A Supervised Region Segmentation using Gabor-wavelet Features in Smoothed Spatial Domain

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International Journal of Research in Information Technology (IJRIT) International Journal of Research in Information Technology (IJRIT)International Journal of Research in Information Technology (IJRIT) International Journal of Research in Information Technology (IJRIT)

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www.ijrit.com ISSN 2001-5569

A Supervised Region Segmentation using Gabor- wavelet Features in Smoothed Spatial Domain

Ms. Sunita Dalai

¹

, Ms. Manaswini Sahu

²

1

Asst. Prof., Dept. of ECE, Centurion University of Technology & Management Bhubaneswar, Odisha, India

[email protected]

2

M.Tech scholar, Dept. of ECE, Centurion University of Technology & Management Bhubaneswar, Odisha, India

[email protected]

Abstract

Texture is a feature which is used to partition an image into different regions and also help to classify those regions. Texture provides vector of values at each pixel, describing the texture in a neighborhood of that pixel. Texture segmentation is defined as splitting up an image into different regions based on their texture.

Texture analysis such as segmentation and classification plays a main role in pattern recognition. Image segmentation is generally used to locate objects and borders in the images. The segmentation process undergoes different steps such as filter bank design, feature extraction and clustering. Then we will get the segmented image.In this paper, a new texture segmentation technique using Gabor-wavelet features and feed-forward back-propagation neural network is proposed. The multi-textured image is filtered into number of filtered images through Gabor-wavelet filters. The useful information from the filtered images are extracted using spatial smoothing method. All the features are clustered in feature space using K-means and Fuzzy c-means clustering in multiple classes. All the clustering algorithms depends on initial centroid assigned in the clustering algorithms. So classification technique is used using Feed-forward Back- propagation Neural Network to get the segmented image. In this paper, clustering through fuzzy c mean is giving better result than the K means clustering and the comparison of segmentation results generated using unsupervised and supervised technique is presented. Supervised classification technique is giving finer result than the unsupervised clustering.

Keywords: Texture Segmentation, Gabor filter, Gabor-wavelet filter, K means clustering, Fuzzy c mean clustering and feed forward back propagation neural network.

1. Introduction

The use of image texture can be used as a description for regions into segments. There are two main types of segmentation based on image texture, region based and boundary based.: Region Based- Attempts to group or cluster pixels based on texture properties together, Boundary Based- Attempts to group or cluster

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the pixels based on edges between pixels that come from different texture properties. Human visual system is very sensitive two three texture properties. They are repetition, directionality and complexity.

Texture segmentation involves accurately partitioning an image into sections according to the textured regions or by recognizing the borders between different textures in the image.

Texture Segmentation process involves the pattern classification problem based on scale invariant and rotation invariant features. The process of texture segmentation using multi-channel filtering involves the following steps [13]:

a) Filter bank design.

b) Feature extraction and

c) Clustering/ Classification of pixels in the feature space.

The functional flow diagram of texture segmentation process is shown in Fig. 1.

Fig. 1 Flow diagram of Texture segmentation process

At present, most of the literature about texture representation via feature extraction relies on method based n signal processing [7], [8], with Gabor [9], [10], [3], and wavelet [11], [12] filters being by far the most used to enhance textural properties.

In this paper, wavelet is incorporated with Gabor filter to obtain Gabor-wavelet filters. Gabor-wavelet filtered images are used to extract the useful features to distinguish among different textures in an image.

All filtered images are not useful directly as rotation and scale invariant features for texture segmentation, further need to be smoothed to extract informative features. Features extracted from Gabor filtered images are only rotation invariant, hence features are extracted from Gabor-wavelet filtered image to obtain rotation and scale invariant features. Here, extracted features are feed to clustering as well as classification algorithm for textured image segmentation. The performance of the segmentation is evaluated by comparing with benchmark problem. The proposed supervised texture segmentation results are compared with different unsupervised clustering results with both Gabor and Gabor-wavelet features.

