Image Processing Samples

Fourier Transform

This is another command line application that process an image in the Fourier Frequency Domain. In this domain the image is a map of the spatial frequencies of the original image. It depends on the IM main library and on the IM_FFTW library. The FFTW is a very fast Fourier transform, but is contaminated by the GPL license, so everything must be also GPL. To use it in a commercial application you must contact the MIT and pay for a commercial license.

Se also Reference / Image Processing / Domain Transform Operations.

You can view the source code here: proc_fourier.cpp

Hough Lines

The Hough transform can be used to detect lines in an image. But it results are highly dependent on other operations done before and after the transform. Here you can see a small pseudo code that ilustrates a possible sequence of operations to detect lines using the hough transform.

First the canny operator will isolate the borders, the threshold will mark the candidate pixels. After the transform the local maximum are isolated to detect the line parameters of the lines that have many pixels from the cadidate ones. The last operation will just draw the detected lines over the original gray scale image.

imProcessCanny(in,out,stddev)
imProcessHysteresisThreshold(in,out,low,high)

imProcessHoughLines(in,out)
imProcessLocalMaxThreshold(in,out,size,min)

imProcessHoughLinesDraw(in1,in2,out)

Or a more complete sequence using another approach:

gray = imImageCreate(width, height, IM_GRAY, IM_BYTE);
binary = imImageCreate(width, height, IM_BINARY, IM_BYTE);
binary2 = imImageClone(binary);

rmax = sqrt(width*width +height*height)/2;
hough_height=2*rmax+1;
hough = imImageCreate(180, hough_height, IM_GRAY, IM_INT);
hough_binary = imImageCreate(180, hough_height, IM_BINARY, IM_BYTE);

imConvertColorSpace(rgb, gray);

// very important step, the quality of the detected lines are highly dependent on
// the quality of the binary image
// Using a simple threshold like in here maybe not a good solution for your image
imProcessPercentThreshold(gray, binary, percent=50); 

// eliminates unwanted objects, depending on the quality of the threshold
// this step can be skiped
imProcessBinMorphClose(binary, binary2, 3, 1); 
imProcessPrune(binary2, binary, 4, size=100, 0);

// Is there any holes in the objects?
// Holes also have borders...
imProcessFillHoles(binary, binary2, 4);

// leave only the object borders
imProcessPerimeterLine(binary2, binary);  

// here you should have near only the lines you want to detect.
// if there are more or less lines that you want redo the previous steps

imProcessHoughLines(binary, hough);
imProcessLocalMaxThreshold(hough, hough_binary, 7, 100);

// this is optional, it will draw the results
imProcessHoughLinesDraw(gray,hough_binary,draw_hough); 

In the result of imProcessLocalMaxThreshold there will be several white pixels. They represent the detected lines. Defining:

Y = a * X + b
cos(theta) * X + sin(theta) * Y = rho

The transform return values in the intervals:

theta = 0 .. 179
rho = -rhomax .. rhomax (origin in the center of the image)

where:
    rhomax = sqrt(width*width + height*height) /2 (width and height of the original image)

For each (xi, yi) point found in the result image:

theta = xi;
rho = yi - rhomax;

then:

a = -cos(theta)/sin(theta);
b = (rho + (width/2)*cos(theta) + (height/2)*sin(theta))/sin(theta);

The complex formula for "b" came from the fact that we have to shift the result to the image origin at (0,0).

Image Analysis

The following pseudo code ilustrates the sequence of operations to measure regions. This is also called Blob Analysis.

First the regions are isolated from background using a threshold. Then regions too small or too large are eliminated and the holes are filled in this example. After the regions are found we can start measuring properties of the regions like area and perimeter.

imProcessSliceThreshold(in, out, level1, level2)
imProcessPrune(in, out, connect, size1, size2)
imProcessFillHoles(in, out, connect)
imAnalyzeFindRegions(in, out, connect)
imAnalyzeMeasureArea(in, area)
imAnalyzeMeasurePerimeter(in, perim)