6
A Sub-Micro Pattern Analysis for Local Rotation, Gray-Scale Transformation and Gaussian Noise Invariant TextureDescriptors Sanun Srisuk Department of Computer Engineering, Mahanakorn University of Technology 140 Cheum-Sampan Rd., Nong Chok, Bangkok THAILAND 10530 e-mail: [email protected] Abstract A new rotation invariant texture descriptor based on the difference of offset Gaussian (DooG) and a sub-micro pattern encoding are proposed. We first apply the Gabor wavelet to texture images. We then utilize the DooG to measure the difference between the center positive Gaus- sian and the neighbor rotated negative one. We encode the local micro texture using our proposed method, a sub-micro pattern analysis. In classification step, we convert the rota- tion problem to the circular shift one by applying the Trace transform on the encoding image to get another 2D im- age and then compute the circular shift invariant features in the Trace transform. A k-nearest neighbor classifier is employed to classify the shift invariant features. The pro- posed method is local rotation invariant texture descriptor and is robust to the additive Gaussian noise as a result of adapting the DooG. We evaluate the proposed method on the Brodatz album with respect to rotation and Gaussian noise. Experimental results have shown that our proposed method outperforms the recent texture analysis methods. 1. Introduction Texture analysis plays a crucial role in many image pro- cessing and computer vision applications including content- based image retrieval, medical imaging, industrial surface inspection, face detection and recognition. The texture anal- ysis has been extensive studied and many techniques have been proposed in the literature [8, 3, 4, 7, 10, 9, 5]. Ojala et al. [8] introduced a new texture descriptor based on the local binary pattern (LBP). The LBP is an operator for gray scale and rotation invariant texture descriptor. The differ- ences between the center and the neighbor pixels were used to encode as a binary number. The nonuniform and uniform patterns were used as a local texture descriptor. This method is invariant against the monotonic gray scale transformation and rotation, but sensitive to the noisy images. Some ex- tensions on local binary pattern can be found in [7, 10]. In this paper, we present a new framework for rotation invari- ant texture descriptor based on the DooG and a sub micro pattern analysis which can be thought of as a local texture enhancement method. 2 A Texture Representation 2.1 The Gabor Wavelet Let us define by x =(x 1 ,x 2 ) and ξ =(ξ 1 2 ) the space coordinates of an image f (x) and the nearby f ( ξ ), respec- tively. The Gabor filter can be written in the complex form of the combination of even and odd symmetry [2]: W μ,ν ( ξ,x) = k μ,ν σ 2 · exp k μ,ν ξ x 2σ 2 · exp[i k μ,ν z] exp[σ 2 /2] , (1) where σ governs the spatial extent and bandwidth of the Gaussian function, μ and ν control the orientation and scale of the Gabor kernel, z =(ξ 1 x 1 2 x 2 ). exp[i k μ,ν z] determines the oscillatory part of the kernel, exp[σ 2 /2] compensates the DC value of the kernel. k μ,ν 2 com- pensates for the frequency-dependent decrease of the power spectrum in natural image. The wave vector k μ,ν is defined as k μ,ν = k ν · exp[μ ], (2) where k ν = k max /Q ν , φ μ = πμ/8, k max is the maximum frequency and Q controls the spacing between kernels in the frequency domain. In this paper, σ =2π, k max = π/2 and Q = 2. The Gabor kernels are all self-similar in which they can be generated from one filter, the mother wavelet, by

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A new rotation invariant texture descriptor based on the difference of offset Gaussian (DooG) and a sub-micro pattern encoding are proposed. We first apply the Gabor wavelet to texture images. We then utilize the DooG to measure the difference between the center positive Gaussian and the neighbor rotated negative one. We encode the local micro texture using our proposed method, a sub-micro pattern analysis. In classification step, we convert the rotation problem to the circular shift one by applying the Trace transform on the encoding image to get another 2D image and then compute the circular shift invariant features in the Trace transform. A {\it k}-nearest neighbor classifier is employed to classify the shift invariant features. The proposed method is local rotation invariant texture descriptor and is robust to the additive Gaussian noise as a result of adapting the DooG. We evaluate the proposed method on the Brodatz album with respect to rotation and Gaussian noise. Experimental results have shown that our proposed method outperforms the recent texture analysis methods.

