ISSN 10546618, Pattern Recognition and Image Analysis, 2010, Vol. 20, No. 4, pp. 505–512. © Pleiades Publishing, Ltd., 2010.
1. INTRODUCTION
Orthogonal moment functions such as Legendre
moment and Zernike moment have long been used in
image analysis as feature descriptors [17, 24]. The
quality of image reconstruction from a finite set of
orthogonal moment provides a measure of informa
tion content in the moment set. Furthermore,
moments are used successfully in applications, for
example, image analysis [23], texture segmentation
[13], multispectral texture [10], pattern recognition
[7, 8], image watermarking [11], monitoring crowds
[4–6] and image reconstruction [19, 20].
Image compression is the art or science of efficient
coding of picture data with a target to decrease the
number of bits required in performing an image [12].
The benefits of this image compression could save the
time for image transmission or to save the memory for
image storage.
According to Nur Azman et al. [15] suggest the use
of moment functions for image compression, due to
the capability of the blockwise moment computation
scheme which avoid numerical instabilities to yield a
perfect reconstruction [14]. Following the JPEG com
pression techniques, blockwise moment computa
tion scheme is used in this study instead of Discrete
Cosine Transform (DCT) [25].
Since blockwise moment computation is used,
experiments with the 8
×
8 and 4
×
4 block size of
images are tested. The 8
×
8 subimage is applied as it
is a standard size meanwhile the latter size is due to
faster and efficiency purposes. The discussion of this
paper is organized as follows. The following section
elaborates on the Tchebichef moment and Discrete
Cosine Transform in Sections 2 and 3, respectively.
The matrix implementation of moment equation is
reviewed in Section 4. Section 5 presents the compari
son between JPEG baseline coding and Tchebichef
Moment Compression. The advantages and disadvan
tages of using 8
×
8 or 4
×
4 block size images using the
Tchebichef Moment techniques for compression is dis
cussed in Section 6 and the conclusion is in Section 7.
2. TCHEBICHEF MOMENTS
Tchebichef moment was first introduced by
Mukundan [21] in 2001, and was proven that it per
formed better than other orthogonal moment. In
this section, the formula of the Tchebichef Moment
is described.
Let
T
mn
be Tchebichef moments based on a discrete
orthogonal polynomial set {
t
n
(
x
)} defined directly on
the image space [0,
S
– 1], thus satisfying all the
Using Tchebichef Moment for Fast
and Efficient Image Compression
1
Hidayah Rahmalan, Nur Azman Abu, and Siaw Lang Wong
Faculty of Information and Communication Technology,
Universiti Teknikal Malaysia Melaka (UTeM), Melaka, Malaysia
email: {hidayah, nura}@utem.edu. my, wong.siawlang@gmail.com
Abstract
—Orthogonal moment is known as better moment functions compared to the nonorthogonal
moment. Among all the orthogonal moments, Tchebichef Moment appear to be the most recent moment
functions that still attract the interest among the computer vision researchers. This paper proposes a novel
approach based on discrete orthogonal Tchebichef Moment for an efficient image compression. The image
compression is useful in many applications especially related to images that are needed to be seen in small
devices such as in mobile phone. Meanwhile, the method incorporates simplified mathematical framework
techniques using matrices, as well as a blockwise reconstruction technique to eliminate possible occurrences
of numerical instabilities at higher moment orders. In addition, a comparison between Tchebichef Moment
compression and JPEG compression is conducted. The result shows significant advantages for Tchebichef
Moment in terms of its image quality and compression rate. Tchebichef moment provides a more compact
support to the image via subblock reconstruction for compression. Tchebichef Moment Compression is able
to perform potentially better for a broader domain on real digital images and graphically generated images.
Key words:
Image Compression, Orthogonal Moment Functions, Tchebichef Moment, JPEG Compression,
Discrete Cosine Transform.
DOI:
10.1134/S1054661810040115
Received March 19, 2010
REPRESENTATION, PROCESSING, ANALYSIS,
AND UNDERSTANDING OF IMAGES
1
The article is published in the original.