The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Voi. XXXVII. Part B4. Beijing 2008
representation method is developed recently, that is Multiscale
Geometric Analysis (MGA).
2. DIRECTIONAL DETAIL PRESERVING IMAGE
CODING SYSTEM
An image contains several features that exhibit the ability
through which the image can offer information to people about
the objects presented in the image.
In order to design a feature preserving lossy image coder it is
important first, identify the features of the image to preserve
and second, spend more bits to represent the important
information and sacrifice fidelity or quality in other image
regions (D. Schilling and P. C. Cosman, 2001).
2.1 Compression scheme
The structure of our compression system is shown below in
Figure 2. We applied typical hierarchical dyadic decomposition
scheme with filter banks: 5/3 biorthogonal. Coding algorithm is
based on bitplane coding method. For wavelet transform, 5-
level (for 512*512 image) decomposition was done. As
directional decomposition is not suit to low-frequency subbands,
only the two high-frequency levels were decomposed by
directional filters, for each subband, 8 directions were made.
After decompression, the images are evaluated by structure
similarity method which is more appropriated here than the
PSNR method.
{ Evaluation By Structure \
V Similarity J
N
Figure 2. The structure of our compression system
2.2 The directional filter banks
Directional Filter Bank (DFB) was designed to capture the high
frequency (representing directionality) of the processing image.
Bamberger and Smith constructed a 2-D directional filter bank
(DFB) that can be maximally decimated while achieving perfect
reconstruction. As shown in Figure 2(a)(LiYu, Lin, 2007).
Do and Vetterli proposed a new construction for the DFB to
avoid modulating input image, which we can obtain the desired
2-D spectrum division as shown in Figure 3(a). The simplified
DFB is intuitively constructed from two building blocks. The
first is a two-D spectrum into two directions: horizontal and
vertical. As shown in Figure 3(b). The second is a shearing
operator, which used to reordering the image samples. By
appropriate combination of shearing operators together with
two-direction partition of quincunx filter banks at each node in
a binary tree-structured filter bank, shown in Figure 3(c).
(a) frequency
partitioning
(b) two-dimensional spectrum
partition using quincunx filter banks
with fan filters
(c) the multichannel view of an 1-
level tree-structured DFB
Figure 3. The directional filter bank
2.3 The Wavelet Based Contourlet Transform (WBCT)
The Contourlet Transform (CT) redundancy occurs at the
Laplacian pyramid decomposition stage. As a result we obtain
two images, the first one resulting from low pass approximation,
and the second one obtained from the high pass approximation.
The image of details obtained (resulting from high pass) has
always the same size of the immediately anterior, because we
do not have resolution reduction. The directional decomposition
is computed with the detailed image, .by that, if we made more
pyramidal decompositions we generate at least a half more
information of the above level as redundancies. In order to take
advantage of the directionality offered by CT and to avoid the
redundancy, we can change the Laplacian pyramid
decomposition with Mallat decomposition. As DFB is not
suitable to handle the low frequency content (Minh N.Do, and
Martin Vetterli, 2005), it is important to combine the DFB with
a multiscale decomposition, where the low frequencies of the
image are removed before applying the DFB. This is the main
idea behind a new transform called Wavelet Based Contourlet
Transform (WBCT) which is a non-redundant transform. For
the WBCT it is important to ensure that we can obtain the
perfect reconstruction of an image for the best case. The process
to compute the WBCT is as follows (Vivien Chappelier, 2004):
1. Compute the DWT of an image, and in this paper we
compute only log2 (image size) -5 levels.