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Page 1: A Sub-Micro Pattern Analysis for Local Rotation, Gray-Scale Transformation and Gaussian Noise Invariant Texture Descriptors

A Sub-Micro Pattern Analysis for Local Rotation, Gray-ScaleTransformation and Gaussian Noise Invariant Texture Descriptors

Sanun SrisukDepartment of Computer Engineering, Mahanakorn Universityof Technology

140 Cheum-Sampan Rd., Nong Chok, Bangkok THAILAND 10530e-mail: [email protected]

Abstract

A new rotation invariant texture descriptor based onthe difference of offset Gaussian (DooG) and a sub-micropattern encoding are proposed. We first apply the Gaborwavelet to texture images. We then utilize the DooG tomeasure the difference between the center positive Gaus-sian and the neighbor rotated negative one. We encode thelocal micro texture using our proposed method, a sub-micropattern analysis. In classification step, we convert the rota-tion problem to the circular shift one by applying the Tracetransform on the encoding image to get another 2D im-age and then compute the circular shift invariant featuresin the Trace transform. A k-nearest neighbor classifier isemployed to classify the shift invariant features. The pro-posed method is local rotation invariant texture descriptorand is robust to the additive Gaussian noise as a result ofadapting the DooG. We evaluate the proposed method onthe Brodatz album with respect to rotation and Gaussiannoise. Experimental results have shown that our proposedmethod outperforms the recent texture analysis methods.

1. Introduction

Texture analysis plays a crucial role in many image pro-cessing and computer vision applications including content-based image retrieval, medical imaging, industrial surfaceinspection, face detection and recognition. The texture anal-ysis has been extensive studied and many techniques havebeen proposed in the literature [8, 3, 4, 7, 10, 9, 5]. Ojalaet al. [8] introduced a new texture descriptor based on thelocal binary pattern (LBP). The LBP is an operator for grayscale and rotation invariant texture descriptor. The differ-ences between the center and the neighbor pixels were usedto encode as a binary number. The nonuniform and uniformpatterns were used as a local texture descriptor. This methodis invariant against the monotonic gray scale transformation

and rotation, but sensitive to the noisy images. Some ex-tensions on local binary pattern can be found in [7, 10]. Inthis paper, we present a new framework for rotation invari-ant texture descriptor based on the DooG and a sub micropattern analysis which can be thought of as a local textureenhancement method.

2 A Texture Representation

2.1 The Gabor Wavelet

Let us define by~x = (x1, x2) and~ξ = (ξ1, ξ2) the spacecoordinates of an imagef(~x) and the nearbyf(~ξ), respec-tively. The Gabor filter can be written in the complex formof the combination of even and odd symmetry [2]:

Wµ,ν(~ξ, ~x) =

~kµ,ν

σ2· exp

~kµ,ν

~ξ − ~x∥

2σ2

·{

exp[i~kµ,νz] − exp[−σ2/2]}

, (1)

whereσ governs the spatial extent and bandwidth of theGaussian function,µ andν control the orientation and scaleof the Gabor kernel,z = (ξ1 − x1, ξ2 − x2). exp[i~kµ,νz]determines the oscillatory part of the kernel,exp[−σ2/2]

compensates the DC value of the kernel.∥

~kµ,ν

∥/σ2 com-

pensates for the frequency-dependent decrease of the powerspectrum in natural image. The wave vector~kµ,ν is definedas

~kµ,ν = kν · exp[iφµ], (2)

wherekν = kmax/Qν , φµ = πµ/8, kmax is the maximum

frequency andQ controls the spacing between kernels in thefrequency domain. In this paper,σ = 2π, kmax = π/2 andQ =

√2. The Gabor kernels are all self-similar in which

they can be generated from one filter, the mother wavelet, by

Page 2: A Sub-Micro Pattern Analysis for Local Rotation, Gray-Scale Transformation and Gaussian Noise Invariant Texture Descriptors

scaling and rotation with varying the wave vector~kµ,ν . TheGabor wavelet representation of an image is the convolutionof the image with a family of Gabor kernels

Oµ,ν(~x) = f(~x) ∗Wµ,ν(~ξ, ~x) = mµ,ν(~x) · e[iφµ,ν(~x)], (3)

where∗ denotes the convolution operator,m is the magni-tude,φ is the phase. By convolving an image with the Ga-bor wavelet at different orientationµ and scaleν, the Gabortexture information is given by

Y(~x) =∑

ν∈{0,...,2}

µ∈{1,...,8}mµ,ν(~x) · ωµ,ν , (4)

whereωµ,ν = 1/∑

∥Wµ,ν(~ξ, ~x)

∥is the total magnitude of

the Gabor wavelet atµ andν.