The experiments carried out on the Prague benchmark [2] data set allow a comparison with other methods using the same benchmark, and prove the potential of the proposed technique which has been also successfully applied to many natural images from the Brodatz dataset [1].

In next section, the basic concept of Gabor-wavelet filter is presented, while Section III deals with different clustering and classification techniques. The experiments on the Prague Benchmark and Brodatz datasets are discussed in Section IV A, while the performance of the texture segmentation is evaluated in Section IV B, and finally Section V draws conclusions and outlines future research.

Bank of Filters

Feature Extraction

Clustering/Classification

Original Image

Filtered Images

Feature Images

Segmented Image

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2. Gabor-Wavelet Feature Extraction

2.1.

Gabor Filters

The process of texture segmentation using Gabor filters involves proper design of a filter bank tuned to different spatial-frequencies and orientations to cover the spatial-frequency space. A Gabor filter is essentially a sinusoid modulated by a Gaussian function. It can be expressed as shown in (1).

2 2 2

2

(x, y) exp cos 2

2

r r r

x y x

G γ π ψ

λ σ

 +   

=    + 

 

  (1)

Where,

cos sin

xr =x θ+y θ yr = ycosθ+xsinθ

θ is the orientation of the filter γ is the filter aspect ratio

σ is the standard deviation of the Gaussian.

λ

is the wavelength of the sinusoid

ψ

is phase offset.

2.2 Gabor-wavelet filters

Elements of family of mutually similar Gabor functions are called wavelets when they are created by dilation and shift form one elementary Gabor function (mother wavelet).The Fourier transform has been the most commonly used tool for analysing frequency properties of a given signal, while after transformation, the information about time is lost and it's hard to tell where a certain frequency occurs. To solve this problem, we can use kinds of time-frequency analysis techniques learned from the course related to wavelet transform [14] to represent a 1-D signal in time and frequency simultaneously. There is always uncertainty between the time and the frequency resolution of the window function used in this analysis since it is well know that when the time duration get larger, the bandwidth becomes smaller. Several ways have been proposed to find the uncertainty bound, and the most common one is the multiple of the standard deviations on time and frequency domain given in Eq. (2).

2 2

( ) ( )

,

( ) ( )

t f

t x t dt f x f df

x t dt x f df

σ ∫ σ ∫

= =

∫ ∫ (2)

1

t f 4

σ σ^× ^≥ π (3)

Among all kinds of window functions, the Gabor function is proved to achieve the lower bound and performs the best analytical resolution in the joint domain [15], [16]. This function is a Gaussian modulated by a sinusoidal signal and shown below in Eq. (4)

^ϕ^{( )}^t ⁼^exp

( )

⁻^α^{2 2}^t ^{exp j}

⁽

²^π^{f t}⁰

⁾

(4) ( )f π2exp

(

π α²/ ²(f f⁰)²

)

Φ = α − − (5)

Where, α determines the sharpness and f₀is modulated centre frequency ofϕ( )t ^{, and}Φ^{( )}^f is its Fourier transform.

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(a) (b) (c)

(d) (e) (f)

Fig. 2 Example of ϕ( )t with three different f0=0, 0.5, and 1 but the same α=0.5 and their time- frequency analysis by Gabor transform, where (a)-(c) show the real part of ϕ( )t and (d)-(f) show the

magnitude of the Gabor transform ofϕ( )t .

Fig. 2shows the example of ϕ( )t with three different f but the same₀ α and their time-frequency analysis by Gabor transform. These three distributions have the same area but don't meet the multi-resolution requirement: the window size should depend on the centre frequency. To achieve this requirement, we substituteα with f₀ γ^{, where}γ is a self-defined constant, and make the time duration ofϕ( )t dependent on the central frequency f .The generalized ( )₀ ϕ t with normalization of the maximum response in frequency domain is now defined as given in Eq. (6).

( ) f⁰ exp f⁰2² ² exp

(

2 0

)

t t j f t

ϕ π

γ π γ

 

=  

  (6)

This 1-D Gabor function could be extended into 2-D form and also achieve the lower bound of uncertainty principle [17]. This 2-D Gabor function [18] is defined as shown in Eq. (7).

