WardLand Spatial Frequency Analysis
We took several Ward Land scenes and did some spatial frequency analysis.
We used our four standard WardLand recipes. These are called "Blobbies", "Mondrian", "NearFarWarehouse", and "PlantAndBarrel". See ExecuteWardLandReferenceRecipes for how to generate these renderings.
For each standard recipe, we go through a few different rendering conditions. These vary the object materials in the scene. They're called "ward", "matte", "mask-1", and "boring".
The net result is that we have a whole bunch of multi-spectral images that we can analyze. These vary in across two big dimensions: which recipe, and which rendering condition. Hopefully, the results of the analysis make sense, given the variations in the renderings.
For each rendering, we took the multi-spectral image and converted to CIE XYZ space. We used the luminance / Y image plane for this spatial frequency analysis.
We used Matlab's fft2() and fftshift() functions on the luminance images. These gave us 2D frequency domain images. We ignores the phase component of these images and considers only the amplitude. We also normalized each frequency domain image by its mean value.
We summarized the spatial frequency distributions by considering concentric "rings" about the center of each frequency domain image. Each pixel belongs to a particular ring. For each ring we plot the mean spatial frequency (i.e. distance to center) and mean amplitude. Since we're using rings, our analysis ignores orientation in the 2D frequency domain images.
We ran these analyses using functions in the WardLandFourier example folder.
Here is a figure summarizing all of the "ward" conditions.
Each column represents a step in our analysis. On the left we have an sRGB representation of the original multi-spectral image. Next, we have the luminance / Y channel of the XYZ image. Next we have a visualization of the frequency domain 2D image. Finally, on the right, we have the frequency distribution that we computed by rings.
Each row shows the analysis for a different standard recipe.
Perhaps the various surface reflectances in the "ward" condition affect luminance spatial frequencies? We can replace them with boring, gray-looking matte reflectances on all objects.
For WardLand, we give each scene object a distinct reflectance. This allows us to identify objects in the scene. It also makes the renderings look different and interesting. What affect does this have on luminance spatial frequencies?
As a check of intuition, what happens when we do the same analysis on a blurred image? Here is the "ward" rendering, but with an arbitrary Gaussian filter passed over the luminance image.
As we would expect / hope, this suppresses the higher spatial frequencies.
We have a whole lot of renderings and plots above. Here is one summary.
This shows all of the same spatial frequency distributions as above, but collected together by recipe. This makes it easier to compare distributions.
For a given recipe, it seems that the blurring filter had the only large effect on frequency distributions.
The recipes themselves also have a large effect.
