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Figure 5.29: The discrete cosine transform breaks up an image area into discrete frequencies in two dimensions.
The lowest frequency can be seen here at the top-left corner. Horizontal frequency increases to the right and
vertical frequency increases downwards.
Increasing the DC coefficient adds a constant amount to every pixel. Moving to the right the coefficients represent
increasing horizontal spatial frequencies and moving downwards the coefficients represent increasing vertical
spatial frequencies. The bottom-right coefficient represents the highest diagonal frequencies in the block. All these
coefficients are bipolar, where the polarity indicates whether the original spatial waveform at that frequency was
inverted.
Figure 5.30 shows a one-dimensional example of an inverse transform. The DC coefficient produces a constant
level throughout the pixel block. The remaining waves in the table are AC coefficients. A zero coefficient would
result in no modulation, leaving the DC level unchanged. The wave next to the DC component represents the
lowest frequency in the transform which is half a cycle per block. A positive coefficient would make the left side of
the block brighter and the right side darker whereas a negative coefficient would do the opposite. The magnitude of
the coefficient determines the amplitude of the wave which is added. Figure 5.30 also shows that the next wave
has a frequency of one cycle per block. i.e. the block is made brighter at both sides and darker in the middle.
Consequently an inverse DCT is no more than a process of mixing various pixel patterns from the wave table
where the relative amplitudes and polarity of these patterns are controlled by the coefficients. The original
transform is simply a mechanism which finds the coefficient amplitudes from the original pixel block.
The DCT itself achieves no compression at all. Sixty-four pixels are converted to sixty-four coefficients. However, in
typical pictures, not all coefficients will have significant values; there will often be a few dominant coefficients. The
coefficients representing the higher two- dimensional spatial frequencies will often be zero or of small value in large
areas, due to blurring or simply plain undetailed areas before the camera.
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