✖Coefficient a is one of the four coefficients determined from the four equations in four unknowns that can be written using the four nearest neighbors of point (x,y).ⓘ Coefficient a [A]			+10% -10%
✖X Co-ordinate of the location to which we want to assign an intensity value.ⓘ X Co-ordinate [X]			+10% -10%
✖Coefficient b is one of the four coefficients determined from the four equations in four unknowns that can be written using the four nearest neighbors of point.ⓘ Coefficient b [B]			+10% -10%
✖Y Co-ordinate of the location to which we want to assign an intensity value.ⓘ Y Co-ordinate [Y]			+10% -10%
✖Coefficient c is one of the four coefficients determined from the four equations in four unknowns that can be written using the four nearest neighbors of point (x,y).ⓘ Coefficient c [C]			+10% -10%
✖Coefficient d is one of the four coefficients determined from the four equations in four unknowns that can be written using the four nearest neighbors of point (x,y).ⓘ Coefficient d [D]			+10% -10%

✖Bilinear Interpolation is a resampling method in image processing that calculates pixel values using a weighted average of the four nearest pixels, providing smoother transitions.ⓘ Bilinear Interpolation [V_x,y]

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Formula

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Bilinear Interpolation

Formula

`"V"_{"x,y"} = "A"*"X"+"B"*"Y"+"C"*"X"*"Y"+"D"`

Example

`"207.85"="3.5"*"7"+"1.15"*"6"+"4.15"*"7"*"6"+"2.15"`

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Bilinear Interpolation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Bilinear Interpolation = Coefficient a*X Co-ordinate+Coefficient b*Y Co-ordinate+Coefficient c*X Co-ordinate*Y Co-ordinate+Coefficient d
V_x,y = A*X+B*Y+C*X*Y+D
This formula uses 7 Variables

Variables Used

Bilinear Interpolation - Bilinear Interpolation is a resampling method in image processing that calculates pixel values using a weighted average of the four nearest pixels, providing smoother transitions.
Coefficient a - Coefficient a is one of the four coefficients determined from the four equations in four unknowns that can be written using the four nearest neighbors of point (x,y).
X Co-ordinate - X Co-ordinate of the location to which we want to assign an intensity value.
Coefficient b - Coefficient b is one of the four coefficients determined from the four equations in four unknowns that can be written using the four nearest neighbors of point.
Y Co-ordinate - Y Co-ordinate of the location to which we want to assign an intensity value.
Coefficient c - Coefficient c is one of the four coefficients determined from the four equations in four unknowns that can be written using the four nearest neighbors of point (x,y).
Coefficient d - Coefficient d is one of the four coefficients determined from the four equations in four unknowns that can be written using the four nearest neighbors of point (x,y).

STEP 1: Convert Input(s) to Base Unit

Coefficient a: 3.5 --> No Conversion Required
X Co-ordinate: 7 --> No Conversion Required
Coefficient b: 1.15 --> No Conversion Required
Y Co-ordinate: 6 --> No Conversion Required
Coefficient c: 4.15 --> No Conversion Required
Coefficient d: 2.15 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_x,y = A*X+B*Y+C*X*Y+D --> 3.5*7+1.15*6+4.15*7*6+2.15

Evaluating ... ...

V_x,y = 207.85

STEP 3: Convert Result to Output's Unit

207.85 --> No Conversion Required

FINAL ANSWER

207.85 <-- Bilinear Interpolation

(Calculation completed in 00.005 seconds)

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< 17 Basics of Image Processing Calculators

Standard Deviation by Linear Function of Camera Exposure Time

Go Standard Deviation = Model Function*(Radiant Intensity)*Model Behaviour Function*(1/Distance between Camera and the IRED^2)*(Model Coefficient 1*Camera Exposure Time+Model Coefficient 2)

Bilinear Interpolation

Go Bilinear Interpolation = Coefficient a*X Co-ordinate+Coefficient b*Y Co-ordinate+Coefficient c*X Co-ordinate*Y Co-ordinate+Coefficient d

Linear Combination of Expansion

Go Linear Combination of Expansion Functions = sum(x,0,Integer Index for Linear Expansion,Real Valued Expansion Coefficients*Real Valued Expansion Functions)

Cumulative Frequency for Each Brightness Value

Go Cumulative Frequency for Each Brightness = 1/Total Number of Pixels*sum(x,0,Maximum Brightness Value,Frequency of Occurrence of Each Brightness Value)

