Data Compression Lec#11-2018

Transformation
Two-dimensional image transforms are extremely important areas of study in
image processing. The image output in the transformed space may be
analyzed, interpreted, and further processed for implementing diverse image
processing tasks. These transformations are widely used, since by using
these transformations, it is possible to express an image as a combination of a
set of basic signals, known as the basis functions. In case of Fourier
transform of an image these basis signals are sinusoidal signals with different
periods which describe the spatial frequencies in an image. Thus such
transforms, such as the Fourier transform, reveal spectral structures
embedded in the image that may be used to characterize the image.
The term Image transform are usually refers to a class of unitary matrices
used for representing images.
large class of image processing transformations is linear in nature; an output
image is formed from linear combinations of pixels of an input image. Such
transforms include convolutions, correlations, and unitary transforms.
Linear transforms have been utilized to enhance images and to extract various
features from images. For example, the Fourier transform is used in highpass
and lowpass filtering as well as in texture analysis. Another application is image
coding in which bandwidth reduction is achieved by deleting low-magnitude
transform coefficients.
The following table illustrate the complexity of transformations
Transform Processing and Encoding
TYPE OPERATIONS COMMENTS
Karhunen -
Loeve
Optimum LMSE Discrete
Transform
Discrete Fourier
Asymptotic to K.L.Transform
HADAMARD
Binary Basis Matrices
4 N
2
2
2 2N log N
2
2
2 2N log N
Subject: Data Compression
Class room no.:
Department of computer science
4th Stage
Lecture time: 10:30 AM-2:30 PM
Instructor: Dr. Ali Kadhum AL-Quraby
د. علي كاظم محمد ا لغرابي Data Compression 2
Lecture No. : 11
Discrete Cosine
More