Video Compression: What is discrete cosine transform?

Question

I've implemented an image/video transformation technique called discrete cosine transform. This technique is used in MPEG video encoding. I based my algorithm on the ideas presented at the following URL:

http://vsr.informatik.tu-chemnitz.de/~jan/MPEG/HTML/mpeg_tech.html

Now I can transform an 8x8 section of a black and white image, such as:

0140  0124  0124  0132  0130  0139  0102  0088  
0140  0123  0126  0132  0134  0134  0088  0117  
0143  0126  0126  0133  0134  0138  0081  0082  
0148  0126  0128  0136  0137  0134  0079  0130  
0147  0128  0126  0137  0138  0145  0132  0144  
0147  0131  0123  0138  0137  0140  0145  0137  
0142  0135  0122  0137  0140  0138  0143  0112  
0140  0138  0125  0137  0140  0140  0148  0143 

Into this an image with all the important information at the top right. The transformed block looks like this:

1041  0039  -023  0044  0027  0000  0021  -019  
-050  0044  -029  0000  0009  -014  0032  -010  
0000  0000  0000  0000  -018  0010  -017  0000  
0014  -019  0010  0000  0000  0016  -012  0000  
0010  -010  0000  0000  0000  0000  0000  0000  
-016  0021  -014  0010  0000  0000  0000  0000  
0000  0000  0000  0000  0000  0000  0000  0000  
0000  0000  -010  0013  -014  0010  0000  0000  

Now, I need to know how can I take advantage of this transformation? I'd like to detect other 8x8 blocks in the same image ( or another image ) that represent a good match.

Also, What does this transformation give me? Why is the information stored in the top right of the converted image important?

Answer 1

The result of a DCT is a transformation of the original source into the frequency domain. The top left entry stores the "amplitude" the "base" frequency and frequency increases both along the horizontal and vertical axes. The outcome of the DCT is usually a collection of amplitudes at the more usual lower frequencies (the top left quadrant) and less entries at the higher frequencies. As lassevk mentioned, it is usual to just zero out these higher frequencies as they typically constitute very minor parts of the source. However, this does result in loss of information. To complete the compression it is usual to use a lossless compression over the DCT'd source. This is where the compression comes in as all those runs of zeros get packed down to almost nothing.

One possible advantage of using the DCT to find similar regions is that you can do a first pass match on low frequency values (top-left corner). This reduces the number of values you need to match against. If you find matches of low frequency values, you can increase into comparing the higher frequencies.

Hope this helps