(x,0,"L"-1,"p"_{"Sxy_ri"}*("r"_{"i"}-"m"_{"Sxy"})^2)`

Example

`"9"=sum(x,0,"4"-1,"0.25"*("15W/m²"-"12")^2)`

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Variance of Pixels in Subimage Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
σ²Sxy = sum(x,0,L-1,p_{Sxy_ri}*(r_i-m_Sxy)^2)
This formula uses 1 Functions, 5 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

Variance of Pixels in Subimage - Variance of Pixels in Subimage represents the variance of pixel intensities in the subimage S_xy. The unit of variance is the square of the unit of the intensity levels.
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 Occurrence of Rith in Subimage - Probability of Occurrence of Rith in Subimage represents the probability of occurrence of the intensity level r_i within the subimage S_xy.
Intensity Level of Ith Pixel - (Measured in Watt per Square Meter) - Intensity Level of Ith Pixel represents the i-th possible intensity level in the image.
Subimage Pixel Mean Intensity Level - Subimage Pixel Mean Intensity Level represents the mean intensity level of pixels in the subimage S_xy.

STEP 1: Convert Input(s) to Base Unit

Number of Intensity Levels: 4 --> No Conversion Required
Probability of Occurrence of Rith in Subimage: 0.25 --> No Conversion Required
Intensity Level of Ith Pixel: 15 Watt per Square Meter --> 15 Watt per Square Meter No Conversion Required
Subimage Pixel Mean Intensity Level: 12 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ²Sxy = sum(x,0,L-1,p_{Sxy_ri}*(r_i-m_Sxy)^2) --> sum(x,0,4-1,0.25*(15-12)^2)

Evaluating ... ...

σ²Sxy = 9

STEP 3: Convert Result to Output's Unit

9 --> No Conversion Required

FINAL ANSWER

9 <-- Variance of Pixels in Subimage

(Calculation completed in 00.020 seconds)

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Credits

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

Variance of Pixels in Subimage Formula

What are the Application's of Variance of Pixels in Subimage ?

1. Image Segmentation: By analyzing variance across different subimages, we can identify regions with similar intensity characteristics, aiding in segmenting objects from the background.
2. Feature Extraction: Variance serves as a quantitative feature, allowing us to extract information about the texture or uniformity within a subimage.
3. Image Quality Assessment: High variance often indicates high contrast, while low variance suggests a more uniform region. This helps assess image quality factors.

How to Calculate Variance of Pixels in Subimage?

Variance of Pixels in Subimage calculator uses 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) to calculate the Variance of Pixels in Subimage, The Variance of Pixels in Subimage formula represents the variance of pixel intensities in the subimage (S_xy). The unit of variance is the square of the unit of the intensity levels. Variance of Pixels in Subimage is denoted by σ²Sxy symbol.

How to calculate Variance of Pixels in Subimage using this online calculator? To use this online calculator for Variance of Pixels in Subimage, enter Number of Intensity Levels (L), Probability of Occurrence of Rith in Subimage (p_{Sxy_ri}), Intensity Level of Ith Pixel (r_i) & Subimage Pixel Mean Intensity Level (m_Sxy) and hit the calculate button. Here is how the Variance of Pixels in Subimage calculation can be explained with given input values -> 9 = sum(x,0,4-1,0.25*(15-12)^2).

FAQ

What is Variance of Pixels in Subimage?

The Variance of Pixels in Subimage formula represents the variance of pixel intensities in the subimage (S_xy). The unit of variance is the square of the unit of the intensity levels and is represented as σ²Sxy = sum(x,0,L-1,p_{Sxy_ri}*(r_i-m_Sxy)^2) or 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). Number of Intensity Levels is the total number of distinct intensity values an image can represent, determined by its bit depth, Probability of Occurrence of Rith in Subimage represents the probability of occurrence of the intensity level r_i within the subimage S_xy, Intensity Level of Ith Pixel represents the i-th possible intensity level in the image & Subimage Pixel Mean Intensity Level represents the mean intensity level of pixels in the subimage S_xy.

How to calculate Variance of Pixels in Subimage?

The Variance of Pixels in Subimage formula represents the variance of pixel intensities in the subimage (S_xy). The unit of variance is the square of the unit of the intensity levels is calculated using 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). To calculate Variance of Pixels in Subimage, you need Number of Intensity Levels (L), Probability of Occurrence of Rith in Subimage (p_{Sxy_ri}), Intensity Level of Ith Pixel (r_i) & Subimage Pixel Mean Intensity Level (m_Sxy). With our tool, you need to enter the respective value for Number of Intensity Levels, Probability of Occurrence of Rith in Subimage, Intensity Level of Ith Pixel & Subimage Pixel Mean Intensity Level 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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