Databases Reference
In-Depth Information
Color
Transform
Tier I
Coder
Wavelet
Transform
Tier II
Component
Tiling
Quantization
Coder
Rate
Control
F I GU R E 16 . 13
A block diagram for the JPEG2000 algorithm.
Wavelet decomposition has been finding its way into various standards. The earliest ex-
ample was the FBI fingerprint image compression standard. The latest is the increasingly
dominant image compression standard developed by the JPEG committee, commonly referred
to as JPEG 2000.
16.5 JPEG 2000
The JPEG standard provides excellent performance at rates above 0.25 bits per pixel. However,
at lower rates there is a sharp degradation in the quality of the reconstructed image. To correct
this and other shortcomings, the JPEG committee developed another standard, commonly
known as JPEG2000. The JPEG2000 standard is based on wavelet decomposition. The
standard hasmultiple parts dealingwith a variety of applications, frombasic image compression
to volumetric imaging and wireless applications. In this section we will look at Part 1 of the
standard, which deals with the basic image compression algorithm.
A block diagram of the JPEG 2000 algorithm is shown in Figure
16.13
.
The coding is based on a scheme originally proposed by Taubman [
217
] and Taubman and
Zakhor [
218
] known as EBCOT. The acronym EBCOT stands for “Embedded Block Coding
with Optimized Truncation,” which nicely summarizes the technique. It is a block coding
scheme that generates an embedded bitstream. The block coding is independently performed
on nonoverlapping blocks within individual subbands. Within a subband all blocks that do not
lie on the right or lower boundaries are required to have the same dimensions. A dimension
cannot exceed 256.
Embedding and independent block coding seem inherently contradictory. The way EBCOT
resolves this contradiction is to organize the bitstream in a succession of layers. Each layer
corresponds to a certain distortion level. Within each layer, each block is coded with a variable
number of bits (which could be zero). Rate control is obtained using a Lagrangian optimiza-
tion, called Post Compression Rate Distortion (PCRD) optimization, that makes use of the
partitioning or truncation points that are part of the EBCOT algorithm. The quality of the
reproduction is proportional to the numbers of layers received. It should be noted that PCRD
is not required by the standard.
In the following, we briefly describe each of these blocks in the JPEG 2000 block diagram.
We will pay particular attention to the process of generating an embedded bitstream for a code-
block. We then give a brief overview of the PCRD optimization used to obtain the quality
