[Insight-developers] is it a bug in mean reciprocal square image to image metric

[Luis Ibanez]

Hi Ashish,

No,
this Metrics *must not* be divided by the number of pixels counted.

In fact, the nice property of this metric is that it gets better
when you use many pixels.

Here is the rationale:

When you use a metric such as mean squares, where the contributions
of individual pixels are "good" when they have numerical values,
you have the conflicting situation that you can get a good value
because the pixels are very close in intensities, or because you
have just a few pixels. Therefore, in order to eliminate the second
case you are forced to divide by the number of pixels.

In the case of the reciprocal metric, the more pixels you count,
the better the metric gets, and the closer their intensities are
between the fixed and the moving image, the better the metric gets.

Dividing by the number of pixels will destroy the most interesting
property of this metric.


Another nice property of this metric is the fact that you know what
the optimal value would be. It is equal to the number of pixels
counted. E.g. this is obtained only when all the intensities of the
fixed image pixels are equal to the intensities of the moving image
pixels.



Please let us know if you have any other questions,


    Thanks



      Luis


---------------------
Ashish Poddar wrote:

> Hi,
> 
> in mean reciprocal square image to image metric, the value being 
> returned is simply the sum of 1.0f / ( 1.0f + m_Lambda* ( diff * diff ) 
> ); for all the differences computed throughout the image. isnt it 
> supposed to be divided by the this->m_NumberOfPixelsCounted in the end 
> before returning?
> 
> with regards,
> Ashish.
>