Upload
kashif-aziz-awan
View
217
Download
0
Embed Size (px)
Citation preview
8/3/2019 FIT 2011 Blok Sort
http://slidepdf.com/reader/full/fit-2011-blok-sort 1/23
by Basar KOC & Ziya ARNAVUT
8/3/2019 FIT 2011 Blok Sort
http://slidepdf.com/reader/full/fit-2011-blok-sort 2/23
What are digital colors? Human beings perceive colors by the nature of the light
reflected from an object!
Achromatic Color: means literally ³without color´
Only intensities (amount of light)
Gray levels as seen on black/white TV-monitor
Ranges from black to white
Chromatic Color: All colors other than neutral colors (white, black,
and the pure grays), are chromatic.
The word ³color´ in ordinary language is often used to refer
exclusively to chromatic colors, e.g., color vs. black-and-white
television.
8/3/2019 FIT 2011 Blok Sort
http://slidepdf.com/reader/full/fit-2011-blok-sort 3/23
RGB Color Theory RGB stands for Red, Green, Blue RGB color is in use in many devices,
Televisions, computer screens, digital cameras.
When the visible color spectrum wavelength (400-700 nm) is
broken into thirds,
RGB colors are the predominant colors.
Three types of cone cells exist in human eye.
Each cell is more sensitive to either short ( S ), medium( M ), or long( L ) wavelength light.
These curves are often also referred as the ³tri-stimulus functions´.
8/3/2019 FIT 2011 Blok Sort
http://slidepdf.com/reader/full/fit-2011-blok-sort 4/23
RGB Color Space A single pixel consists of three components each in range of
[0,255].
Each pixel is a triplet
128 251 60 =
Pixel vectorin memory Final pixel inthe image
8/3/2019 FIT 2011 Blok Sort
http://slidepdf.com/reader/full/fit-2011-blok-sort 5/23
Size consideration in an RGB image
The lowest resolution for a monitor
Displaying a Windows desktop is 640 x 480 pixels.
In a bitmap of this resolution, then, there would be 3 bytes per
pixel, For a total of 640 x 480 x 3, or about 900 kilobytes.
8/3/2019 FIT 2011 Blok Sort
http://slidepdf.com/reader/full/fit-2011-blok-sort 6/23
Bit-Depth = Color-Depth Number of Colors = 2^(Bit-depth) Bit-depth is the number of bits.
It is also called ³Color resolution´.
Bit depthBit depth Color resolutionColor resolution CalculationCalculation1-bit 2 colors 2^1 = 2
2-bits 4 colors 2^2 = 4
3-bits 8 colors 2^3 = 8
4-bits 16 colors 2^4 = 16
8-bits 256 colors 2^8 = 256
16-bits 65,536 colors 2^16 = 65536
24-bits 16,777,215 colors 2^24 = 16.7 million
8/3/2019 FIT 2011 Blok Sort
http://slidepdf.com/reader/full/fit-2011-blok-sort 7/23
Color Palettes Images look best
If they¶re stored with as RGB images with 16,777,216 colors.
However, file seizes may be very large.
For practical purposes,
we would like to reduce the number of colors from 16,777,216 to
256 colors.
Such files are referred to as using palette-color.
The colors in a palette-color file are derived from a potential paletteof 16,777,216 colors, but no more than 256 of them can be used in
any one image.
8/3/2019 FIT 2011 Blok Sort
http://slidepdf.com/reader/full/fit-2011-blok-sort 8/23
Graphics Interchange Format (GIF)
The GIF is one of the most commonly used graphic file formats,
especially on the Internet.
an indexed color image format.
The color of the image is indexed in a palette. (a color-table)
The GIF is only capable of supporting a maximum of 256 colors.
Uses lossless compression algorithm.