2.2 A Sub-Micro Pattern Rotation Invari-ant Encoding Operator

In general, a 2-D isotropic Gaussian function is defined

asGσ(~ξ, ~x) = 1√2πσ

e[−‖~ξ−~x‖ / 2σ2], whereσ is a standarddeviation of the associated probability distribution. Thedif-ference of offset Gaussian (DooG) is used here to estimatethe changes in different direction and can be defined as [6].

DooGσ,d(~ξ, ~x) = Gσ(~ξ, ~x) −Gσ((ξ1, ξ2 + d), ~x)

=1√2πσ

e[−[(ξ1−x1)2+(ξ2−x2)2]

2σ2 ]

− 1√2πσ

e[−[(ξ1−x1)2+((ξ2−x2)2+d)]

2σ2 ],

(5)

whered is the offset between the centers of the two Gaus-sian kernels. Formally, a family of the DooG functionsalong the different orientationsθ can be generated as

DooGσ,d,θ(~ξ, ~x) = Gσ(~ξ′, ~x′)−Gσ((ξ′1, ξ′2 + d), ~x′), (6)

whereξ′1 = ξ1 cos θ+ξ2 sin θ andξ′2 = −ξ1 sin θ+ξ2 cos θ

with ~x′ defined similarly. It should be noted that DooGis very similar to the first derivative of Gaussian function(GD) in the sense that they measure the differences at a localneighborhood between the positive and negative areas. GDmeasures the differences in local changes such as edge, i.e.the magnitude is high when GD is on the edge. In DooG,however, the distance between the positive and negative ar-eas can be adjusted by varying parameterd. Hence, DooGis useful in which it can be used to measure the differences

in a more farther away such as the differences between twoobjects or textures. Therefore, GD may be appropriate, forexample, for an edge detection while a more useful DooGcan be used to measure the texture differences. Let(σ, d, θ)be the triple parameters for texture descriptor. The DooGcoding function is defined by

ψσ,d,θ(~x) =

∫ ∞

−∞

∫ ∞

−∞Y(~x)DooGσ,d,θ(~ξ, ~x) d~ξ. (7)

ψ measures the texture variations around the center pos-itive Gaussian. Figure 1 illustrates the DooG coding whereσ, d andθ are varied. In Figure 1(a), 8 codings forθ = 45◦

are given while in Figure 1(c), for example, 24 codings aregiven forθ = 15◦. ψ gives the differences as the positive ornegative values, therefore, we define theζ function as

ζ(z) =

{

1 if z ≥ 0;0 if z < 0.

(8)

ζ encodes the sign of the differences as 0 or 1. Conse-quently, the texture coding for each pixel can be written as

C(~x) = {c1, c2, . . . , cn}, (9)

with

ci = ζ(ψσ,d,θi(~x)), (10)

whereθi is a specified orientation of the DooG, e.g.θi =0◦, 15◦, . . . , 345◦ for θ = 15◦, andn = 360

θ .

(b) (c)(a)

d

Negative Gaussian

Positive Gaussian

�θ

C1

C2

C3

C4

C5

C6

C7

C8

Figure 1. The DooG with different values ofparameters. (a) the DooG with θ = 45◦ (b) θ =30◦ and (c) θ = 15◦.

It is known that a pixel in an image can be encoded asa micro pattern representation [8, 7, 10]. In this paper, wepropose a sub-mirco pattern analysis for rotation invarianttexture descriptor in which a more discriminative informa-tion should be achieved. In addition, the unique number oflocal textures must not be changed with respect to rotation.Figure 1 (a) shows an example of the pattern used to en-code the DooG withθ = 45◦. We start the encoding fromc1 to cn wheren is the number of texture bit codings. Thesub-mirco pattern encoding operator can be formulated as

Page 3: A Sub-Micro Pattern Analysis for Local Rotation, Gray-Scale Transformation and Gaussian Noise Invariant Texture Descriptors

