Posts Tagged ‘comparison’

## Evaluating noise filters

Saturday, September 1st, 2012

Most of the new papers that I come across that propose a new or improved way of filtering out noise from images use the Peak Signal-to-Noise Ratio (PSNR) as a means to evaluate their results. It has been shown again and again that this is not a good way of evaluating the performance of a filter. When people compute the PSNR for a filtered image, what they actually do is compare this filtered image to an undistorted one (i.e. known ground truth). This is very different from what the name PSNR implies: the ratio of peak signal power to noise power. Of course, that is something that cannot be measured: if we’d be able to separate the noise from the signal and measure the power of the two components, then we wouldn’t need to write so many papers about filters that remove noise! So instead, the typical PSNR measure in image analysis uses the difference between the filtered image and the original (supposedly noise-free) image, calls this difference the noise, and computes its power (in dB):

## The distance transform, erosion and separability

Thursday, November 6th, 2008

David Coeurjolly from the Université de Lyon just gave a presentation here at my department. He discussed, among other things, an algorithm that computes the Euclidean distance transform and is separable. The distance transform is an operation that takes a binary image as input, and writes in each object pixel the distance to the nearest background pixel. All sorts of approximations exist, using various distance measures that approximate the Euclidean distance. Using truly Euclidean distances is rather expensive. However, by making an algorithm that is separable, the computational cost is greatly reduced.

David’s algorithm computes the square distance first along each of the rows of the image, then modifies these distances by doing some operations along the columns. In higher-dimensional images you can just repeat this last step along the other dimensions. The operation to modify these distance values sounded very much like parabolic erosions to me, so I just gave this a try.