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Texture Features Analysis Based on GLCM and Law MasksBy. Darshan Venkat and Sharib Ali
Masters in Computer Vision,University of Burgundy, Le Creusot, [email protected], [email protected]
Instructors: Proff. Robert Marti Marly & Jordi Freixenet [email protected], [email protected]
Keywords: GLCM, Laws Masks, texels
Abstract:This report is based on the study of different texture features in images using descriptors like GLCM(Gray Level Co-occurrence Matrix) and Law Masks. GLCM is used to derive various statistical indicators of texture including contrast, correlation, energy and entropy. Evaluation of Law Mask involves determining of the different convolution masks and finding which is best suited for the texture feature identification for different statistical measures like mean, absolute mean and standard deviation. These methods are used for different images having different pixel intensities and the best suited statistical parameter for a given methodology applied is analyzed in this report for a given image. In addition, this report also contains short description on GLCM and Law Masks which has been used for our feature analysis of a texture. Both the graylevel and color images has been considered.
Contents1 Introduction2 Methodologies Used for Texture Analysis
2.1 GLCM 2.2 Law Masks
3 Design and Implementation4 Experiments and Result Analysis5 Computation Analysis6 Conclusion
1. Introduction Image texture defined as the spatial variation in the pixel intensities is a wide research area with many methods. However, we have applied two most distinct and promising descriptors, GLCM and Laws masks. The basic idea behind this was to classify different feature pixels in an image called 'texels'. These periodic property of an image often gives the texture of an image.
2. Methods Used for Texture Analysis:
2.1 Gray-level Co-Occurrence Matrices : One of the defining quality of texture is the spacial distribution of pixel values (Tuceryan and Jain 1993). Statistical indicator have therefore been one of the oldest method to describe texture. The aim of statistical methods of texture analysis is to characterize the stochastic process of spacial distribution of pixel values in an image(He and Wang 1991).
The occurrence of the gray level values can be tabulated as a matrix called gray level co-occurrence matrix. To explain how a GLCM is constructed, lets consider an image P of dimension N x N and G gray levels. The image block used to derive the GLCM is based on the nearest neighborhood cells (Haralick, Dinstein and Shanmugam 1973).In this method we assume that the information about the texture is provided by a matrix of relative frequencies where two neighboring pixels that are separated by a distance 'd' and an angle angle theta occur in a block. The gray value of the two pixels involved being 'i' and 'j' respectively. These matrices are a function of angle and distance between two pixels.
Consider a small block of image I of size 5x5,and having 4 gray levels.
0 2 0 2 00 2 0 2 00 2 0 2 01 1 1 3 11 1 1 3 1
The gray level for the above image clip where d=1 and theta =0,45,90,135 are shown below.I(d=1,theta = 0)
0 1 2 30 0 0 9 01 0 8 0 42 9 0 0 03 0 4 0 0
I(d=1,theta = 90)
0 1 2 30 12 3 0 01 3 8 1 02 0 1 8 13 0 0 1 1
I(d=1,theta = 135)
0 1 2 30 0 1 4 11 1 4 2 12 4 2 0 03 1 2 0 0
I(d=1,theta = 45)
0 1 2 30 0 1 4 11 1 4 1 22 4 1 0 03 1 2 0 0
The Co-occurrence matrix is symmetric in nature. The number of operations required to compute a gray level co- occurrence matrix is directly proportional to the number of pixels and the number of gray levels present in the image. All the information required for characterizing the image texture can be obtained for the GLCM. So different type of texture descriptors can be extracted from the matrix. Different type of texture descriptor is tabulated in the table below.
Descriptor Formula Explanation1 Correlation
Where
A measure of how correlated a pixel is to its neighbor over the entire image. The value ranges from 1 to -1.
2 Contrast A measure of intesity contrast between a pixel and its neighbourhood over the entire image.The value ranges from 0 to
(K=-1)^2
3 Energy The range of energy is between 0 and 1.for a unform image uniformity is 1.
4 Homogeneity Measures the spatial closeness of the distribution of elements in the co- occurrance matrix to the diagonal .The range is between 0 and 1.The maximum is achieved when the co-occurance matrix is a diagonal matrix.
5 Entropy The entropy measures the Randomness of the co-occurrence matrix. The entropy is 0 when all the pixels are 0 and is maximum when all the pixels are equal.
2.2 Laws Masks : Law Masks are a set of convolution masks used for deriving texture indicators by using
a set of gradient operators. These operators are based on combining the result of first and second order derivatives on an image block.(Lam and Li 1995).Laws texture are computed by applying a convolution kernel to a digital image and then performing a nonlinear windowing operation. There are mainly 5 types of masks of size 3x3 and 5x5.These can be used to represent features such as Edge,holes,spots,ripple and level.
