
Research Article


Texture Classification Based on Extraction of Skeleton Primitives Using Wavelets 

U.S.N. Raju,
B. Eswara Reddy,
V. Vijaya Kumar
and
B. Sujatha



ABSTRACT

A novel method for dominant skeleton extraction of textures
using different wavelet transforms, is proposed in this study. The skeleton
varies depending on the shape of structuring element. If the structuring
element is homothetic to the object, the object is covered with only one
magnification of the structuring element. By this, the skeleton is reduced
to one point. The present study considers the skeleton from a binary texture.
The proposed method derives from the above that a total number of pixels
within the skeleton is the minimum when structuring element is homothetic
to the primitive. This provides the scope that the texture is composed
of one primitive, which minimizes the total number of pixels. For evaluating
such skeleton primitive the present study utilized a 3x3 structuring element,
as the skeleton primitives. All possible skeleton primitives combinations
of 3x3 mask are evaluated on all textures. The skeleton primitive that
is making the least number of skeleton points is considered as dominant
skeleton primitive. Based on the extraction of skeleton primitives a classification
is made on textures using Haar, Daubechies, Coiflet and Symlet wavelets.
Experimental results indicate a good classification and also a comparison
is made among these four wavelet results. Present method is experimented
on Brodatz textures using these four wavelets.







