Small radius Gaussian blur is asymmetric

[BarrettSA]

I've recently been experimenting with the Gaussian blur filter to try to establish the relationship between the "radius" slider value and the standard deviation (sigma) of the resulting Gaussian filter. In doing so, I've found that the filter output is not rotationally symmetric for small radius values. I've attached a file that illustrates the issue.

The steps to see the problem in version 1.8.4 of Affinity Photo on macOS 10.15.7 are as follows:

1) Create a small new document (I created a 100x100 RGB/8).

2) Select black (RGB 0, 0, 0) and fill the document, thereby creating a pixel layer.

3) Zoom way in (e.g., to fit). Using the Pixel tool and setting the color to white (RGB 255, 255, 255), create a single white pixel in the center of the layer.

4) Select Gaussian Blur from Layer > New Live Filter Layer > Blur.

5) Set the Radius value to a value in the range [0.1 - 0.7].

6) With the Info view visible, mouse over the formerly white pixel and its surrounding pixels to see the pixel values resulting from the blur.

The blur will have greater horizontal extent than vertical extent (and different intensity values). The attached file shows the resulting intensity values for several blur radius values that were explicitly typed into the radius field. The blur first becomes symmetrical for radius value of 0.8.

It appears that the blur may be implemented as a separable filter, but with different sized kernels being used in the horizontal and vertical directions.

GaussianBlurImpulse.pdf

[walt.farrell]

Welcome to the Serif Affinity forums.

I am not sure that you have used a valid method for examining the results. With the live filters it is critical that one views the results at a zoom level of 100% (or, possibly, larger). If you view them zoomed-in they adjust in some way based on the zoom level and do not give results that match what you see at a 100% zoom.

I think you would need to insert into your workflow:

3.5: Zoom to 100%

5.5: Merge the Gaussian Blur live filter

5.6 Zoom in to do the investigation.

The results at that point might be the same, but only with the added steps will you know for sure how the filter is acting.

[BarrettSA]

Thanks, Walt. After merging the live filter, I see the differences in extents disappear. The few remaining asymmetries are small.

[walt.farrell]

You're welcome, and thanks for confirming the behavior.