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Variance of Pixels in Subimage Formula

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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. Check FAQs

σ sxy = \sum (x, 0, L - 1, p Sxy_ri \cdot {(r i - m Sxy)}^{2})

σ_sxy - Variance of Pixels in Subimage?L - Number of Intensity Levels?p_{Sxy_ri} - Probability of Occurrence of Rith in Subimage?r_i - Pixel Intensity Level?m_Sxy - Subimage Pixel Mean Intensity Level?

Variance of Pixels in Subimage Example

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Here is how the Variance of Pixels in Subimage equation looks like with Values.

Here is how the Variance of Pixels in Subimage equation looks like with Units.

Here is how the Variance of Pixels in Subimage equation looks like.

9 = \sum (x, 0, 4 - 1, 0.25 \cdot {(15 - 12)}^{2})

9 = \sum (x, 0, 4 - 1, 0.25 \cdot {(15W/m² - 12)}^{2})

9 = \sum (x, 0, 4 - 1, 0.25 \cdot {(15 - 12)}^{2})

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Variance of Pixels in Subimage Solution

Follow our step by step solution on how to calculate Variance of Pixels in Subimage?

FIRST Step Consider the formula

σ sxy = \sum (x, 0, L - 1, p Sxy_ri \cdot {(r i - m Sxy)}^{2})

Next Step Substitute values of Variables

∴

σ sxy = \sum (x, 0, 4 - 1, 0.25 \cdot {(15W/m² - 12)}^{2})

Next Step Prepare to Evaluate

∴

σ sxy = \sum (x, 0, 4 - 1, 0.25 \cdot {(15 - 12)}^{2})

LAST Step Evaluate

∴

σ sxy = 9

Variance of Pixels in Subimage Formula Elements

Variables

Functions

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.

Symbol: σ_sxy

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Variance of Pixels in Subimage

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 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.

Symbol: p_{Sxy_ri}

Measurement: NAUnit: Unitless

Note: Value should be less than 1.1.

Formulas to find Probability of Occurrence of Rith in Subimage

Pixel Intensity Level

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.

Symbol: r_i

Measurement: IntensityUnit: W/m²

Note: Value should be greater than 0.

Formulas to find Pixel Intensity Level

Subimage Pixel Mean Intensity Level

Subimage Pixel Mean Intensity Level represents the mean intensity level of pixels in the subimage S_xy.

Symbol: m_Sxy

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Subimage Pixel Mean Intensity Level

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 Variance of Pixels in Subimage?

Variance of Pixels in Subimage evaluator uses Variance of Pixels in Subimage = sum(x,0,Number of Intensity Levels-1,Probability of Occurrence of Rith in Subimage*(Pixel Intensity Level-Subimage Pixel Mean Intensity Level)^2) to evaluate 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 σ_sxy symbol.

How to evaluate Variance of Pixels in Subimage using this online evaluator? To use this online evaluator for Variance of Pixels in Subimage, enter Number of Intensity Levels (L), Probability of Occurrence of Rith in Subimage (p_{Sxy_ri}), Pixel Intensity Level (r_i) & Subimage Pixel Mean Intensity Level (m_Sxy) and hit the calculate button.

FAQs on Variance of Pixels in Subimage

What is the formula to find Variance of Pixels in Subimage?

The formula of Variance of Pixels in Subimage is expressed as Variance of Pixels in Subimage = sum(x,0,Number of Intensity Levels-1,Probability of Occurrence of Rith in Subimage*(Pixel Intensity Level-Subimage Pixel Mean Intensity Level)^2). Here is an example- 9 = sum(x,0,4-1,0.25*(15-12)^2).

How to calculate Variance of Pixels in Subimage?

With Number of Intensity Levels (L), Probability of Occurrence of Rith in Subimage (p_{Sxy_ri}), Pixel Intensity Level (r_i) & Subimage Pixel Mean Intensity Level (m_Sxy) we can find Variance of Pixels in Subimage using the formula - Variance of Pixels in Subimage = sum(x,0,Number of Intensity Levels-1,Probability of Occurrence of Rith in Subimage*(Pixel Intensity Level-Subimage Pixel Mean Intensity Level)^2). This formula also uses Summation Notation (sum) function(s).

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Variance of Pixels in Subimage Formula

Variance of Pixels in Subimage Example

Variance of Pixels in Subimage Solution

Variance of Pixels in Subimage Formula Elements

Other formulas in Intensity Transformation category

How to Evaluate Variance of Pixels in Subimage?

FAQs on Variance of Pixels in Subimage

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