Here is code to perform 2D Frouier transforms on jepg files. fft.c is a C program to perform the Fast Fourier Transform. ft.c is a multi threaded 2D FFT considerably adapted from this.
The following shell commands build and demonstrate the code on the Mac (and some Linuxes). You will need h.h.
javac cim.java gcc fft.c -O3 -c -Wmost gcc ft.c -O3 -Wmost -c -fnested-functions java j2b th.jpg out.bma java b2j out.bma out.jpg gcc man.c fft.o ft.o -O3 -o trans -Wmost ./trans nop out.bma outt.bma 8 java b2j outt.bma outt.jpg open outt.jpgThe trans command reads and writes a file with a name ending in “.bma” in these demos. Such files hold raw 24 bit RGB pixel values preceded by image dimensions. In general the command:
./trans op in.bma oqut.bma rtransforms the input image to frequency space, calls the one of the functions, in the file man.c, and transforms back to image space and writes the output file. The parameter r is a floating point value used by most of the variations and is in units of pixels.
The high level mechanics of this process can be learned by examining which files are created by each command.
The file out.bma is produced to show that we can translate to and from the raw byte format with minimal damage. open out.jpg to see it.
To undo build and run files:
rm outt* trans *.o *.class out.bma
The three 2D arrays cr, cg, cb are also byte per pixel arrays with as many elements and indexed the same as the complex array. They hold the segregated color components of the entire image. The gross information flow is: file to 3 byte arrays; to complex array a; to in-place transform of a; to one of the special routines in man.c; again to transform of a; to 3 byte arrays (scaled to peak value in a); to file. The code has been arranged to facilitate modifications such as averaging the input colors to produce a gray scale image, doing one transformation, and then using color to portray the vital convex numbers of the results of one transform.
Nested routine dc is executed once for each of the 3 primary colors. It moves the data from one of the one byte arrays into array a and does the transforms, and then back into the one byte arrays.
Routine pp(i, j) reports the value of a[i, j] for debugging and understanding. It has no side internal effects. d2Dft() causes the complex array to be transformed in place.
Routine fp(th, comment) scans the entire complex array and reports subscripts and values of components within th of the maximum magnitude. (“th” is a floating point real.) It returns the linear index of the max element.
The if(1) on the line with comment “Choice of two demos” selects the first piece of code which performs two 2D transforms calling routine manip between these two transforms. manip is supplied separately in another file such as mana.c which in this case replaces each complex number with its complex conjugate and that prevents the yield from being inverted. Many interesting experiments can be done by variations on routine manip.
If the 2nd demo is chosen (if(0)) the three colors are averaged for each input pixel and one transform is performed. Constant brightness color is used to code the complex number.
Other cruft is inherited from here.
|./trans nop in out 0|
|FT unmodified (except for conjugating each element to avoid rotation of image.)|
|./trans ct in out 8|
abrupt frequency cutoff
|All spatial frequency components greater than 1/r are removed.|
|./trans Gauss in out 8|
gaussian frequency attenuation
|attenuate each frequency f by e–(r*f)2. This is sometimes referred to as a Gaussian blur.|
|./trans unf in out 4|
Convolution with disk
|Compute transform of uniform circular disk inorder to convolve via FFT. r = 4 here.|
|./trans up in out 100|
|Translates up r pixels with wraparound.|
|./trans db in out 100 47 0.30|
General translation with
|2D translation with wraparound and double exposure with original position.|
javac cim.java gcc fft.c -O3 -c -Wmost gcc ft.c -O3 -Wmost -c -fnested-functions gcc man.c fft.o ft.o -O3 -o trans -Wmost java j2b th.jpg out.bma ./trans nop out.bma outt.bma 0 java b2j outt.bma nop.jpg ./trans ct out.bma outt.bma 8 java b2j outt.bma ct.jpg ./trans Gauss out.bma outt.bma 8 java b2j outt.bma Gauss.jpg ./trans unf out.bma outt.bma 4 java b2j outt.bma unf.jpg ./trans up out.bma outt.bma 100 java b2j outt.bma up.jpg ./trans db out.bma outt.bma 100 47 0.30 java b2j outt.bma db.jpg
javac cim1.java java b2j1 out.bma out1.jpg open out1.jpg