To use the Haar transform on selector indices, I prepare the input samples by adding .5 to each selector index (which range from [0,3] in ETC1), do the transform, uniform quantize, then do the inverse transform and truncate the resulting values back to the [0,3] selector range. (You must shift the input samples by .5 or it won't work.)
The quantization stage scales the the floating point coefficient by 4 (to get 2 bits to the right of the decimal point, which in experiments is just enough for 4x4) and converts to integer. This integer is then divided by a quantization value, then it's converted to float and divided by 4
For this uniform quantization matrix:
1 1 1 2 2 3 3 4
1 1 2 2 3 3 4 4
1 2 2 3 3 4 4 5
2 2 3 3 4 4 5 5
2 3 3 4 4 5 5 6
3 3 4 4 5 5 6 6
3 4 4 5 5 6 6 7
4 4 5 5 6 6 7 7
I get this ETC1 image after 8x8 Haar transform+quantization+inverse transform:
The original ETC1 compressed texture (before Haar filtering):
Selector visualization:
1x difference image (the delta between the original and filtered ETC1 images):
There is error in high frequencies, which is exactly what is to be expected given the above quantization matrix.
Here's a more aggressive quantization matrix:
2 4 6 8 10 12 14 16
4 6 8 10 12 14 16 18
6 8 10 12 14 16 18 20
8 10 12 14 16 18 20 22
10 12 14 16 18 20 22 24
12 14 16 18 20 22 24 26
14 16 18 20 22 24 26 28
16 18 20 22 24 26 28 30
ETC1 image:
Selector visualization:
An even more aggressive quantization matrix:
3 6 9 12 15 18 21 24
6 9 12 15 18 21 24 27
9 12 15 18 21 24 27 30
12 15 18 21 24 27 30 33
15 18 21 24 27 30 33 36
18 21 24 27 30 33 36 39
21 24 27 30 33 36 39 42
24 27 30 33 36 39 42 45
Selector visualization:
I have some ideas on how the 4x4 Haar transform could be very useful in Basis, but they are just ideas right now. I find it amazing that the selectors can be transformed and manipulated in the frequency domain like this.