INTRODUCTION
Analysis of texture requires the identification of proper attributes
or features that differentiate the textures for classification, segmentation
and recognition. The features are assumed to be uniform within the regions
containing the same texture. Various feature extraction and classification
techniques have been suggested in the past for the purpose of texture
analysis. Initially, texture analysis was based on the first order or
second order statistics of textures (Haralick et al., 1973; Weszka
et al., 1976; Chen and Pavlidis, 1983). It is well known that the
cooccurrence matrix features are first proposed by Haralick et al.
(1973). However, there are 14 features to be computed for different distances
at different orientations which increase the computational and time complexity.
Even if all the features are used, the correct classification rate of
6070% was only reported in the literature. Then, Gaussian Markov Random
Fields (GMRF) and Gibbs random fields were proposed to characterize textures
(Chellappa and Chatterjee, 1985; Cohen et al., 1991). Later, local
linear transformations are used to compute texture features (Laws, 1980;
Unser, 1986). The above traditional statistical approaches to texture
analysis such as cooccurrence matrices, second order statistics, GMRF
and local linear transforms are restricted to the analysis of spatial
interactions over relatively small neighborhoods on a single scale. As
a consequence, their performance is best for the analysis of microtextures
only (Unser, 1995). More recently methods based on multiresolution or
multichannel analysis such as Gabor filters and wavelet transform have
received a lot of attention (Bovik et al., 1990; Chang and Jay
Kuo, 1993; Unser, 1995). A major disadvantage in using Gabor transform
is that the output of Gabor filter banks are not mutually orthogonal,
which may result in a significant correlation between texture features.
Moreover, these transformations are usually not reversible, which limits
their applicability for texture synthesis. Most of these can be avoided
if one uses the wavelet transform, which provides a precise and unifying
frame work for the analysis and characterization of a signal at different
scales (Unser, 1995). Another advantage of wavelet transform over Gabor
filter is that the low pass and high pass filters used in the wavelet
transform remain the same between two consecutive scales while the Gabor
approach requires filters of different parameters (Chang and Jay Kuo,
1993). In other words, Gabor filters require proper tuning of filter parameters
at different scales.
Study of patterns on textures is recognized as an important step in characterization
and classification of textures. Textures are classified recently by various
pattern methods: preprocessed images (Vijaya Kumar et al., 2007a)
long linear patterns (Krishna et al., 2005; Vijaya Kumar et
al., 2007b) and edge direction movements (Eswara Reddy et al.,
2007), Avoiding Complex Patterns (Vijaya Kumar et al., 2008a) marble
texture description (Suresh et al., 2008). Textures are also described
and classified by using various wavelet transforms: one based on primitive
patterns (Vijaya Kumar et al., 2008b) and another based on statistical
parameters (Raju et al., 2008).
Skeletonization is an important tool for many image processing applications.
The result of the skeletonization of an image is its skeleton. Skeleton
is essentially a onepixelthick line that passes through the centre,
or medial axis, of an object. An accurate skeleton possesses significant
properties that makes it suitable for pattern recognition, machine vision
and image compression. Skeletonization allows the extraction of important
features such as an image`s topology, orientation and composition. Since
its conception by Blum (1967) skeletonization has been studied extensively
and there now exist many techniques and algorithms for performing skeletonization.
There currently exist many skeletonization methods, each utilizing different
algorithms and different information contained in an image. Recently new
algorithms for skeletonizaiton and thinning for 2D images based on primitive
concept approach are proposed by Vijaya Kumar et al. (2008c, d).
Most of the methods, however, fall into one of the two broad categories:
Pixel based method and Nonpixel based method. In the pixelbased method,
each foreground pixel is utilized for computation in the skeletonization
process. Techniques used in the pixelbased method include thinning (Lam
et al., 1992; Unser, 1986) and distance transform (Unser, 1986).
In the nonpixel based method, the skeleton of a shape is analytically
derived from the border of the image. There are two types of nonpixel
based methods, which are based on either cross section (Pavlidis, 1986)
or Voronoi diagrams (Ogniewicz and Kubler, 1995). These methods attempt
to determine the symmetric points of a shape without the intermediate
step of the grassfire propagation. The fundamental concept of these methods
is that the local symmetric axes of a shape are derived from pairs of
contour pixels or a contour segment representing a sequence of the contour
pixels. Although more than 300 skeletonization algorithms have been proposed
by Lam (1992) the improvement is still required, since the existing approximation
algorithms of skeletonization often suffer from one or more of the drawbacks
(Chang and Yan, 1999; Ge and Fitzpatrick, 1996; Lam, 1992; Smith, 1987;
Zou and Yan, 1999). To overcome these problems, a novel waveletbased
method is presented in this study.
The wavelet transform is a multiresolution technique, which can be implemented
as a pyramid or tree structure and is similar to subband decomposition
(Antonini et al., 1992; Daubechies, 1992). There are various wavelet
transforms like Haar, Daubechies, Coiflet, Symlet and etc. They differ
with each other in the formation and reconstruction. The wavelet transform
divides the original image into four subbands and they are denoted by
LL, HL, LL and HH frequency subbands. The HH subimage represents diagonal
details (high frequencies in both directions ), HL gives horizontal high
frequencies (vertical edges), LH gives vertical high frequencies (horizontal
edges) and the image LL corresponds to the lowest frequencies. At the
subsequent scale of analysis, the image LL undergoes the decomposition
using the same filters, having always the lowest frequency component located
in the upper left corner of the image. Each stage of the analysis produces
next 4 subimages whose size is reduced twice when compared to the previous
scale. i.e. for level n it gives get a total of 4+(n1)*3 subbands. The
size of the wavelet representation is the same as the size of the original.
The Haar wavelet is the first known wavelet and was proposed in 1909 by
Alfred Haar. Haar used these functions to give an example of a countable
orthonormal system for the space of squareintegrable functions on the
real line. The Haar wavelet`s scaling function coefficients are h{k} =
{0.5, 0.5} and wavelet function coefficients are g{k} = {0.5, 0.5}. The
Daubechies (1992) are a family of orthogonal wavelets defining a discrete
wavelet transform and characterized by a maximal number of vanishing moments
for some given support. With each wavelet type of this class, there is
a scaling function which generates an orthogonal multiresolution analysis.
MATERIALS AND METHODS
On a 3x3 structuring element by assuming always center pixel as one,
one can have 2^{8} combinations. However the present study has
not considered the following structuring element as shown in Fig.
1 for extracting skeleton primitives. By this there will be a total
of 255 structuring elements on a 3x3 mask. These structuring elements
are used for evaluating skeleton points, means the skeleton of an object
has the property that it is reduced to one point when the structuring
element used for the skeletonization is exactly homothetic to the object.

Fig. 1: 
Structuring element that has not been considered for
skeletonization 

Fig. 2: 
Structuring element weight representation 
This method minimizes the number of pixels contained in the skeleton.
If the texture is composed of one primitive, the structuring element minimizes
the number of pixels which is homothetic to the primitive because of the
above property of the skeleton.
The structuring elements are represented by weight based system as shown in
Fig. 2 which are called as Structuring Element Weight (SEW).
Some of the skeleton structuring elements with their weights are represented
The present study proposes a novel method of the texture primitive description
that requires no assumption on the distribution of grain sizes or the
granulometric moments of the primitives. The present study employs the
morphological skeleton for this method. The most commonly employed morphological
skeleton of a binary object is explained intuitively as follows: At first
it locate the largest magnification included within the object and cover
the object by sweeping the magnification within the object. Then gradually
smaller magnifications are employed for covering the residual area until
the whole object is covered. The skeleton varies depending on the shape
of the structuring element. If the structuring element is homothetic to
the object, the object is covered with only one magnification of the structuring
element. In this case the skeleton is reduced to one point. The present
study consider here obtaining the skeleton from a binary texture. It is
derived from the above property that the total number of pixels within
the skeleton is the minimum when the structuring element is homothetic
to the primitive, if the present paper assumes that the texture is composed
of one primitive, i.e., contains grains that are magnifications of the
primitive. This indicates that the primitive is described by the optimal
structuring element minimizing the total number of pixels within the skeleton.