8/3/2019 FIT 2011 Blok Sort
http://slidepdf.com/reader/full/fit-2011-blok-sort 9/23
Structure of a BMP
Color-Palette Image
Information ± 56 bytes
Size
Dimensions Width, height
Bit per pixel 8, 4, 2, 1
Color Table 3 x 256 bytes at most
The color-mapped table of an image
Index R G B
0 28 0 1
1 19 2 5
2 34 1 1
3 39 2 3
4 44 0 2
.. .. .. ..
254 193 211 223
255 206 212 222
8/3/2019 FIT 2011 Blok Sort
http://slidepdf.com/reader/full/fit-2011-blok-sort 10/23
Euclidean Distance Metric
Let E[a,b] be the Euclidean distance between two color indices
a and b.
(0 a, b 255)
where,
E[a,b]: Distance between index a and index b. eR: Difference between R values of a and b indices.
eG: Difference between G values of a and b indices.
eB: Difference between B values of a and b indices.
8/3/2019 FIT 2011 Blok Sort
http://slidepdf.com/reader/full/fit-2011-blok-sort 11/23
Euclidean and Pseudo Distance
matrices
Pseudo-distance matrix
Distance matrix
created from the color palette
converted
Index R G B
0 28 0 1
1 19 2 5
2 34 1 1
3 39 2 3
4 44 0 2
.. .. .. ..
254 193 211 223255 206 212 222
Color-map table
8/3/2019 FIT 2011 Blok Sort
http://slidepdf.com/reader/full/fit-2011-blok-sort 12/23
Encoding
Reference pixel x and its neighbors Ranking with pseudo-distance matrix
X is the index value to be predicted. a, b, c are neighboring indices.
Using (a, x) we determine ranking value, or error e.
Pseudo-distance matrix
8/3/2019 FIT 2011 Blok Sort
http://slidepdf.com/reader/full/fit-2011-blok-sort 13/23
Decoding
In error matrix E,
the index number of the first pixel at the top-left corner, call it a, is
copied to I. Later we apply the following:
Receive the error signal e of the next pixel from the encoded image.
In row a of the pseudo-distance matrix search the error signal value e.
Emit the corresponding column value x as the original index value of
the image.
Let x be a and repeat the process until we reach to the end of file.
Clearly, in decoding process, we obtain original index valueswithout any loss.
8/3/2019 FIT 2011 Blok Sort
http://slidepdf.com/reader/full/fit-2011-blok-sort 14/23
a1 x1 x2e11
e12
e13
e14
e15
..
e21
e22
e23
e24
..
..
ei1
..
.. x12 .. x13 ..
.. .. .. .. .. ..
a1 .. e12 .. .. ..
.. .. .. .. ..
a2 .. .. .. e13 ..
«. .. .. .. .. ..
Copy e11 to I(1,1)
Let a1 e11
Determine x12 by searching e12 in row a1.
I(1,2)
x12Let a2 x12
Determine x13 by searching e13 in row a2.
I(1,3) x13
We repeat the process similarly.
1
2
3
Decoding (cont.)
E: Encoded image P: Pseudo-distance matrix I: Image
8/3/2019 FIT 2011 Blok Sort
http://slidepdf.com/reader/full/fit-2011-blok-sort 15/23
Why do we use the pseudo-distance
transformation?
0%
10%
20%
30%
40%
50%
60%70%
80%
90%
100%
01
2
3Sunset Serrano Sea_dusk Yahoo
0%
10%
20%
30%
40%
50%
60%70%
80%
90%
100%
01
2
3Sunset Serrano Sea_dusk Yahoo
Before transformation After transformation
8/3/2019 FIT 2011 Blok Sort
http://slidepdf.com/reader/full/fit-2011-blok-sort 16/23
Distribution of Music.bmp (n = 8) before and after transformation
Distribution of Serrano.bmp (n = 256) before and after transformation
Why do we use the pseudo-distance
transformation?
8/3/2019 FIT 2011 Blok Sort
http://slidepdf.com/reader/full/fit-2011-blok-sort 17/23
Block-sorting Transformations
After the pseudo-distance technique, we apply block
sorting transformations on the data.