Ξ =

n∑

i=1

[(αci − (ci · ci−1 · ci+1)) + |ci − ci+1| · ω1]

+∣

∣ci − (ci+ n2 −1 · ci+ n

2 +1)∣

∣ · ω2

+

n/2∑

i=1

∣ci − ci+ n2

∣ · ω3, (11)

whereα andωi are constant values defined by user to deter-mine the number of unique values,|ci − ci+1| is the succes-sive absolute different operator,

∣ci − (ci+ n2 −1 · ci+ n

2 +1)∣

is the symmetric Y structural absolute different operator and∣

∣ci − ci+ n2

∣ is the opposite absolute different operator. Wecall this the sub-micro pattern (SMP) analysis. The Y struc-ture is shown, for example, in Figure 2 (tag B4). Let usdefine byς1 = i − 1, ς2 = i + 1, ς3 = i + n

2 − 1, andς4 = i + n

2 + 1 the indices used in encoding. Ifς1 < 0then ς1 = n − 1, if ς2 ≥ n then ς2 = 0, if ς3 ≥ n thenς3 = ς3 mod n and if ς4 ≥ n thenς4 = ς4 mod n. Theoperatorci − (ci · ci−1 · ci+1) in equation (11) indicates thedifference between the current positionci and that of themultiplication ofci with ci−1 andci+1. We call this the selfderivative. Let us define byχ = αci − (ci · ci−1 · ci+1)the self derivative encoding operator, its properties are asfollows:

• If ci = 0 thenχ = 0,

• If ci = ci−1 = ci+1 = 1 thenχ = α− 1,

• If ci = 1 andci−1 or ci+1 is zero thenχ = α.

The patterns for the current bit codingci are shown inTable 1. The operator|ci − ci+1| is the successive differ-ence used to measure the variations in the micro features.Based on our knowledge, the variations in the micro featureare useful information and, hence implied us that, they mustbe used to measure the pattern alternation [5]. The opera-tors

∣ci − ci+ n2

∣ and∣

∣ci − (ci+ n2 −1 · ci+ n

2 +1)∣

∣ measure thesub-micro structure in the texture features and help us dis-criminating the similar structure as shown, for example, inFigure 2 (B51 and C8).

Figure 2 shows the bit coding for the possible micro pat-terns in texture descriptor. The tag B5 indicates the crossing+, A4 corner, A1 flat area, A9 dot, B1 thin line, C9 thickline and A6 line end. Therefore, the SMP can be used, forexample, as the rotation invariant interesting point detec-tion. It can be seen that, in the even column, the uniquevalue for each rotated version of the micro feature is un-changed. Hence, our proposed encoding method is thegray scale and rotation invariant sub-micro feature encod-ing which is robust against the Gaussian noise. In addition,our proposed method is rotation invariant without perform-ing the circular bit-wise right shift on then bit as the LBPdoes [8].

bit codings(ci−1, ci, ci+1) and(ci+ n

2 −1, ci, ci+ n2 +1) χ Y structure

000 0 0001 0 0010 α 1011 α 1100 0 0101 0 1110 α 1111 α− 1 0

Table 1. The encodings of the self derivativeand the Y structural operators.

3 Classification

Our proposed encoding method is local rotation invari-ant, i.e. the descriptor for each pixel is not changed whenthe texture image is rotated, however, the global texture isrotated with respect to the rotation degree. We now need aclassification method for identifying the original image andthe distorted one. Figure 3 (a) and (b) show our texture de-scriptor for the original and rotated images.

Let us assume that the texture image is subject to rota-tion. We can see that, the image remains the same but it isviewed from a linearly distorted coordinate systemC2 withrespect to the original coordinate systemC1. If we knownthe rotation angleφ of an image in coordinate systemC2,the linet1 andt2, for coordinate systemC1 andC2 respec-tively, are equivalent by whicht2 is rotated by−φ. Let usdefine byΛ the set of all scanning lines in an image with alldirections. The Trace transform is a functionG defined onΛ with the help of trace functionalT along a tracing linet.For a lineL(C1;φ, p, t) in coordinate systemC1, the Tracetransform is defined as