ϕ^{( , )}^{x y} ^f²^exp ^f₂²^xr² ^f₂²^yr² ^exp

(

^j²π^fxr

)

πγη γ η

  

  

= − + 

 

(7) x_r =xcosθ+ysinθ (8) y_r = −xsinθ+ycosθ (9)

Where f is the frequency of the modulating sinusoidal plane wave andθis the orientation of the major axis of the elliptical Gaussian. The 2-D Fourier transform of ϕ( , )x y is shown below in Eq. (10).

( , )u v exp ² ²2

(

u_r f

)

² ²2v_r

f f

γ η

 π  

  

 

Φ = − − + (10) u_r =ucosθ+vsinθ (11) v_r = −usinθ+vcosθ (12) We know that a set of 1-D wavelets is defined as:

ψ(t, a, b)=ψ((t a) / b)− (13)

Where ψ( , )x y is the mother wavelet and aandbdetermines the temporal shifting and scaling of this function. This definition could be further extended into 2-D wavelet transform as defined in Eq. (14).

(

^x^, ^y^{, , ,} ⁰^, ⁰

)

¹ ⁰ ⁰

x y

x x y y

b b x y x y

b b

θ b b θ

ψ = ψ ^ ⁻ + ⁻ ^

 

(14)

where, ψ_θ( , )x y is the 2-D mother wavelet, with b and _x b_y the scaling parameters,

x

₀ and

y

₀ the spatial shifting, and θ the orientation parameter. The 2-D Gabor function defined in Eq. (14) meets this form and

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could be seen as a set of self-similar Gabor wavelets. The spatial shifting terms are missing in Eq. (14) while these could be compensated by the convolution operation between this equation and the input image.

To make ϕ( , )x y as a set of continuous wavelets, we should make sure that ϕ( , )x y obeys the five constraints: compact support, real, even symmetric or odd symmetric, vanishing moments, and admissibility criterion. The former three constraints are achieved by setting a magnitude threshold to

( , )x y

ϕ and separate it into real and imaginary part, while the later two need the DC-free modification to make this wavelet transform reversible and with at least one vanishing moment. This modified Gabor wavelet is defined as:

( , ) f² exp f²2 _r² f2² _r²

(

exp( 2 _r)

)

x y x y j fx K

ϕ π

πγη γ η

= − +  −

  

 

 

  (15)

Where,

K is an offset parameter dependent onγ ^andη. In practical cases, the Gabor wavelet is used as the discrete wavelet transform with either continuous or discrete input signal, while there is an intrinsic disadvantage of the Gabor wavelets which makes this discrete case beyond the discrete wavelet constraints:

the 1-D and 2-D Gabor wavelets do not have orthonormal bases. If a set of wavelets has orthonormal bases, the inverse transform could be easily reconstructed by a linear superposition, and we say this wavelet transform provides a complete representation. The non-orthonormal wavelets could provide a complete representation only when they form a frame [16]. The concepts of the frame are beyond the scope of this paper because it's too theoretical, while in most of the applications, we don't really care about these non- orthonormal properties if the Gabor wavelets are used for “feature extractions”. When extracting features for pattern recognition, retrieval, or computer vision purpose, the transformed coefficients are used for distance measure or compressed representation but not for reconstruction, so the orthogonal constraint could be omitted.

2.3 Features extraction

Filtered outputs by default are not appropriate for identifying key texture features. A number of feature extraction methods were proposed to extract useful information from the filter outputs. Clausi and Jernigan reviewed some feature extraction methods reported in [3]. In this paper, spatial smoothing is applied on filtered images to extract key texture features.

