2.4 Near Lossless Compression of Edge Protected Images
If demand for lossless compression can be loosen to a near-
lossless compression, the compression rate is expected to be
further improved.
The stereo measurements in modern photogrammetry are
basically accomplished by means of automatic stereo image
matching. The principal factor affecting the accuracies of stereo
measurements is the edge features of images. As long as the
edge features are immune to destructions, the accuracies may be
expected to be consistent. Therefore, an edge protection
operator is utilized to appropriately filter out the high frequency
noises which could help to magnify the signals and further
improve the compression rates.
Figure 1. Edge Protection Smoothing Operator
An edge protection smoothing operator is shown in Figure 1, in
which the black solid circles represent pixels and the red and
blue polygons represent directional pointers. In a window of 5
by 5 pixels, the pointers cover eight directions. The steps for
executing this operator include: (1) computing the variance of
gray values of the covered pixels in each pointer; (2) treating
the direction with maximum variance as an edge, while
regarding the minimum variance as plainness; (3) substituting
the average value for the central value in the direction with the
minimum variance; (4) shifting the window until the image 1s
ergodic. After the application of this operator, the compression
rate of a certain image is expected to be further improved.
3. EXPERIMENTS AND ANALYSIS
3.1 Differential Coding
Two remote sensing images, as shown in Figure 2, are utilized
to test the effects of differential encoding. (a) is a Landsat-5 TM
image consisting of Band 5, Band 4 and Band 3, the spatial
resolution of which is resampled to 28.5 meters. And the main
land cover types of this image include water body, farmland,
built-up areas and mountain areas. (b) is a SPOT-5
panchromatic image with a spatial resolution of 2.5 meters, in
which built-up areas and farmland are the main land cover types.
Both of the images are made up of 500 by 500 pixels.
The following experimental steps are carried out for the
aforementioned images:
1. Compute entropies, auto-correlation coefficients and
information amount of the images
2. Apply Huffman coding to the images without any
decorrelation process.
3. Utilize differential
encoding to eliminate the
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B7, 2012
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia
correlation of pixels and encode the difference images.
4. Compute the average code lengths and compression
rates of the Huffman coding and differential encoding,
respectively.
(a) Landsat-5 T (b) SPOT-5
Figure 2. Testing images for differential coding
The results are listed in Table 2. The average code lengths of
the compressed images are very close to the entropies of the
original images. It confirms that Huffman coding is definitely a
good entropy encoding algorithm. Compared to the Huffman
coding, the average code lengths of the compressed images by
differential encoding are much more close to the corresponding
information amounts. Especially, the average code length of
compressed SPOT panchromatic image by bidirectional
differential coding is 3.66, which is very close to the
information amount of 3.44. Moreover, the compression rate is
nearly two times as large as that of Huffman coding. By means
of the information measures, analysis on data characteristics
and a sufficient consideration of the correlativity of data will
help to find effective data transform algorithms, which is
capable of reducing the data redundancy and improving the
compression rates of lossless compression.
Both of the unidirectional and bidirectional differential coding
algorithms are first order. Although the average code lengths of
the compressed images are closer to the information amounts of
the original images, the still remained difference manifests an
incomplete decorrelation. Hence, second order or higher order
differential coding algorithms may be adopted to further reduce
the variance of data and to reduce correlativity.
The essence of differential transform is equivalent to a
reduction of the variance of gray values. The range of grayscale
after the transform is so remarkably narrowed that the standard
deviation is decreased from 23.05 (in Figure 3) to 3.25, which
greatly cuts down the dispersion of the grayscale distribution.
Moreover, a significant characteristic of normal distribution
appears after the differential transform, as is shown in Figure 4.
The purpose of differential encoding is to reduce the correlation
among pixels to the maximum extent. This algorithm is easy
and simple to implement which makes it worthy of application
in satellite Earth data transmission to economize in resources
and improve transmission efficiency. Besides, Deng and Lin
(2009) applied this algorithm to the remote sensing images of
“Beijing-1” micro-satellite. Compared with the experiments of
DPCM, the effect of this algorithm is more favorable due to its
decorrelation process which achieves a more than two times
compression rate.
