# Local signal-to-noise ratio for an image

I want to do one of these common experiments to see the effect of increased noise on the performance of a feature detector.

To do this add zero mean gaussian noise with fixed sigma to the image and look at the result. To vary the amount of noise I multiply the noise signal by different amounts before adding.

Since the detector uses a bandpass filter as a first step, to calculate the SNR of the noisy image I calculate the energy of the bandpassed original image, and the energy of the band passed noise signal (before adding them together).

Does this sound reasonable (and is that method of adding noise correct)? My concern is that because the image is being bandpassed, if I evaluate the performance of the detector at a specific point I should be using an SNR value for that local area, rather than the whole image.

How would one go about calculating local signal to noise ratio?

• Bandpassing the noise will affect its statistics (i.e. variance), but the noise will still be Gaussian and the noise statistics will still be the same for each point in the image (assuming that the noise statistics are the same for each point before you bandpassed). – jstarr Jan 26 '13 at 2:59
• I dont think that assumption is met. For example, imagine evaluating a line detector. You have an image of a line of fixed width and height on a black background. The energy of the image would be the same regardless of image size because the line is fixed. But if you add some noise, then the noise energy would depend on the image size, even though the actual amount of noise in the local area remains the same. – geometrikal Jan 26 '13 at 3:23
• Without knowing more about your application, it seems reasonable to me to evaluate the performance of your detector by running it on fixed-size images over many Monte Carlo varying-energy noise realizations. A plot of detection error versus noise-energy per pixel generated using this method seems like a useful way to evaluate your approach against other detection methods. I would not recommend using a local signal to noise ratio. – jstarr Jan 26 '13 at 5:14