3. Clustering/Classification

3.1. Clustering

At the end of the feature extraction step we are left with a set of feature images extracted from the filtered outputs. Pixels that belong to the same texture region have the same texture characteristics, and should be close to each other in the feature space. The final step in unsupervised texture segmentation is to cluster the pixels into a number of clusters representing the original texture regions. Labeling each cluster yields the segmented image. There are two approaches are reported to clustering the feature vector.

a. K Means clustering b. Fuzzy C Mean clustering

3.1.1 K Means clustering

Here, we use the basic K-means clustering algorithm for simplicity. It is a hard partitive technique.

Algorithm:

1. Assign initial means

v_i

(centroid),

i=1, 2,K,C

.

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2. Assign each data pattern (point)

X_k

to the cluster

U_i

for the closest mean.

3. Calculate new updated centroid,

_i ^X^k ^Uⁱ ^k

i

X

v C

∑ ∈

=

4. Repeat step (2) and (3) until the updated centroid become stable.

3.1.2 Fuzzy C-mean clustering

FCM is soft partitive clustering. Each data point is associated with every cluster using a membership function, which gives degree of belonging to the clusters.

Algorithm:

The FCM algorithm consists of the following steps:

1. Assign initial means

v_i

(centroid),

i=1, 2,K,C

Choose value of fuzzifier

m

and threshold

t_max

. Set iteration counter

t=1

.

2. Repeat step (3)-(4) by incrementing

t

until

^µ^ik^(t)⁻^µ^ik^{(t 1)}^{− >}^t^max

3. Compute

µ_ik

for

C

clusters and

N

data patterns

2 1 1

1

ik c m

ik j

jk

d d µ

−

=

 

 

 

∑

4. Update means v

_i

, using

¹

1

( )

N m

k ik k

i N

m

k ik

v µ X

µ

=

∑

Clustering generally depends upon the initial centroid. If the centroid will not correctly assign, then the segmentation will not be perfect. So classification technique is to be used.

3.2 Classification

In this section, the classification problem using neural network is discussed. Neural network is used as an adaptive retrieval system which incorporates learning capability into the network module where the network weights represent adaptability. This learning approach has several advantages over traditional retrieval approaches. In this paper, a three layer feed-forward back-propagation neural network is modelled for feature classification. These three layers are input, hidden, and output layer. The number of neurons in input layer is decided by the number of feature images extracted from the filtered images and number of output neuron is equal number of textures present in the image. Hidden layer neurons are decided by 2n+1, where n is the number of input neurons.Every neurons in the input layers is connected to the every neurons of hidden layer. There must be some weight between each pair of layers to decide the boundary among different classes. For example, first neuron is connected to first neurons of hidden layer, so the weight is

w . Weight is also assigned between hidden layer and output layer. Weights are updated during each 11

iteration of training by minimizing the mean square error. It will be done iteratively until the weight will be updated. Some error will be found. Then it will be passed through the sigmoidal function. But during training we calculate error (desired output-calculated output) using feed forward calculation. To learn nonlinear relationships between input and output vectors, a Multi-Layer Perceptron (MLP) has multiple layers with nonlinear transfer functions. Feed forward networks often have one or more hidden layers of sigmoid neurons followed by an output layer. MLP is trained by adjusting the weights using Least Square Error (LSE) that minimizes the mean square error.

The total square error between the desired class and the actual output in output layer K is calculated. To train the neural network, the gradient is determined by using a back propagation technique which

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involves performing computations backwards through the network. After the back propagation network is trained properly, it typically provides reasonable answers when presented with that it has never seen. Our MLP uses the sigmoid transfer function in all three layers. During training, random selected quantized feature vectors are assigned to properclasses. After MLP is trained, quantized feature vectors corresponds to each pixel of the image are classified to proper regions.

4. Results and Discussion

4.1 Datasets

For experimental purposes, two different texture database is used – (i) Brodatz texture database, and (ii)as the natural texture samples [1]. Thedatabase was formed by cropping nine 128 128× sub-images from the centers of 111 different original 8-bit 512 512× images. Samples of Brodatz grayscale textures are shown in Fig. 3.

Fig. 3 Samples of Brodatz grayscale texture database

The Prague texture segmentation data generator and benchmark database is used. For each texture mosaic there is also the corresponding ground truth and mask images are taken from Prague texture database [2].