Linear Ordering Transformation (LOT)
Context-level one
Burrows-Wheeler Transformation (BWT)
Context-level n
8/3/2019 FIT 2011 Blok Sort
http://slidepdf.com/reader/full/fit-2011-blok-sort 18/23
Linear Ordering Transformation For example, let w = [1, 3, 1, 3, 2]
Original l l -1
1 2 3 4 5 1 4 2 5 3 1 3 5 2 4
1 3 1 3 2 1 3 1 3 2 1 1 2 3 3
Note that, the inverse permutation of LOT l isl -1 = [1 ,3, 5, 2, 4]. l -1 is called the Canonical SortingPermutation of w.
Also, elements of w is sorted in non-decreasing order by l -1 and consists of m-blocks of different sizes.
Sorted data can be encoded cheaply.
8/3/2019 FIT 2011 Blok Sort
http://slidepdf.com/reader/full/fit-2011-blok-sort 19/23
Burrows-Wheeler Transformation
Let w = [3,1,3,1,2] be a data string. Construct
3 1 3 1 2
M= 1 3 1 2 33 1 2 3 1
1 2 3 1 3
2 3 1 3 1by forming the successive rows of M , which are
consecutive cyclic left-shifts of w.
8/3/2019 FIT 2011 Blok Sort
http://slidepdf.com/reader/full/fit-2011-blok-sort 20/23
Note that the original data string w is the 5throw of M ¶ .
Given the I = 5 (row index) of w in M ¶ and
L¶ = [3, 3, 1, 1, 2] we can recover w .
1 3
1 3
M ¶
= 2 13 1
3 _ _ _ 2
Burrows-Wheeler Transformation
8/3/2019 FIT 2011 Blok Sort
http://slidepdf.com/reader/full/fit-2011-blok-sort 21/23
Binary Arithmetic Coder
We observed that after the pseudo-distance metric is applied to
indices of various color-mapped images, on some images
percentage of 0s varies from 72-90.
Hence, we applied context-adaptive binary arithmetic coder which includes run length coding and context modeling.
This yields better compression gain than Huffman coder, which
was originally proposed by Kuroki et al.
8/3/2019 FIT 2011 Blok Sort
http://slidepdf.com/reader/full/fit-2011-blok-sort 22/23
Images #Colors Size GIF PDT+SAC
PDT+LIN+BAC
PDT+BWT+BAC
Benjerry 48 28,326 1.239 1.218 1.255 1.182
Books 7 29,338 3.046 3.447 3.121 2.757
Clegg 256 719,158 3.623 2.808 2.474 1.972
Cwheel 256 481,078 1.492 0.984 0.957 0.919
Descent 122 64,542 2.928 2.765 2.731 2.716
Fractal 256 389,190 6.923 5.335 5.355 5.354
Frymire 256 1,238,678 1.485 1.373 1.426 1.276
Gate 84 61,302 2.939 2.471 2.418 2.376
Ghouse 256 481,078 3.713 3.219 3.169 3.128
Music 8 6,302 2.482 2.305 2.356 2.037
Netscape 32 61,382 2.113 1.922 1.880 1.825
Party8 12 75,606 0.854 0.778 0.772 0.699
Pc 6 1,721,858 1.694 1.723 1.594 0.977
Sea_dusk 46 157,538 0.323 0.052 0.052 0.048
Serrano 256 502,886 1.629 1.389 1.341 1.211
Sunset 204 308,070 2.601 1.590 1.557 1.550
Winaw 10 148,894 0.997 0.980 0.933 0.856
Yahoo 229 28,110 1.983 1.818 1.855 1.777
Average 361,296 2.337 2.010 1.958 1.814
W. Avg. 2.328 1.974 1.899 1.629
Normalized 1.429 1.212 1.166 1.000
Experimental Results
8/3/2019 FIT 2011 Blok Sort
http://slidepdf.com/reader/full/fit-2011-blok-sort 23/23
Thank You!
Questions?