Fig. 3: 
Representation of structuring element with corresponding
weights (a) 3 (b) 5 (c) 7 (d) 23 (e) 31 (f) 63 (g) 165 (h) 207 and
(i) 255 
This primitive description method has an advantage that no assumption
on the sizing distribution of grains in the texture is required.
The entire process is explained in Algorithm 1 and 2. The present study
have used four wavelet transforms namely, Haar, Daubechies (Db6), Coiflet
(Cf6) and Symlet (Sym8) Wavelet transform.
Algorithm 1: To find Skeleton of an image
Begin
End
Algorithm 2: Texture skeleton primitive extraction
Begin
End
RESULTS
The Table 14 indicate the dominant
skeleton primitives on all 24 Brodatz textures (Brodatz, 1966) using Haar,
Db6, Cf6 and Sym8 wavelet transforms, respectively. Based on this the
dominant skeleton subset is applied on all 24 Brodatz textures for skeletonization
purpose using Haar, Db6, Cf6 and Sym8 wavelet transforms.
Table 1: 
Textures with least skeleton points corresponding to
their SEW by using Haar wavelet transform 

Due to lack
of space the present paper is presenting three Brodatz skeletonized textures
using Haar, Db6, Cf6 and Sym8 in Fig. 46,
respectively.
The skeleton images of dominant primitive skeleton with weight 255 is
not showing any difference for textures D_{2} and D_{10}
in all four wavelet transforms. However the skeletoned image D_{25}
with weight 255 is not similar in the four wavelet transformed images.
Table 2: 
Textures with least skeleton points corresponding to
their SEW by using Db6 Wavelet Transform 

Table 3: 
Textures with least skeleton points corresponding to
their SEW by using Cf6 Wavelet Transform 

Table 4: 
Textures with least skeleton points corresponding to
their SEW by using Sym8 Wavelet Transform 


Fig. 4: 
The skeletonization of the Texture D_{2} using
(a) Haar wavelet (b) Db6 wavelet (c) Cf6 wavelet and (d) Sym8 wavelet 
Textures are also grouped by the skeleton primitive weight. The groups
are listed in the following Table 5.
From Table 5, it is clearly evident that a total of
17 textures are having a common structuring element weight of 255. One
texture is having a common structuring element weight of 24. That is 18
out of 24 textures are showing a common classification in all four wavelets,
which results a 75% correct classification.

Fig. 5: 
The skeletonization of the Texture D_{10} using
(a) Haar wavelet (b) Db6 wavelet (c) Cf6 wavelet and (d) Sym8 wavelet 

Fig. 6: 
The skeletonization of the Texture D_{25} using
(a) Haar wavelet (b) Db6 wavelet (c) Cf6 wavelet and (d) Sym8 wavelet 
Table 5: 
Texture groups according to SEW 

CONCLUSION
The present research have proposed a novel scheme of texture classification
using skeleton primitives. The results indicate that even though the structuring
element weight is same for some texture, the result may vary depending
on the wavelets that are used. The common classification rate is 75% among
the four wavelets for the 3x3 structuring element. The present paper has
not used 2x2 square structuring element, for images because they are sensitive
to stroke thickness, size and orientations. To reduce the orientation
effect and sensitiveness to skeletonization, the present paper employed
in the present system a 3x3 skeleton primitive. The same method can be
extended to 5x5, 7x7...NxN masks also.
ACKNOWLEDGMENTS
The authors would like to express their gratitude to Sri K.V.V. Satya
Narayana Raju, Chairman and K. Sashi Kiran Varma, Managing Director, Chaitanya
group of Institutions for providing necessary infrastructure. Authors
would like to thank anonymous reviewers for their valuable comments and
Dr. G.V.S. Ananta Lakshmi for her invaluable suggestions which led to
improvise the presentation quality of this study.

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