Transcript Compression - Boston University

Compression
Monica Stoica, [email protected]
Boston University
Books used: Information Technology by David Cyganski
Why Image Compression?


A high-quality image may require 10 to 100 million
bits for representation. For example, a nearly
photographic image requires approximately 1,280 rows
of 800 pixels each, with 24 bits of color information
per pixel; that is, a total of 24,576,000 bits, or
3,072,000 bytes. The large data files associated with
images thus drive the need for extremely high
compression ratios to make storage (particularly of
movies) practical.
Without compression, a CD with a storage capacity of
approximately 600 million bytes would only be able to
store about 200 pictures like that above, or, at the 24
frames per second rate of a motion picture, about 8
seconds of a movie.
Why can we do compression?



Suppose we agree with a friend that from now on,
whenever we would have spoken the word ``information,''
we will instead simply say ``eep.'' And, in the odd situation
in which we should ever actually need to say eep itself one
or more times, we will simply tack on an extra eep, for
example, saying eepeepeep to convey the unusual message
``eepeep.'' Consider the benefits:
We have reduced every occurrence of the common foursyllable word, information, into a single syllable word;
We have a simple scheme that we can use to still convey an
eep or even an eepeep when we really want to do so; The
penalty is that we need to add a syllable to every eep
utterance we make. But how often does it happen that we
need to say eep or any of its derivatives?
Images have redundant data


Imagery data has more redundancy than we can
generally find in other types of data. For example, a
pair of adjacent rows of picture elements in an image
are usually nearly identical, while two adjacent lines of
text in a book have essentially no commonality.
The human eye is very tolerant of approximation error
in an image. We may decide to exploit this tolerance to
produce increased compression, at the expense of
image quality (that is, we may intentionally introduce
some error into the image). This approach would never
be applied to financial data, for example, but for
imagery the information loss may be irrelevant.
Loss less vs. Lossy


Usual methods of compression are called loss less coding
techniques. With loss less coding, we restore every detail of
the original data upon decoding. Obviously this is a
necessity for numerical, financial documents.
Our tolerance of image approximation and need for high
compression opens the opportunity to exploit a new form
of coding: lossy coding. Lossy coding can only be applied
to data such as images and audio for which humans will
tolerate some loss of fidelity(faithfulness of our
reproduction of an image after compression and
decompression with the original image). Because we are no
longer being held to the same requirements that underline
the reproduction of financial or engineering data, we
should be able to realize greater compression of the data as
we increase the allowed loss of information.
Run Length Encoding



Is a common method that does not attempt to achieve the
maximum compression available, but that is simple to
implement.
For example, take the case of facsimile (fax) images of
typical office documents. These two-color images (black
and white) are predominantly white.
Many entire horizontal lines of picture elements are
entirely white. Furthermore, if a given pixel is black or
white,the chances are very good that the next pixel will
match it. We call these groups of identical picture elements
``runs,'' and can assign codes to them that are much shorter
than would be the case if the intensity and color of each
individual picture element were transmitted. This form of
data compression is called ``run length coding.''
Example of fax – Run length Coding
Run length Coding


The purpose of run length encoding is to
achieve easy compression by exploiting
this special structure of images (runs)
It is done at very little computational
expense in the coding and decoding
process, so the computer takes a very small
time to run it.
Example of Run length Coding in everyday life

Suppose you and a friend were given the task of
counting the number of men and the number of
women exiting a certain building. To make sure that
no one is missed, you will simply watch the door
and call out the sex of the person leaving. Your
friend will make the appropriate notations in a
notebook that you can later tally. After a half hour
of calling out ``man, man, man, woman, woman,
woman, woman, man, woman,...,'' you are getting
quite tired of talking so much and your friend is
getting quite tired of making little stroke marks in
the man and woman columns. Your frustration
causes you to become innovative
Continuation


There is no reason to call out and write down a
result at each and every event. You could have
called out the same sequence we described above in
this way: ``Three men, four women, man,
woman,....'' This is called run length encoding.
Your friend, knowing the two categories, does not
confuse the numbers for genders.
Hence, numbers can be intermixed in the stream of
words to compress the amount of talking and
writing involved in recording an unbroken sequence
of one gender.
R
L
C
The JPEG Standard for Lossless Compression


while run length encoding is suitable where
moderate compression is sufficient and fast
processing of the compression by a computer is
desired, there are needs for better compression of
images as well.
For example, if data transmission rates are very
slow, or if the amount of data storage that is
available is very small, then high compression is
needed even though it might take longer to compute
once the image makes to the local computer.
JPEG


Joint Photographic Experts Group - the group of
vendors and researchers that cooperated to design
this industry standard for image compression.
The JPEG image compression standard 8.1 is
actually not a single approach to compressing
images. Rather, the standard describes 29 distinct
coding systems for compression of images. The
standard includes so many options because the
needs of users vary so much with respect to quality
versus compression, and compression computation
time. The committee of experts developing these
standards decided to provide abroad selection from
which to choose.
JPEG


These various approaches can be divided into two
basic groups: those that are loss less, like the run
length encoding method we just described, and
those that are lossy.
The lossy JPEG compression options are often used
in practice. In this presentation, we discuss the loss
less approach first, which includes only two of the
29 JPEG versions. Both of these use a technique
called predictive coding to attempt to identify pixels
later in the image in terms of previous pixels in that
same image.
JPEG




There is not just a single prediction process that is used.The
predictive process that is used in the loss less JPEG coding
is varied automatically for any image on a line by line
basis. The choice is made according to that prediction
method that yields the best prediction overall for the entire
line. There are seven prediction methods available in the
loss less JPEG coding standards. These may be divided into
the following categories:
1.Predict the next pixel on a line in the image as having the
same value as the previous pixel on that line.
2.Predict the next pixel on the line as having the same
value as the pixel on the line directly above it.
3.Predict the next pixel on the line as having a value related
to the values of three nearby pixels, such as the average of
the three nearby pixel values.
JPEG


