Cris' Image Analysis Blog

I recently got a question from a reader regarding Gaussian filtering, in which he says:

I have seen some codes use 3×3 Gaussian kernel like

    h1 = [1, 2, 1]/4

to do the separate filtering.

The paper by Burt and Adelson (The Laplacian Pyramid as a Compact Image Code, IEEE Transactions on Communication, 31:532-540, 1983) seems to use 5×5 Gaussian kernel like

    h1 = [1/4 - a/2, 1/4, a, 1/4, 1/4-a/2],

and a is between 0.3-0.6. A typical value of a may be 0.375, thus the Gaussian kernel is:

    h1 = [0.0625, 0.25, 0.375, 0.25, 0.0625]

or

    h1 = [1, 4, 6, 4, 1]/16.

I have written previously about Gaussian filtering, but neither of those posts make it clear what a Gaussian filter kernel looks like.

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I just came across an editorial in the Journal of the American Society of Nephrology (Kirsten M. Madsen, Am Soc Nephrol 10(5):1124-1125, 1999), which states:

A considerable number of manuscripts submitted to the Journal include quantitative morphologic data based on counts and measurements of profiles observed in tissue sections or projected images. Quite often these so-called morphometric analyses are based on assumptions and approximations that cannot be verified and therefore may be incorrect. Moreover, many manuscripts have insufficient descriptions of the sampling procedures and statistical analyses in the Methods section, or it is apparent that inappropriate (biased) sampling techniques were used. Because of the availability today of many new and some old stereologic methods and tools that are not based on undeterminable assumptions about size, shape, or orientation of structures, the Editors of the Journal believe that it is time to dispense with the old, often biased, model-based stereology and change the way we count and measure.

It then goes on to say that the journal would require appropriate stereological methods be employed for quantitative morphologic studies. I have never read a paper in this journal, but certainly hope that they managed to hold on to this standard during the 15 years since this editorial was written. Plenty of journals have not come this far yet.

“How did this get published?” is a question I regularly ask myself when reading new papers coming out. I just came across another one of these jewels, and because the topic is that of a previous blog post here, I thought I’d share my frustration with you.

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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):

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