G(F ;C1;φ, p) = T (F (C1;φ, p, t)), (12)

whereF (C1;φ, p, t) is the values of the image, e.g. the im-age from SMP, along the specified linet. The result is a 2-Dimage with parametersφ andp which can be represented asanother image defined onΛ. It is known that the rotated linein image space with angleφ is equivalent to the Trace trans-form with shiftingφ in the Trace transform space. Hence,the Trace transform converts the rotation problem to the cir-cular shift one. The Trace functional for this paper is de-scribed as [9]

T (f(t)) =

[∫ x

0

|F{f(t)}|u dt]v

, (13)

whereu andv are the parameters of the trace functional.Fdenotes the discrete Fourier transform, withu = 4, v = 1/u

Page 4: A Sub-Micro Pattern Analysis for Local Rotation, Gray-Scale Transformation and Gaussian Noise Invariant Texture Descriptors

andx = ‖t‖ /2 where‖t‖ is the size of a tracing line. Fig-ure 3 (c) shows the results from the Trace transform wherethe rotated image is circular shifting in the Trace transformspace. Hence, the effect of rotated image is along the vari-able φ. Let us define byφ, p where 1 ≤ φ ≤ Φ and1 ≤ p ≤ P the parameters in the Trace transform. Wecalculate the circular shift invariant features as

Ψ(p) =Φ

φ=1

(G(φ, p) − µp)2, (14)

whereµp is the mean ofG(φµ, p) with 1 ≤ φµ ≤ Φ. Fi-nally, the features for the classification algorithm is

F = {Ψ(1),Ψ(2), . . . ,Ψ(P )} . (15)

The result from equation (15) is shift invariant as shownin Figure 3 (d). It is clear that the original and rotatedversions of the texture image become the identical featurewhen applying the SMP, the Trace transform and, finally,the shift invariant feature. Hence, this helps us classifyingthe texture image more correctly. In our approach, we em-ploy thek-nearest neighbor classifier to classify each shiftinvariant feature in equation (15) into an appropriate class.The texture feature is classified by a majority vote of itsneighbors in which it being assigned to the class most com-mon amongst itsk nearest neighbors. The Euclidean dis-tance is used as the distance metric. The training phase ofthek nearest neighbor algorithm consists of storing the fea-ture vectors and the assigned class labels. In the classifica-tion phase, the unknown test sample is represented as a vec-tor in the feature space. The euclidean distance between thetest sample and all features in the training set are computedwith selectedk closest samples. Hence, the test sample isassigned to the class of its nearest neighbor.

4 Experimental Results

We demonstrated the efficiency of our approach usingthe publicly Brodatz1 texture database [1]. Each texture im-age was assigned as a class in classification process. Wesubsampling all images to the size420 × 420 for efficiencyof the algorithm and used in all of the experiments. Fig-ure 4 showed the examples of the proposed method withseveral texture images. Figures 4 (a) and (b) were theoriginal and the Gabor wavelet texture images. Figures 4(c) and (d) were the corresponding SMP and rotated ver-sion. It should be noted that the micro features, enhancedby the SMP, of the original and rotated versions still re-main the same regardless of the degree of rotation. In the

1The Brodatz texture database is publicly available. It can be down-loaded free of charge at http://www.ux.uis.no/∼tranden/brodatz.html.

experiments, we need to check the robustness of the pro-posed method. We performed many systematic experimentsusing different rotation angles and levels of the additiveGaussian noise. In all experiments, the parameters for theSMP and the Trace transform were setup as follows. TheDooG parameterd was set with proportional to theσ i.e.d = DOOGOFFSET· σ where DOOGOFFSET= 5 isthe offset value for the DooG.σ = 3.0 was used in allexperiments. The parameters for encoding operator wereα = 256

n , ω1 = 1, ω2 = 5, andω3 = 3, respectively. TheTrace transform parameters were as follows:p was sam-pling with 210 values in the range[0,

√4202 + 4202] and

parameterφ was rotated with1◦ of rotation to get 360 val-ues in the range[0◦, 359◦]. k = 5 for k-nearest neighbors.

