Digital Signal Processing Reference
In-Depth Information
In the JPEG standard, first the input image is level shifted. (For an eight-bit
image, the value 128 is subtracted from each pixel.) Then the image is divided
into pixel blocks. The 64 DCT coefficients are then uniformly scalar
quantized. The lowest frequency DC term, is coded predictively on the
basis of the DC terms from previous image blocks, and the remaining
63 DCT coefficients are coded in a zigzag pattern by means of lossless
compression.
The DCT works well for image compression because it provides
energy com-
paction
. This means that the energy in the spatial, or image, domain is typically con-
centrated in a smaller number of DCT coefficients; hence, the low-magnitude DCT
coefficients can be coded at very low bit rates without degrading the image quality
significantly.
As an example, Figure 12.35 shows the basis functions of the two-dimensional
DCT for an 8
8 * 8
F[u, v]
F[0, 0],
8 * 8
8 image matrix of pixels [8]. Notice that the lowest frequency basis
function (upper left-hand corner) is completely smooth, while the highest frequency
basis function (lower right-hand corner) varies the most from dark to light in both
the horizontal and vertical directions. The DCT coefficients can be seen as the
“weights” assigned to the basis functions.
Figure 12.36 (a)-(d) shows the progression of image quality, as the lowest 1,
3, 6, and 21 DCT coefficients are included in the reconstructed image. Notice
that even with 1 DCT coefficient, the image is recognizable, and the image with
21 reconstructed coefficients is virtually indistinguishable from the original
image [Figure 12.36(e)].
Figure 12.35
The basis functions for the
two-dimensional discrete cosine transform.
