Size Reduction: Binary Image Test

For my first test, I used the black-and-white Table of DWT Coefficients seen in the main body of this report. The original image was 512x512. I used three methods to halve the size of the table to 256x256 pixels.

Pixel Skipping
The image is legible, but most of the lines dividing the coefficient matrices are gone. This is clearly not acceptable.

Pixel Averaging
Pixel Averaging produces a grayscale version of the original image in the averaging process. We can threshold it to get back to a black and white image:
Pixel Averaging (After Thresholding)
This version isn't quite as legible as the grayscale version.

Discrete Wavelet Transform

Note that the DWT produces a grayscale version of the original image (which is quite readable. The DWT produces a smoothing effect which actually makes the letters appear sharper than if each pixel was only white or black. This has a technical name, but I can't remember what it is...)

If we want a black and white image like the original, we can threshold the grayscale version:
Discrete Wavelet Transform (Thresholded)

This image is more legible than the thresholded Pixel Averaged image. This is probably due to a more complex filtering function providing lateral inhibition, which tends to preserve edges. However, this also introduces some artifacts, such as missing line junctions.

If we take this image one more step, to 128x128, the results are more dramatic:
Pixel Skipping
All but one line is gone and the letters are totally illegible.

Pixel Averaging (After Thresholding)
All of the lines are preserved, but the largest words are legible only if you already know what it says. The smaller aren't even if you have foreknowledge.

Discrete Wavelet Transform (Thresholded)

This image looks very similar to the Pixel Averaged image. If we blow up both images, parts of the DWT image are more legible than the Averaged image and vice versa. The DWT image has more black, so it suffers from smearing the letters together, while the Averaged image loses some parts of the letters. In terms of overall legibility, it's a toss-up.

Go to the next example: Greyscale Image Go to the main text: Image Size Reduction Algorithms