In the experiments on the rotation problem, the originaltexture images were used to create a training set (111 tex-ture images). The test set was created by rotating the tex-ture images with several degree of rotations (15◦, 20◦, 30◦,45◦, 60◦, 70◦, 90◦, 105◦, 120◦, 135◦ and150◦). Hence,1,221 (111 × 11) rotated texture images were created andused them as a test set (approximately8.33% for trainingand91.67% for testing). Table 2 presented the classifica-tion rates using the two methods, LBP and SMP. The aver-age of the maximum classification accuracy was97.68% forSMP and88.32% for LBP. Please note that a similar resultof the LBP classification rate has been reported in [4]. Itis clear that our proposed method is not sensitive to the ro-tated texture images as long as the bit coding patterns werenot changed. Hence, our proposed method outperformedthe LBP with respect to the rotation problem. When usinguniform LBP,LBP riu2

P,R , its disadvantage is that it discardedall nonuniform patterns such as patterns B1 to B9 and C1 toC9 in Figure 2. These micro features were very significancefor texture analysis [5]. The more the micro features can berepresented, the more the textures can be discriminated. Interms of micro feature texture descriptor, the SMP affordedmore advantages over the LBP method.

To evaluate the robustness of the proposed method tothe additive Gaussian noise, we compared the classifica-tion rates with several levels of noise. The training textureimages were created with original version. We generatedthe additive Gaussian noise to the texture images with zeromean and standard deviation varying from 2 to 30. Hence,111 texture images were used for training and 1,221 noisytexture images were used for testing. Table 3 showed the re-sults of experiments with comparing the texture images thathave been corrupted by additive Gaussian noise. The max-imum accuracy of our SMP method was92.86% comparedto 75.8% for GM+LBP and71.94% for LBP. LBP methodis robust to gray scale transformation which can be seen asa linear transformation, i.e. the texture image was variedfor all pixels with the same constant. For additive Gaussiannoise, however, the texture image was changed with differ-

Page 5: A Sub-Micro Pattern Analysis for Local Rotation, Gray-Scale Transformation and Gaussian Noise Invariant Texture Descriptors

Testing Rotation AngleOperator Parameters 15

20◦

30◦

45◦

60◦

70◦

90◦

105◦

120◦

135◦

150◦ Avg

LBP riu2

P,R [8]P = 8, R = 1 50.2 51.1 59.3 55.4 52.5 51.8 52.0 53.1 51.9 52.4 55.3 53.18P = 16, R = 2 81.5 81.7 80.2 82.1 79.9 80.7 81.0 81.7 79.9 81.2 80.7 80.96P = 24, R = 3 88.6 87.3 88.2 87.6 89.0 88.8 87.5 87.9 88.2 89.4 89.1 88.32

SMPθ = 45

◦, n = 8 91.3 90.2 91.5 92.0 91.8 90.9 91.4 91.7 91.6 91.9 91.8 91.46θ = 30

◦, n = 12 92.8 92.7 93.8 92.6 93.9 92.7 93.9 92.8 92.5 93.2 93.1 93.09θ = 15

◦, n = 24 97.4 97.3 97.5 97.8 98.0 96.9 97.7 98.2 97.9 98.0 97.8 97.68

Table 2. Comparison of the classification accuracies (%) for rotated texture image where the trainingis done with rotation 0◦ and test with the other degree.