Laws texture energy measures are derived form 3 simple vector of length 3.Convolve these three features we can obtain vectors of length 5.
L3(Level) [ 1 2 1]E3(Edge) [-1 0 1]S3(Spot) [-1 2 -1]
L5(level) L3*L3 [1 4 6 4 1]E5(Edge) L3*E3 [-1 -2 0 2 1]S5(spot) L3*S3 [-1 0 2 0 -1]R5(ripple) S3*S3 [1 -4 6 -4 1]W5(Wave) E3*S3 [-1 2 0 -2 1]
The level (L5) vector gives a center weighted local average. Edge (E5) is similar to gradient operator and responds to row or column stepped edges in an image. Spot (S5) is based on the second derivative and is similar to performing Laplacian over a Gaussian. Wave responds to slight changes in pixel intensities in an image and ripple(R5) is used to detect ripples in an image.
Laws convolution masks are derived by multiplying the two vectors while considering one vector as row and other vector as a column vector respectively. A set of such combinations of 3x3 and 5x5 are shown below.-1 4 6 -4 -1 1 -4 6 -4 1 -1 0 2 0 -1-2 -8 -12 -8 -2 -4 16 -24 16 -4 -2 0 4 0 -2 0 0 0 0 0 6 -24 36 -24 6 0 0 0 0 0 2 8 12 8 2 -4 16 -24 16 -4 2 0 -4 0 2 1 4 6 4 1 1 -4 6 -4 1 1 0 -2 0 1
E5L5 R5R5 E5S5
L3L3 1 2 1 2 4 11 2 1
L3E3 -1 0 1-2 0 2-1 0 1
L3S3 -1 2 -1-2 4 -2-1 2 -1
E3L3 -1 -2 -10 0 01 2 1
E3E3 1 0 -10 0 0-1 0 1
E3S3 1 -2 10 0 0-1 2 -1
S3L3 -1 -2 -12 4 2-1 -2 -1
S3E3 1 0 -1-2 0 21 0 -1
S3S3 1 -2 1-2 4 -21 -2 1
Two steps are involved in obtaining the laws of texture descriptors-1)Applying a convolution over a image using the above masks.2)Obtain the statistical measure using the convolution result. We can obtain three statics such as mean ,absolute mean and standard deviation.
3. Design and Implementation
Following steps has been taken for the implementation of the algorithms-
(A)Gray Level Co-occurrence Matrix(for gray level images): output= GrayCooccuranceMatrix(image_test,R,C,offset_value,gap); Features: 1. User is given to enter the offset direction like 0,45,90 or 135. 2. User is given to enter the mask size. 3. It computes all the statistical parameters which we have described in the function. 4. Output comes as an array of outputs in a cell of 1x5.
(B)Gray level Co-occurrence matrix(for color images): colorGLCM(image_test1,offset_value,gap); Features: 1. Calculates all the statistical parameters similar to GrayLevelCoccurence Matrix function used for gray level images but it does this for each channel
2. Finally, both the color texture images and average channel images are shown for each statistical parameter.
(C)Law_Mask(for gray level images): [output_image_mean,output_image_abs_mean,image_std]=Law_Mask(image_test,mask); Features: 1.The user is allowed to input 1D filters type (both 3 size and size 5) are accepted (calculation is made by using the same function so it removes tough computation and lengthy code. 2.The mask is calculates taking the transpose of the first. 3.The function is easy and fast to compute the mean, abs mean and the standard deviation of the input gray level image.
Fig1. GLCM with different Statistical Parameters
(D)Law_Mask(for colored images):
LawMaskColor(image_test1,mask); Features: 1. It calls passes the colored image 'image_test1' and 'mask' as input parameters 2. It determines the Law Mask calling the Law_Mask function above explained for the all the three channels to extract the features. 3. Finally, these features of the texture are represented as a color of texture. 4. Texture features are also shown as by calculating the average of all the channels for different features.
a.
Fig2.(a)Law Masks L5S5 (b)Law Masks L3E3(color channels)
b.
