Information Technology Reference
In-Depth Information
Table 11.1 Fractal image
compression parameters
Low
Medium
High
Image size
256
×
256 pixels
Minimum partition level
2
2
3
Maximum partition level
4
5
6
Maximum error per pixel
8
8
8
which means no transformation applied; Sobel-based (Sobel 1990 ) and Canny-
based (Canny 1986 ) edge detection of horizontal and vertical edges, horizontal
edges, vertical edges.
Metrics Application A set of metrics is applied to the images resulting from
the pre-processing operations. The FE calculates the following metrics: average (i)
and standard deviation (ii) of the image pixel values; complexity estimates based
on JPEG (iii) and fractal compression (iv); Zipf Rank-Frequency (v) and Size-
Frequency (vi), which result from the application of the Zipf's law (Zipf 1949 );
(vii) Fractal dimension estimates using the box-counting method (Taylor et al.
1999 ).
The average (i) and standard deviation (ii) are calculated using the pixel intensity
value of each image, except for the H channel image. Since the Hue channel is
circular, the average and the standard deviation are calculated based on the norm
and angle of Hue values. In addition, a multiplication of the Hue angle value by the
CS value is made and consequently a norm is calculated using Hue and CS values.
The image compression schemes used are lossy and so there will be compression
errors, i.e. the compressed image will not exactly match the original. All other fac-
tors being equal, complex images will tend toward higher compression errors and
simple images will tend toward lower compression errors Additionally, complex im-
ages will tend to generate larger files than simple ones. Thus, compression error and
file size are positively correlated with image complexity.
We consider three levels of detail for the JPEG (iii) and Fractal compression
(iv) metrics: low, medium, and high. For each compression level the process is the
same, the image is encoded in JPEG and fractal format. In the experiments described
herein, we use a quad-tree fractal image compression scheme (Fisher 1995 ) with the
set of parameters given in Table 11.1 .
The calculation of the Zipf Rank Frequency (v) metrics implies: counting the
number of occurrences of each pixel intensity value in the image; ordering them
according to the number of occurrences; tracing a rank vs. number of occurrences
plot using a logarithmic scale in both axis; calculating the slope of the trendline and
the linear correlation with the trendline.
For the Hue channel, this metrics is calculated in two ways: (i) as described
above; (ii) instead of counting the number of occurrences of each Hue value, we
add the CS channel values of the corresponding pixels (and divide them by 255 for
normalisation purposes). The rationing is that the perceived Hue depends on the
saturation and value of the corresponding pixel.
Search WWH ::




Custom Search