0

0

0

0

00

00

1

1

1

1

11

11

00

1

0

0

00

00

0

1

0

0

01

00

1

1

0

0

01

00

1

1

0

0

11

00

1

1

0

1

11

00

1

1

0

1

11

10

1

1

1

1

11

10

1

1

0

1

00

00

0

0

0

0

11

10

0

1

0

1

00

00

0

0

0

0

10

01

1

1

1

1

00

00

0

0

0

0

11

11

0

1

0

1

10

10

0

1

1

0

10

01

1

1

1

1

10

10

1

0

0

1

11

11

1

1

1

0

10

10

1

0

0

1

01

11

0

1

0

0

10

10

1

1

0

0

00

10

52

10

21

66

23

02

88

28

62

69

24

8

18

0

18

0

20

5

20

5

25

6

25

6

14

1

14

1

27

4

27

4

18

2

18

2

98

98

0

0

0

0

00

00

1

1

1

1

11

11

0

0

1

0

00

00

1

0

0

0

10

00

0

0

1

1

00

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1

1

0

01

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10

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0

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1

11

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1

1

1

1

11

01

05

21

02

16

62

30

28

82

86

26

92

48

0

1

0

0

11

11

1

1

1

1

00

10

27

3

27

3

1

0

1

0

10

10

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0

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01

10

A1

A2

A3

A4

A5

A6

A7

A8

A9

B1

B2

B3

B4

B5

B6

B7

B8

B9

C1

C2

C3

C4

C5

C6

C7

C8

C9

A1

1A

21

A3

1A

41

A5

1A

61

A7

1A

81

A9

1

B1

1B

21

B3

1B

41

B5

1B

61

B7

1B

81

B9

1

C1

1C

21

C3

1C

41

C5

1C

61

C7

1C

81

C9

1

0

1

0

1

10

00

0

1

0

1

11

11

1

1

0

1

10

00

1

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1

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10

11

1

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1

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11

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1

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1

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1

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1

00

10

0

0

0

0

01

01

1

0

1

1

00

01

21

3

14

82

27

10

42

41

19

21

69

14

82

27

10

42

41

19

21

69

11

9

11

9

20

0

20

0

28

4

28

4

21

3

Figure 2. The examples of rotation invariantencoding operator using equation (11) whereα = 256

n , ω1 = 1, ω2 = 5 and ω3 = 3. The darkcircle stands for the bit values of 1 and brightfor 0. The odd column shows the examples ofthe possible patterns and the correspondingrotation patterns are shown in the even col-umn. For each pattern, the number inside thepattern is its unique value.

ent positive/negative values based on Gaussian distribution,hence, degrades the performance of the LBP vastly. Al-though, for GM+LBP, the Gaussian smoothing was appliedbefore encoding process. The recognition accuracy was in-creased with factor of3.86%. Instead of using the pixelvalues directly, the SMP differentiates the pixels in the cen-ter positive Gaussian and the neighbor rotated negative one.Therefore it can be used to encode the micro features that isrobust against the additive Gaussian noise.

5. Conclusions

We have presented a new rotation invariant local texturedescriptor based on the DooG and a sub-micro pattern anal-ysis. The textures were first characterized by exploitingthe Gabor wavelet. The DooG was employed to measurethe center surround difference. We also proposed a newlocal rotation invariant encoding operator based on a sub-micro pattern analysis. We applied the Trace transform onthe SMP image to get a 2D image and then computed thecircular shift invariant features in the Trace transform. A

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

Figure 3. The features for classification. (a)the original and rotated images (b) the corre-sponding rotation invariant SMP (c) the Tracetransform and (d) the shift invariant features.

Page 6: A Sub-Micro Pattern Analysis for Local Rotation, Gray-Scale Transformation and Gaussian Noise Invariant Texture Descriptors

Testing Standard DeviationOperator Parameters 2 5 10 15 20 25 30 Avg

LBP riu2

P,R [8]P = 8, R = 1 48.2 46.5 42.3 38.5 33.6 26.9 20.5 36.64P = 16, R = 2 77.4 75.9 72.5 68.2 60.1 54.9 49.8 65.54P = 24, R = 3 85.3 84.2 80.9 70.6 67.5 60.9 54.2 71.94

GM+LBP riu2

P,R

P = 8, R = 1 52.1 50.6 46.3 42.59 37.68 31.18 25 40.78P = 16, R = 2 81.1 80 76.7 71.9 64.2 59.7 54.2 69.69P = 24, R = 3 89.1 88 84.6 74.6 71.4 64.5 58.4 75.80

SMPθ = 45

◦, n = 8 90.9 89.2 87.6 85.4 82.2 78.6 72.4 83.76θ = 30

◦, n = 12 91.5 90 88.9 86.2 83.2 80.1 79.8 85.67θ = 15

◦, n = 24 97.2 96.7 95.3 94.2 93.6 87.4 85.6 92.86

Table 3. Comparison of the classification accuracies (%) for additive Gaussian noise. Please notethat GM+LBP riu2

P,R is a process of Gaussian smoothing ( σ = 3) with LBP method.

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

Figure 4. Examples of the SMP. (a) the origi-nal texture image (b) the magnitude of the Ga-bor wavelet (c) the corresponding SMP and(d) rotated SMP.

k-nearest neighbors classifier was employed to classify thetexture patterns. Experimental results have shown that weachieved97.68% for rotation problem and92.86% for ad-ditive Gaussian noise one. Based on the unique value of theSMP, our proposed method can be applied to several appli-

cations such as corner detection, interesting point detection,face detection and face recognition.

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