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| − | Introduction & Background | + | '''Introduction & Background''' |
Generally, there are two criteria to determine image similarity, the coefficient of determination (R2) and the mean absolute error (MAE). Here in this project, I use the coefficient of determination for similarity analysis. | Generally, there are two criteria to determine image similarity, the coefficient of determination (R2) and the mean absolute error (MAE). Here in this project, I use the coefficient of determination for similarity analysis. | ||
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or <math>R2 = \frac{SS_{xy}^2}{SS_{xx} SS_{yy} }</math> ( 2 ) | or <math>R2 = \frac{SS_{xy}^2}{SS_{xx} SS_{yy} }</math> ( 2 ) | ||
| − | | + | where <math>SS_{xy} = \sum_{i=1}^N (y_i - y_{avg})(x_i - x_{avg})</math> ( 3 ) |
| − | <math>SS_{yy} = \sum_{i=1}^N (y_i - y_{avg})^2</math> ( 4 ) | + | <math>SS_{yy} = \sum_{i=1}^N (y_i - y_{avg})^2</math> ( 4 ) |
| − | <math>SS_{xx} = \sum_{i=1}^N (x_i - x_{avg})^2</math> ( 5 ) | + | <math>SS_{xx} = \sum_{i=1}^N (x_i - x_{avg})^2</math> ( 5 ) |
| + | |||
| + | Where N is the total number of the components. x is the value of reference image, y is the value of the other image. x<sub>avg</sub> is the mean of the x values and y<sub>avg</sub> is the mean of the y values. | ||
| + | |||
| + | The meaning of R2: R2 value varies from 0 to 1. 1 means perfect fit between models, 0 means very poor fit; a good fit if R2 >0.8, and poor fit if R2<0.3. | ||
<br> <br> | <br> <br> | ||
Revision as of 06:54, 6 December 2011
Similarity analysis of images
Look at the Mona Lisa(s) above. They are very similar, aren't they? It's obvious, and you can say that they have high similarity. But given the pictures below, how to determine the similarity? Let's see!
Introduction & Background
Generally, there are two criteria to determine image similarity, the coefficient of determination (R2) and the mean absolute error (MAE). Here in this project, I use the coefficient of determination for similarity analysis.
The computation of R2 is:
$ R2 = 1 - {\sum_{i=1}^N (y_i - y_{pre})^2 / \sum_{i=1}^N (y_i - y_{avg})^2 } $ ( 1 )
or $ R2 = \frac{SS_{xy}^2}{SS_{xx} SS_{yy} } $ ( 2 )
where $ SS_{xy} = \sum_{i=1}^N (y_i - y_{avg})(x_i - x_{avg}) $ ( 3 )
$ SS_{yy} = \sum_{i=1}^N (y_i - y_{avg})^2 $ ( 4 )
$ SS_{xx} = \sum_{i=1}^N (x_i - x_{avg})^2 $ ( 5 )
Where N is the total number of the components. x is the value of reference image, y is the value of the other image. xavg is the mean of the x values and yavg is the mean of the y values.
The meaning of R2: R2 value varies from 0 to 1. 1 means perfect fit between models, 0 means very poor fit; a good fit if R2 >0.8, and poor fit if R2<0.3.
...to be continued
