BlockMean

Mean of rectangular submatrices, fast C-Mex (no running mean)

Description

BLOCKMEAN - Fast mean of rectangular submatrices

The mean of V*W elements along the 1st and 2nd dimension is calculated. This is no running mean filter: The sizes of the 1st and 2nd dimension are reduced by the factors V and W.
I use this as cheap anti-aliasing of RGB images, therefore it is implemented for DOUBLE and UINT8 input.

Y = BlockMean(X, V, W)
Input:
  X: UINT8 or DOUBLE array of any size.
  V, W: 2 scalars as size of the window. Each element of the output is the
     mean over V*W neighbouring elements of the input.
     V and W are limited to 256 to limit memory usage.
Output:
  Y: UINT8 or DOUBLE array, the 1st and 2nd dimensions are V and W times shorter:
     [FIX(X / V) x FIX(Y / W) x (further dims...)]
     If the size of the 1st or 2nd dimension is not a multiple of V and W, the
     remaining elements at the end are skipped.

E.g. for 4x4 blocks of a 1024x768x3 double array, this MEX implementation is about 5 times faster than the corresponding Matlab method (Matlab 2009a, 1.5GHz Pentium-M, WinXP, MSVC 2008):
  reshape(sum(sum(reshape(X, 4, 256, 4, 192, 3), 1), 3), 256, 192, 3).
Run the unit-test uTest_BlockMean to check validity and speed.

Tested with: LCC v2.4, v3.8, Open Watcom 1.8, BCC 5.5, MSVC 2008, Matlab 6.5, 7.7, 7.8, WinXP 32 bit
Compatibility assumed: Linux, MacOS, 64bit.

Pre-compiled Mex: http://www.n-simon.de/mex

I'd appreciate suggestions for improvements and bug reports sent through email - thanks.

• MATLAB release: MATLAB 7.8 (R2009a)

[Dominik Brands]

Hi,
I want to use your BlockMean-Function with Matlab on Linux. But I got two errors on compiling.
First one using
mex -O CFLAGS="\$CFLAGS -std=C99" BlockMean.c
as written in the header of BlockMean.c results in
>> cc1: error: unrecognized command line option "-std=C99"
>> mex: compile of ' "BlockMean.c"' failed.
Okay, this error I correct by myself using the option "c99" instead of "C99" since Linux is case sensitive.
But then I get a new error
>> BlockMean.c: In function ‘mexFunction’:
>> BlockMean.c:181: warning: implicit declaration of function ‘_control87’
>> BlockMean.c:181: error: ‘MCW_PC’ undeclared (first use in this function)
>> BlockMean.c:181: error: (Each undeclared identifier is reported only once
>> BlockMean.c:181: error: for each function it appears in.)
>> BlockMean.c:182: error: ‘PC_64’ undeclared (first use in this function)
using the command
mex -O CFLAGS="\$CFLAGS -std=c99" BlockMean.c
For this I found a hint at
http://www.fortran-2000.com/ArnaudRecipes/CompilerTricks.html .
The varaibels MCW_PC and PC_64 are only available at windows. On the mentioned homepage there was show a trick for correct this under thetopic "Floating point precision mode". I do following changes to your code in BlockMean.c
The code-lines after "// Set the floating point precision:" I replace by the code given at the homepage. Additionally I remove the calls to "control87" under comment "// Set precision to 64 bit.." and "// Reset floating point precision"
and use instead the new functions "x86_SetPrecision" and "x86_RestorePrecision".
After compiling again no errors occur and the test with TestBlockMean was succesfully due to the messages from "TestBlockMean"

I hope this modifications was correct for you.
Regards
Dominik

[Jan Simon]

@Dominik: Thanks for the helpful comments!
Unfortunately I do not have a Linux machine for testing and I've included the wrong uppercase "-std=C99" in all my submissions.
As far as I understand from the very impressive document you've cited, Linux systems run with 80bit precision as default. Therefore I'll submit an updated version, which omits the FPU control under linux completely.
If the increase of the precision from 64 to 80 bits is omitted on Windows machines, the accuracy of the method equals at least the results of SUM obtained inside Matlab. Therefore the extended precision is more a gimmick than a necessary feature for BlockMean.