Page 131 - Digital Analysis of Remotely Sensed Imagery

102 Cha pte r T h ree

Stored in the compressed image are only the transform coefficients
rather than pixel values of the image. During uncompression the
JPEG decoder re-creates the normalized transform coefficients first.
This can be achieved easily via a lookup table as they are coded
using the uniquely decodable Huffman coding. These coefficients are
plugged into the formula to generate pixel values that best represent
the original ones. An approximate version of the original 8 8
subarea is created via the inverse transform. Tiling of all subimages
restores the original uncompressed image. JPEG compression has the
drawback of introducing artifacts along the border of subimages after
they are mosaicked to form the original image, because each subimage
is compressed separately. This problem disappears with JPEG 2000.
JPEG 2000 is a new image compression standard that is backward
compatible with, and further extends, the current standard JPEG with
increased flexibility in image compression and in access to the
compressed data. Unlike JPEG that can compress RGB imagery at
most, JPEG 2000 is able to compress images up to 256 bands. A very
large compression ratio can be achieved with very little appreciable
degradation in image quality. Unlike JPEG, which uses a Fourier
transform, JPEG 2000 uses two coding modes, DCT coding and
wavelet coding, to achieve more efficient compression.
Based on wavelet technology, JPEG 2000 enables an image to be
compressed with or without loss of information. Error-free
compression is achieved using a biorthogonal, 5/3 coefficient scaling
and wavelet vector at an expected compression ratio of 2:1 (Le Gall
and Tabatabai, 1988). Ordinary lossy compression, if implemented
with a 9/7 coefficient scaling-wavelet vector, is able to achieve a
compression ratio of up to 200:1 (Antonini et al., 1992). Such a large
ratio is achieved because the “mother wave,” which best represents
the wavelet signature generated from scanning an image, does not
accompany the compressed image data. Instead, the JPEG 2000
decoder is equipped with a universal mother wave. Whenever the
decoder is supplied with a compressed image, it can detect the mother
wave used. Furthermore, lossy compression can be embedded into
lossless compression. Since an image can be regarded as composed of
different regions of interest (e.g., images embedded into text), different
compression schemes can be applied to different regions of interest in
the image to help preserve the image quality of those regions. The
shape of a region can be square or rectangular. However, it can also
be a circle, oval, triangle, or bloblike.
In JPEG 2000, the original image is optionally divided into
multiple, nonoverlapping subimages called tiles. In case of three
components (e.g., color composite), all components (e.g., red, green,
and blue layers) are divided identically. Alternatively, these com-
ponents can be linearly combined either reversibly or irreversibly to
be decorrelated with each other to achieve a high compression ratio.
The dimension of each tile is always dividable by 2. Arbitrary tile sizes