Images with negative pixels value

Question

Consider a simple black (0) and white (255) image composed by 3 vertical bands : the first is white, the second is black and the third is white. Image size is W columns by H lines. Band width is W1, W2, W3 for bands 1, 2 and 3 respectively (W1+W2+W3=W).
Consider now a first order edge detecting operation, for example Sobel for vertical edges :
1 0 -1
2 0 -2
1 0 -1
The corresponding edge image is composed of H identical lines (because the image is only varing horizontally). Each line is 0 everywhere, except on transitions : on column W1, there is a positive value of 4*255 and on collumn W1+W2 there is a negative value of -4*255.
Using the following java source code, we obtain an image which have only the positive (>=0) part of each line :
  Image img = (new ImageIcon("bands.png")).getImage();
  BufferedImage bimg = toBufferedImage(img); // not part of JDK1.4
  ConvolveOp sobel = new ConvolveOp(new Kernel(3,3,new float[]{ 1, 0,-1,2,0,-2,1,0,-1})); // vertical Sobel filter
  BufferedImage bimg_cont = sobel.filter(bimg, null);To have an edge image that contains the negative part of edges, we do need a specific image format with specific ColorModel and SampleModel. Ideally, we will need a grayscale image (1 sample/pixel) where all elements can represent values from -4*255 to 4*255. So we need a signed type like DataBuffer.TYPE_SHORT, DataBuffer.TYPE_FLOAT or DataBuffer.TYPE_DOUBLE.
Note : it is possible to apply the filter twice, with a mirrored filter, but time to compute will be also twice the normal computational time (very inefficient).
Now, this is the question : do anyone have a solution to compute a sobel filter (or any other filter type which produces negative values) with a resulting image containing positive and negative values ?

Answer 1

The problem is the size of the number you have to work with. You can store values ranging from 0 to 255 (the max index for a byte-sized variable) so the total numbers you can store is 256. However, if you want to go from -255 to 255, thats about 512 values, which is twice the size of your max. You would need one more bit on that variable to do that. You could make the far left variable be the positive or negative sign (know as a signed variable) which is how computers do it anyway. The only drawback is it will only range from -127 to 127, which is half as much detail.