Samples of Prague grayscale texture database with benchmark are shown in Fig. 4.

(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

Fig. 4 Samples of Prague grayscale texture database with multi-textured and ground truth image 4.2 Segmentation Results

For the segmentation of textured image, we have extracted Gabor-wavelet features in smoothed spatial domain. A set of Gabor-wavelet filters were designed to extract the Gabor-wavelet features. In this paper, we have designed Gabor-wavelet filters at 5 scales and 8 orientations. The real part of Gabor wavelets with 5 scales and 8 orientations are shown in Fig. 5.

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Fig. 5 An example of the real part of Gabor wavelets with 5 scales and 8 orientations

To test the performance of the proposed algorithm, we have generated textured images from the Brodatz texture database. Multiclass textured images were passed through a set of Gabor-wavelet filters, resulting a set of filtered image. To extract rotation and scale invariant featured images, filtered images were processed for smoothing in spatial domain.

The number of featured images was equal to number of Gabor-filtered images. This paperconcentrate on pixel based texture segmentation. The feature vector correspond to individual pixel in textured image consist of corresponding pixels of all featured images. All the feature vectors correspond to all pixels in textured image were clustered using K-means and Fuzzy C-means algorithm. The quality of the segmentation results were compared in Fig. 6 and Fig. 7.

Multi- textured

Image

Gound Truth Image

K-means Fuzzy c- means

Multilayer Percepron

(a) (b) (c) 91.22 (d) 94.62 (e) 97.63

(f)

(g)

(h) 81.55 (i) 93.11 (j) 97.24

Fig. 6 Segmentation results using K-means (3^rd column), Fuzzy C-means (4^th column) and Multilayer perceptron (5^th Column) for Brodatz texture database.

The pixel based segmentation was also performed using feed-forward back-propagation neural network.

The network is trained using raw texture images collected from the Prague texture segmentation data generator and benchmark database. The benchmark database was automatically generated with multiclass segmentation problem as shown in Fig. 4. The multi-textured images were feed to the network for testing and compared with ground image. The classification performance was calculated by comparing segmented output image and respective ground truth. The comparative result of segmentation for the Prague texture database is shown in Fig. 7.

Multi- textured Image

K-means Fuzzy c- means

Multilay er Percepr on

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(a) (b) (c) 82.60 (d) 83.98 (e) 88.34

(f) (g) (h) 83.24 (i) 87.72 (j) 95.30

(k) (l) (m)72.58 (n) 78.35 (o) 97.17

(p) (q) (r)88.18 (s) 89.57 (s) 95.18

Fig. 7 Segmentation results using K-means (3^rd column), Fuzzy C-means (4^th column) and Multilayer perceptron (5^th Column) for Prague texture database

Figure 8 and 9 show the segmentation performance which means how many pixels are correctly classified for both Brodatz texture database and Prague texture database.

Gabor wavelet feature 2 class 4 class

K means ^91.22 ^81.55

Fuzzy c mean ^94.62 ^93.11

Multi layer perceptron ^97.63 ^97.24

Fig. 8: segmentation performance of Brodatz texture database.

Fig. 9: segmentation performance of Prague texture database

Figure 10 shows the segmentation result of the scenery image.

Multi- textured

Image

K-means Fuzzy c- means

Multilayer Percepron

(a) (b) (c) (d) (e)

Fig. 10: Segmentation results using K-means (3^rd column), Fuzzy C-means (4^th column) and Multilayer perceptron (5^th Column) of scene image.

Gabor wavelet feature

3 class 4 class 5 class

K means ^82.60 ^83.24 72.58

Fuzzy c mean ^83.98 ^87.72 78.35

Multi layer perceptron ^88.34 ^95.30 97.17

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5. C

ONCLUSION

The supervised texture segmentation using Gabor-wavelet features is already presented in this paper. The segmentation results of different clustering technique and classification techniques are compared. The result shows that feed-forward back-propagation neural network gives better result compared to other clustering techniques.

R

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