The next encoding step after the predicted pixel
value is formed, is to compare that value to the
actual pixel value. The difference, if any, forms that
output stream of information to be sent to the next
encoder step. If these differences are large, nothing
is gained by this prediction process.
However, as a result of the smoothness and general
redundancy of most pictures, the differences
generally consist of a series of relatively small
positive and negative numbers that represent the
typically small errors in the prediction. The
probabilities associated with these values are high
for small error values, and are quite small for large
JPEG Loss less better
than Run Length Code


The typical loss less compression that we
can achieve in this way for natural images
is 2:1, or a 50% reduction in image data.
While this is substantial, it does not in
general solve the problem of storing or
moving very large sequences of images as
encountered in high quality video.
GIF: Another Lossless Image Compression



GIF stands for Graphics Interchange Format and
was developed by CompuServe. CompuServe was
one of the pioneering companies in providing
telephone-based computer network access, initially
to its own bulletin boards and other services, and
more recently to the Internet.
Their interest in creating the GIF compression
scheme was that of making the exchange of pictures
via telephone connections to their system practical.
GIF compression is much faster than is a direct
application of the LZ algorithm, on which it is
based.
GIF


we treat each byte of data as a indivisible message
(one of the 256 colors allowed by the GIF format)
and code strings of these whole bytes. This
approach takes advantage of the fact that our
images are structured and that strings of color
patterns will be quite common.
Here we see GIF as occupying a place between that
of run length encoding and loss less JPEG encoding
in the spectrum of possibilities between low
complexity and low compression systems (RLE)
and high complexity and high compression systems
(JPEG).
Lossy Compression


lossy compression algorithms obtain greater compression
by allowing distortion of the image that will be recovered
on decompression. In effect, these systems simplify the
image by removing information from them. The more the
degree of simplification, the less the recovered image will
look like the original.
Because the allowable distortion varies according to the
purpose of the image, the amount of compression is
typically set by the user of the compression system. Thus,
little if any lossy compression is typically acceptable for
spy satellite and medical images, while considerable
compression is applied to the screen saver and icon images
that are displayed on one's computer.
Simple Lossy Compression Method



It subtracts from each pixel the value of the pixel before it
in a line. Now, it scans the result looking for patterns of the
form (1,-1), (-1,1), (1,0,-1), (-1,0,1), (1,0,0,-1), (-1,0,0,1)
and replaces them with strings of two, three, or four zeros,
respectively. These patterns correspond to locations where
the adjacent pixels are very similar in color values.
What this is doing is replacing changes in intensity that
reverse themselves with no change at all.
The pattern (1,-1) for example would be caused by a
string of pixels in which an increase in brightness by a
single level is immediately followed by a decrease by a
single level. Under our compression scheme, the change
will not be found in the new, compressed, image.
Simple Lossy Compression Method


Thus we have simplified the picture, but in such a
way that it would only be revealed upon
extremely careful inspection.
Next, a run length encoding is applied. Thanks to
the simplification step,there ought now to be more
long runs of similar pixel values. Hence the
compression should be better than before at a
small loss of fidelity.
Example of Compressed Image Using
Lossy: very good quality
JPEG Lossy Compression


The JPEG standard includes a set of sophisticated lossy
compression options, which resulted from much
experimentation by the creators of JPEG with regard to
human acceptance of types of image distortion. The JPEG
standard was the result of years of effort by the Joint
Photographic Experts Group, which was formed as a joint
effort by two large, standing, standards organizations,the
CCITT (European Telecommunications Standards
Organization) and the ISO (International Standards
Organization).
The JPEG lossy compression algorithm consists of an
image simplification stage, which removes image
complexity at some loss of fidelity, followed by a loss less
compression step based on predictive filtering and
Huffman or arithmetic coding.
JPEG Lossy Compression



Recall that to represent color images, three values per pixel
are needed. These may be the intensities of the three
primary colors(red, green, and blue), or three other values
that can be related mathematically to the primary colors.
The lossy JPEG approach requires that color images be
treated in such an alternative form. That is, the original
color image is separated into three images, one of which
represents the brightness of each pixel, and the others
of which represent color information.
In the JPEG image reduction process, if the image is pixels
in size, we break it into square blocks of pixels and treat
each block independently. The 64 pixel values in each
block are transformed into a new set of 64 values.However,
these new 64 values, known also as weights, form an
entirely new way of representing an image than we have
treated so far.
JPEG Lossy Compression


Imagine 64 slide projectors all playing light on a single
screen. Further imagine that each of these projectors
projects a different picture so that what we see is the
result of overlapping all the pictures.Finally, imagine that
we can control the brightness of each projector
independently. The 64 weights tell us how bright or dim
to make each projector so that the overlapped image
forms a desired picture.
The 64 images that the weights refer to are pixel images
that don't resemble anything from a particular image.
However, it can be shown that any image can be created
by superimposing all 64 images with appropriate scaling
of the intensities of each one.
Advantages



It is fast to compute compared to many
other suitable image transformations,
It usually tends to result in low values for
the weights of some of its basis images.
The image that results from deleting low
weight components is generally pleasing to
the eye.
Last, but not the least…



The JPEG lossy compression algorithm next simplifies
(throws away information) the weight data to reduce
the number of bits in the images while doing minimal
damage to the image quality. The process used is as
follows:
First the smallest weights are eliminated, by setting
them to zero.
The remaining weights are rounded off so that they
may be represented with few bits. The amount of
rounding, and hence then umber of bits transmitted,
varies among all the weights,according to observed
levels of sensitivity of viewers to these degradations.