I have a faster, SIMD IIR filter implementation, but have accuracy problems
All,
I have ported the IIR filter implementation to use SSE intrinsics and have achieved a 2.5x speedup so far. But I'm having accuracy problems for large blurs due to using single precision instead of double.
I've attached examples outputs that blurs a box with several sizes. For sigma=120, the annoying mach bands start getting noticeable. At sigma=200, it looks very bad, and at 350, you might as well use it as a sharpen filter :)
This is the first graphics application I've seen where single precision isn't enough. Is the reason due to the recursive behavior of IIR (more accumulation of error) ?
Basically, for large blurs (stdev > 100), 24 bits of precision isn't sufficient and you end up getting very annoying mach bands. For sigma = 100, the filter coefficients are:
b[0] = 0.00000387430191040 b[1] = 2.96391582489013672 b[2] = -2.92843437194824219 b[3] = 0.96451467275619507
If I add b[0] to the other terms last (b[1] + b[2] + b[3]) + b[0], (earlier, when I added the b[0] term to b[1], the accuracy was even worse as expected), the alignment of the operands in binary is approximately:
1.00000000000000000000000 0.00000000000000000100000
meaning the addition loses a lot of the b[0] term's precision.
Can anyone suggest how to proceed next and how useful you think this speedup is? (for me it's a moderate improvement because in my comic, I use marble and brick textures for the walls and floors - I also vectorized the turbulence generator).
I would like to avoid using double precision since SSE supports only 2 doubles per operation instead of 4 floats.
The things I thought about of trying next are: 1. Use int32 arithmetic (that would add 9 extra bits of precision) 2. Use 4 taps instead of 3. Would this really help? I don't know much about IIR filter design. Can someone give me the coefficient formula for 4 taps?
Thanks for helping,
Yale
2013/5/28 Yale Zhang <yzhang1985@...400...>:
All,
I have ported the IIR filter implementation to use SSE intrinsics and have achieved a 2.5x speedup so far. But I'm having accuracy problems for large blurs due to using single precision instead of double.
I've attached examples outputs that blurs a box with several sizes. For sigma=120, the annoying mach bands start getting noticeable. At sigma=200, it looks very bad, and at 350, you might as well use it as a sharpen filter :)
This is the first graphics application I've seen where single precision isn't enough. Is the reason due to the recursive behavior of IIR (more accumulation of error) ?
Basically, for large blurs (stdev > 100), 24 bits of precision isn't sufficient and you end up getting very annoying mach bands. For sigma = 100, the filter coefficients are:
b[0] = 0.00000387430191040 b[1] = 2.96391582489013672 b[2] = -2.92843437194824219 b[3] = 0.96451467275619507
If I add b[0] to the other terms last (b[1] + b[2] + b[3]) + b[0], (earlier, when I added the b[0] term to b[1], the accuracy was even worse as expected), the alignment of the operands in binary is approximately:
1.00000000000000000000000 0.00000000000000000100000
meaning the addition loses a lot of the b[0] term's precision.
Can anyone suggest how to proceed next and how useful you think this speedup is? (for me it's a moderate improvement because in my comic, I use marble and brick textures for the walls and floors - I also vectorized the turbulence generator).
I would like to avoid using double precision since SSE supports only 2 doubles per operation instead of 4 floats.
The things I thought about of trying next are:
- Use int32 arithmetic (that would add 9 extra bits of precision)
- Use 4 taps instead of 3. Would this really help? I don't know much about
IIR filter design. Can someone give me the coefficient formula for 4 taps?
I would try using int32 first, though I know even less about filtering than you.
There is also: 3. Implement approximate Gaussian blur as a sequence of three box blurs, as described in the SVG specification. This could be quicker than the IIR filter, and the results would be indistinguishable.
Regards, Krzysztof
participants (2)
-
Krzysztof Kosiński -
Yale Zhang