# Accuracy of polygon approximation

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Mohammad Abu Haifa
on 19 Nov 2021

Answered: Kelly Kearney
on 19 Nov 2021

I have 2 matrices; one for the a data set (x,y), and the second one for the approximated shape of the points using polygon approximation techniques.

The size of the first one is 277*2 (green points) and the size of the second one is 5*2 (red line with five vertices).

I need to find the accuracy of the approximation such as R^2 value or any other parameter.

Can anyone please help me with how I can find the accuracy of the approximation?

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### Accepted Answer

John D'Errico
on 19 Nov 2021

R*2 is not remotely meaningful here, unless you find a way to intelligently extend it to this situation.

I would probably find the closest point on the curve for each data point. What is the distance to that curve, for each point. Now you might compute the sum of squares of those distances. Call that A. Finally, compute the sum of squares of the distances for each point to the mean of all of your data. Call that B.

Finally, compute the parameter

P = 1 - A/B

Note that P might be considered to be somewhat analogous to an R^2 parameter. It will be 1 when the polygon passes exactly through the points. It will be 0 for the simple polygon that lies exactly at the mean of your data, thus just a single point.

### More Answers (2)

Matt J
on 19 Nov 2021

Edited: Matt J
on 19 Nov 2021

Perhaps the Dice Coefficient would be an appropriate metric. This would be a very easy calculation if the shapes are stored as polyshape objects:

DSC = 2*area(intersect(red,green))/(area(red)+area(green))

##### 1 Comment

Image Analyst
on 19 Nov 2021

Or, if you have the Image Processing Toolbox:

dice

Sørensen-Dice similarity coefficient for image segmentation

Syntax

Description

similarity = dice(BW1,BW2) computes the Sørensen-Dice similarity coefficient between binary images BW1 and BW2.

Kelly Kearney
on 19 Nov 2021

##### 0 Comments

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