IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 19, NO. 5, MAY 2010 1371
Correspondence
Texture Classification Using Refined Histogram
L. Li, C. S. Tong, Member, IEEE, and S. K. Choy
Abstract—In this correspondence, we propose a novel, efficient, and
effective Refined Histogram (RH) for modeling the wavelet subband
detail coefficients and present a new image signature based on the RH
model for supervised texture classification. Our RH makes use of a step
function with exponentially increasing intervals to model the histogram
of detail coefficients, and the concatenation of the RH model parameters
for all wavelet subbands forms the so-called RH signature. To justify the
usefulness of the RH signature, we discuss and investigate some of its
statistical properties. These properties would clarify the sufficiency of the
signature to characterize the wavelet subband information. In addition,
we shall also present an efficient RH signature extraction algorithm based
on the coefficient-counting technique, which helps to speed up the overall
classification system performance. We apply the RH signature to texture
classification using the well-known databases. Experimental results show
that our proposed RH signature in conjunction with the use of sym-
metrized Kullback–Leibler divergence gives a satisfactory classification
performance compared with the current state-of-the-art methods.
Index Terms—Histogram, statistical modeling, texture classification.
I. INTRODUCTION
Texture classification is one of the fundamental problems in com-
puter vision and has a wide variety of potential applications (see, e.g.,
[33]). Examples include classification of regions in satellite images [8]
and detection of defects in industrial surface inspection [30]. In med-
ical image analysis, texture signature is also applied to classification
of pulmonary disease [31] and diagnosis of leukemic cells [32]. As a
result, it has received a lot of research interest and a number of ap-
proaches have been proposed in the past decades. Among these ap-
proaches, texture characterization based on wavelet analysis, which
provides a multiresolution and orientation representation that is con-
sistent with the human visual system [1], may be the most popular.
Essentially, the widely used wavelet signatures include the energy sig-
nature [3], [9], [35], [36], histogram-based signature [3], [4], [7], [13],
[15], [34], co-occurrence signature [3], [8], hidden Markov model [10],
[11], level sets [24], and so on. In addition to wavelet transforms, tex-
ture features extracted from the Gabor filters [25]–[28] are the popular
texture representations, which are often adopted in the literature. Other
widely used signal processing or filtering features such as Bessel K
forms [23], spectral histograms [20]–[22], and independent component
analysis features [29] were applied successfully to texture classifica-
tion, synthesis, and segmentation.
Among the wavelet histogram-based signatures, the General-
ized Gaussian Density (GGD) signature [3]–[6], [12]–[14], which
is induced from a well-established GGD model for the wavelet
Manuscript received April 03, 2009; revised December 21, 2009. First pub-
lished January 26, 2010; current version published April 16, 2010. This work
was supported in part by the HKBU’s Centre for Mathematical Imaging and Vi-
sion and in part by the RGC GRF under Grant HKBU 202108. The associate
editor coordinating the review of this manuscript and approving it for publica-
tion was Dr. Maya R. Gupta.
The authors are with the Department of Mathematics, Hong Kong Baptist
University, Kowloon Tong, Hong Kong (e-mail: creatorlarryli@gmail.com;
cstong@hkbu.edu.hk; skchoy@math.hkbu.edu.hk).
Digital Object Identifier 10.1109/TIP.2010.2041414
subband detail coefficients, is widely used in various areas. Many
studies showed that the GGD signature together with the use of Kull-
back–Leibler Divergence (KLD) gives a high classification/retrieval
rate in texture classification/retrieval. Moreover, the GGD model uses
only two parameters (scale and shape parameters) to characterize the
wavelet subband leading to small storage requirement. However, the
GGD signature has several disadvantages. First, Meignen and Meignen
[14] showed that the GGD signature extracted in the Maximum Like-
lihood (ML) framework does not exist for some images (usually when
the number of detail coefficients is sufficiently small). Even if it exists,
a transcendental equation [4], which involves the gamma and digamma
functions, needs to be solved numerically to obtain the estimator for
each subband. Thus, a considerable amount of time is necessary and
numerical problems may occur when the shape estimator is close to
zero. Second, as shown in [7], the performance of GGD signature with
the use of
L
1
-metric (or in general
L
p
-metric) as a similarity measure
is poor compared to that of GGD with KLD. But when the KLD is
employed, the computational cost to compute the KLD between two
GGDs is high that will slow down the overall classification process.
Third, it has been shown [15] that there are no sufficient statistics
for the GGD parameters since the Fisher–Neyman factorization [19]
does not exist. This means the usual GGD estimators (e.g., ML or
moment estimators) cannot capture all the information about the
model parameters that are contained in the data, and, therefore, the
direct use of GGD estimators as the signature is not well justified.
The modeling of wavelet detail subband histograms via the Product
Bernoulli Distributions (PBD) [7], [15] has also received a lot of in-
terest. The PBD model makes use of a binary bit representation for
wavelet subband histograms and the so-called Bit-plane Probability
(BP) signature is constructed based on the model parameters. The PBD
has been shown to perform similarly to the GGD in terms of modeling
histogram and classification performance. Essentially, the main merits
of BP approach are its efficiency for signature extraction and similarity
measurement based on Euclidean metric, and the statistical justifica-
tion of the model parameters for use in image processing applications
[15]. However, it has two main problems. First, the interpretation of
the BP signature is not clear since each element in the BP signature is
the probability of 1-bit occurrence for each bit-plane and so there is no
intuitive explanation (or physical meaning) for these “probabilities”.
Second, the Euclidean metric used for measuring distance between BP
signatures and image models is not well justified.
Motivated by the advantages and disadvantages of the GGD and
PBD, we aim at combining the key advantages of the GGD and PBD to
construct our model. In this correspondence, we present a Refined His-
togram (RH) to model the wavelet subband detail coefficients and pro-
pose a new image signature, namely, the RH signature, based on the RH
model parameters for supervised texture classification. Our proposed
RH model is established by using a step function with exponentially
increasing intervals to approximate the wavelet detail histogram and
the RH signature is constructed by the concatenation of the RH model
parameters for all wavelet subbands. Our RH signature can be extracted
efficiently by making use of the coefficient-counting technique that in-
volves only multiplication and counting. In particular, we shall investi-
gate some statistical properties of the RH signature and these properties
can justify its sufficiency to characterize wavelet subbands. Finally, we
study and compare the classification performance of the RH method
with some existing approaches on the well-known texture databases.
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