Band Loads Associated with Principle Components

Go K Band Loads with P Principle Components = Eigen Band k Component P*sqrt(Pth Eigenvalue)/sqrt(Band Variance Matrix)

Run-Length Entropy of Image

Go Run Length Entropy Image = (Entropy Black Run Length+Entropy of White Run Length)/(Average Black Run Length+Average White Run Length)

Wavelet Coefficient

Go Detail Wavelet Coefficient = int(Scaling Function Expansion*Wavelet Expansion Function*x,x,0,Integer Index for Linear Expansion)

Quantization Step Size in Image Processing

Go Quantization Step Size = (2^(Nominal Dynamic Range-Bits Allotted Exponent Number))*(1+Bits Allotted to Mantissa Number/2^11)

Digital Image Row

Go Digital Image Row = sqrt(Number of Bits/Digital Image Column)

Digital to Analog Converter

Go Digital to Analog Converter Resolution = Reference Voltage Image/(2^Number of Bits-1)

Rejection of Image Frequency

Go Customer Selling Price = (1+Quality Factor Image^2*Rejection Constant Image^2)^0.5

Probability of Intensity Level Occurring in given Image

Go Probability of Intensity = Intensity Occurs in Image/Total Number of Pixels

Digital Image Column

Go Digital Image Column = Number of Bits/(Digital Image Row^2)

Number of Bits

Go Number of Bits = (Digital Image Row^2)*Digital Image Column

Image File Size

Go Image File Size = Image Resolution*Bit Depth/8000

Energy of Various Components

Go Energy of Component = [hP]*Frequency

Number of Grey Level

Go Grey Level Image = 2^Digital Image Column

Bilinear Interpolation Formula

Bilinear Interpolation = Coefficient a*X Co-ordinate+Coefficient b*Y Co-ordinate+Coefficient c*X Co-ordinate*Y Co-ordinate+Coefficient d
V_x,y = A*X+B*Y+C*X*Y+D

What is Bilinear Interpolation?

Bilinear Interpolation, is in which we use the four nearest neighbors to estimate
the intensity at a given location.

How to Calculate Bilinear Interpolation?

Bilinear Interpolation calculator uses Bilinear Interpolation = Coefficient a*X Co-ordinate+Coefficient b*Y Co-ordinate+Coefficient c*X Co-ordinate*Y Co-ordinate+Coefficient d to calculate the Bilinear Interpolation, Bilinear Interpolation is a method for interpolating functions of two variables (e.g., x and y) using repeated linear interpolation. It is usually applied to functions sampled on a 2D rectilinear grid, though it can be generalized to functions defined on the vertices of (a mesh of) arbitrary convex quadrilaterals. Bilinear Interpolation is denoted by V_x,y symbol.

How to calculate Bilinear Interpolation using this online calculator? To use this online calculator for Bilinear Interpolation, enter Coefficient a (A), X Co-ordinate (X), Coefficient b (B), Y Co-ordinate (Y), Coefficient c (C) & Coefficient d (D) and hit the calculate button. Here is how the Bilinear Interpolation calculation can be explained with given input values -> 207.85 = 3.5*7+1.15*6+4.15*7*6+2.15.

FAQ

What is Bilinear Interpolation?

Bilinear Interpolation is a method for interpolating functions of two variables (e.g., x and y) using repeated linear interpolation. It is usually applied to functions sampled on a 2D rectilinear grid, though it can be generalized to functions defined on the vertices of (a mesh of) arbitrary convex quadrilaterals and is represented as V_x,y = A*X+B*Y+C*X*Y+D or Bilinear Interpolation = Coefficient a*X Co-ordinate+Coefficient b*Y Co-ordinate+Coefficient c*X Co-ordinate*Y Co-ordinate+Coefficient d. Coefficient a is one of the four coefficients determined from the four equations in four unknowns that can be written using the four nearest neighbors of point (x,y), X Co-ordinate of the location to which we want to assign an intensity value, Coefficient b is one of the four coefficients determined from the four equations in four unknowns that can be written using the four nearest neighbors of point, Y Co-ordinate of the location to which we want to assign an intensity value, Coefficient c is one of the four coefficients determined from the four equations in four unknowns that can be written using the four nearest neighbors of point (x,y) & Coefficient d is one of the four coefficients determined from the four equations in four unknowns that can be written using the four nearest neighbors of point (x,y).

How to calculate Bilinear Interpolation?

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