Anti-aliasing of random dot stereograms

I recently completed some Python (2.7) code for generating random dot stereograms based on this paper. The output is fairly good, though I have noticed that, even with a smooth gradient in the depth map, the output stereogram lacks these smooth gradients, instead having varying levels of depth. I believe this to be due to the DPI chosen when generating the image. While the detail of the depth can be increased by increasing the DPI, this becomes impractical as the convergence point becomes more difficult to reach.

Here are two examples. First at 75 DPI and second at 175 DPI. On the 75 DPI image, distinct "triangles" of depth can be seen. In the 175 DPI image, these are less pronounced but the guidance dots at the bottom of the image are further apart, and therefore viewing the 3D image is more difficult.

I'm looking to modify my current code to anti-alias the 3D image in order to smooth out the gradients even with a lower DPI. I have tried using SSAA on the depth map and pattern and generating the stereogram, then reducing the image size again with an antialiasing filter. However this seems to just contain the stereogram to the left of the image. For example, if I make the image 4 times bigger, the stereogram is limited to the left hand quarter of the image. The rest is just random noise and cannot be viewed. How would I go about antialiasing the image hidden in the stereogram? My code is almost the same as the algorithm described in the paper, so an antialiasing algorithm based on that would be perfect.

The solution for the problem I was having, with the stereogram being contained to the left of the image, was caused by not extending the same array to reflect the larger depth map. This caused everything beyond the original length of the depth map to be randomly generated noise.

After solving this problem, a second problem arose, in that the 3D image was distorted by the anti-aliasing, causing more gradient issues than it was solving. My solution for this was to increase the DPI setting in the code. For example, if I increased the size of the depth map by 4x, the stereogram must be generated with a DPI 4 times greater (300, rather than 75). When scaled down again, this produced excellent results.

This image uses 2x SSAA, making the gradients comparable with the 175DPI image from the question, but with a much easier converging point.

This image uses 4x SSAA, and I find the jaggies barely visible at all. The noise here becomes a lot more blurred and the general colour of the image becomes quite grey. I have found this effect can be avoided by pregenerating the noise and scaling that up by the same AA factor. This is demonstrated in the next image.