Image Characteristics
Summary: This module discusses the statistical characteristics of typical images which can permit compression.
We now consider statistical characteristics of typical images which can permit compression. If all images comprised dots with uncorrelated random intensities, then each pel would need to be coded independently and we could not achieve any useful gains. However typical images are very different from random dot patterns and significant compression gains are possible.
Some compression can be achieved even if no additional distortion is permitted (lossless coding) but much greater compression is possible if some additional distortion is allowed (lossy coding). Lossy coding is the main topic of this course but we try to keep the added distortions near or below the human visual sensitivity thresholds discussed previously.
Statistical characteristics of signals can often be most readily
appreciated by frequency domain analysis since the power
spectrum is the Fourier transform of the autocorrelation
function. The 2-D FFT is a convenient tool for analysing
images. Figure 1 shows the
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The bright region near the centre of the spectrum shows that the main concentration of image energy is at low frequencies, which implies strong correlation between nearby pels and is typical of real-world images. The diagonal line of spectral energy at about -30° is due to the strong diagonal edges of the hat normal to this direction. Similarly the near-horizontal spectral line comes from the strong near-vertical stripe of hair to the right of the face. Any other features are difficult to distinguish in this global spectrum.
A key property of real-world images is that their statistics are
not stationary over the image. Figure 2 demonstrates this by splitting the 'Lenna' image
into 64 blocks of
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We conclude that in many regions of a typical image, most of the signal energy is contained in a relatively small number of spectral components, many of which are at low frequencies. However, between regions, the location of the main components changes significantly.
The concentration of spectral energy is the key to compression. If a signal can be reconstructed from its Fourier transform, and many of the transform coefficients are very small, then a close approximation to the original can be reconstructed from just the larger transform coefficients, so only these coefficients need be transmitted.
In practice, the Fourier transform is not very suitable for compression because it generates complex coefficients and it is badly affected by discontinuities at block boundaries (half-sine windowing was used in Figure 1 and Figure 2 to reduce boundary effects but this would prevent proper reconstruction of the image). In further discussion, we demonstrate the principles of image compression using the Haar transform, perhaps the simplest of all transforms.
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This work is licensed by Nick Kingsbury under a Creative Commons Attribution License (CC-BY 1.0).
Last edited by Elizabeth Gregory on Jun 8, 2005 9:10 am GMT-5.