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Bilinear Interpolation Formula

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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. Check FAQs

V x,y = A \cdot X + B \cdot Y + C \cdot X \cdot Y + D

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

Bilinear Interpolation Example

With values

With units

Only example

Here is how the Bilinear Interpolation equation looks like with Values.

Here is how the Bilinear Interpolation equation looks like with Units.

Here is how the Bilinear Interpolation equation looks like.

207.85 = 3.5 \cdot 7 + 1.15 \cdot 6 + 4.15 \cdot 7 \cdot 6 + 2.15

207.85 = 3.5 \cdot 7 + 1.15 \cdot 6 + 4.15 \cdot 7 \cdot 6 + 2.15

207.85 = 3.5 \cdot 7 + 1.15 \cdot 6 + 4.15 \cdot 7 \cdot 6 + 2.15

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Bilinear Interpolation Solution

Follow our step by step solution on how to calculate Bilinear Interpolation?

FIRST Step Consider the formula

V x,y = A \cdot X + B \cdot Y + C \cdot X \cdot Y + D

Next Step Substitute values of Variables

∴

V x,y = 3.5 \cdot 7 + 1.15 \cdot 6 + 4.15 \cdot 7 \cdot 6 + 2.15

Next Step Prepare to Evaluate

∴

V x,y = 3.5 \cdot 7 + 1.15 \cdot 6 + 4.15 \cdot 7 \cdot 6 + 2.15

LAST Step Evaluate

∴

V x,y = 207.85

Bilinear Interpolation Formula Elements

Variables

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.

Symbol: V_x,y

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Bilinear Interpolation

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).

Symbol: A

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Coefficient a

X Co-ordinate

X Co-ordinate of the location to which we want to assign an intensity value.

Symbol: X

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find X Co-ordinate

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.

Symbol: B

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Coefficient b

Y Co-ordinate

Y Co-ordinate of the location to which we want to assign an intensity value.

Symbol: Y

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Y Co-ordinate

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).

Symbol: C

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Coefficient c

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).

Symbol: D

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Coefficient d

Other formulas in Basics of Image Processing category

Go Digital Image Row

M = \sqrt{\frac{n b}{N}}

Go Digital Image Column

N = \frac{n b}{M^{2}}

How to Evaluate Bilinear Interpolation?

Bilinear Interpolation evaluator uses Bilinear Interpolation = Coefficient a*X Co-ordinate+Coefficient b*Y Co-ordinate+Coefficient c*X Co-ordinate*Y Co-ordinate+Coefficient d to evaluate 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 evaluate Bilinear Interpolation using this online evaluator? To use this online evaluator 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.

FAQs on Bilinear Interpolation

What is the formula to find Bilinear Interpolation?

The formula of Bilinear Interpolation is expressed as Bilinear Interpolation = Coefficient a*X Co-ordinate+Coefficient b*Y Co-ordinate+Coefficient c*X Co-ordinate*Y Co-ordinate+Coefficient d. Here is an example- 207.85 = 3.5*7+1.15*6+4.15*7*6+2.15.

How to calculate Bilinear Interpolation?

With Coefficient a (A), X Co-ordinate (X), Coefficient b (B), Y Co-ordinate (Y), Coefficient c (C) & Coefficient d (D) we can find Bilinear Interpolation using the formula - Bilinear Interpolation = Coefficient a*X Co-ordinate+Coefficient b*Y Co-ordinate+Coefficient c*X Co-ordinate*Y Co-ordinate+Coefficient d.

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Bilinear Interpolation Formula

Bilinear Interpolation Example

Bilinear Interpolation Solution

Bilinear Interpolation Formula Elements

Other formulas in Basics of Image Processing category

How to Evaluate Bilinear Interpolation?

FAQs on Bilinear Interpolation

Variable Name