4.Experiments and Results
GLCM Result Analysis We got better results with 'feli.tif' and other images except the 'mosaic8.tif' which showed some satisfactory result with the laws masks. The various images with its output as a texture descriptor using different statistical measures explained above has been listed with their brief explanation.Fig. a. 0degree,mask[11 11],Contrast we have taken computed GLCM in this case for all the R,G→ and B channels and then taken then converted it to gray level image. It is the best result we got with 'feli.tif'. Here, the object is distinctly identified from the background and thus proves to be better image for the purpose of segmentation.Fig. b. 135degree,mask[5 5],Energy This clearly separates the background from the objects but→ some part of the hand will be merged in the background so we will be losing information in this case. However, the texture identification is good enough.Fig. c. 0degree,d=1,mask[7 7],Correlation → We can distinguish the texture here as well. But, the idea behind putting this image is to make an approach towards edge detection and then making the segmentation. So, this correlation feature analysis can also be result promising statistical measure for GLCM.Fig. d,e. 0degree,mask[7 7],Entropy This worked well but we expected more dark black for the→ hand and some distinct white for the rubber. But, this was better than other experimental results though we tried randomly with very few for 'hand2.tif'.(e) better for segmentation. Its the entropy calculated for each channel.Fig.f. 0Degrees, mask[15 15], Correlation → This was the most difficult image for us. However, we thought the vaiation in contrast and texture marking a clear edge makes some sense of identification. However, we are not so sure of this result and we think that laws masks does some justice to this texture classification.
a
b.
c.
d.
Fig.5 Texture Analysis for GLCM Laws Masks: Below we have analyzed with those laws masks which shows best, better or the worst results. The remaining masks has been discarded and not explained as it is almost impossible to show all and explain all of them. Those masks which are discarded is because they produce some intermediate results.
The best result for 'feli.tif' was with the masks L3 and E3 which is shown in green. The best was seen when it was calculated for all the pixels in each channel and the absolute mean so calculated for then after convolution was averaged to get the image. However, nearly similar result was obtained with direct computation of the absolute mean from the gray image but previous was more better. The image with L5E5 was somewhat blurred so we have not placed here. The image for standard deviation showed some distict texture feature in some cases like one best we got was with R5E5 in fig.c. But, the features were totally degraded in the case of mean computations with this image. We have highlighted the best result in 'green rectangle'.
a.
b.
c.
e. f.
Fig.3 Texture Analysis with 'Feli.tif'
a. L3E3 (abs Mean for Average Channel) -Bestb. L3E3(abs Mean) -Betterc. R5E5(std deviation) -Better for Standard deviation(Texture distinct)d. Mean with E5S5 -Worste. E3L3 with abs mean (for color Texture) -Not much Clear(doesn't make sense)
Fig.4 Texture Analysis with 'hand2.tif'
d. e.
a.
c.
d.
b.
a. L5R5 (Mean- RGB channels used) → Shows distinct difference in textures (smoothness of hand and rubber clearly outlines the rough
backgound) b. E5E5(standard deviation) → identifies the texture of hand, rubber and background clearlyc. R5R5(standard deviation) → it has almost similar feature identification but its blurredd..E3E3(abs mean) → Hand and the rubber is almost mingled in one so its the worse among all.
Fig.5 Texture Analysis with 'pingpong2.tif'
a. S5E5(Standard Deviation) → We can clearly distinguish between the rough background and the smooth tennis bat but ball cant be seen which is its defect. We kept this image because it can easily detect the curvy lines of the board however the image is blurred so its not better for texture feature manipulation.
b. L3E3(abs mean) → This cannot properly give clear remark on particular features because surfaces are seen to be uniform so its not better.
c. L5S5(abs mean) → It gives better result with clear rough background and other plain objects are given similar shade. In addition, the ball has some reflectance which makes it distinct. So,this image can also be considered as a better image which gives the texture features classification.
d. L3L3(Standard deviation) → This looks more like edge detection derivatives like 'sobel'. Actual texture of the image is not clear.
c.
c.
a. b.
d.
With the mosaic, we didn't get satisfactory result with the law masks. However, fig4a. gives some sense of texture feature.
5. Computation Analysis The key factor of running the program with the 1.8GHz processor, core 2 duo, 1GB RAM and using MATLAB as the working platform gave satisfactory running speed of less than 3 secs for all the images for Laws Masks. However, it took nearly 4-6 minutes to get an output for GLCM with the images. So, looking the cost of computation laws masks proves to have an upper hand over GLCM.
Fig. Table for Computational Time for Texture DesriptorsImage “Pingpong2.tif” → Size:228x344x3
a. b.
d.c.
Fig.4 Texture Analysis with 'mosaic8.tif'
a. L3L3(Standard deviation)b.S3E3(abs. Mean)c. L5L5(Std. Deviation-color)d. R5L5(mean-RGB)
GLCMImage mask direction time(in secs)
PingPong2(gray) [3 3] 0 180,98PingPong2(color) [3 3] 0 587,9PingPong2(gray) [5 5] 45 214PingPong2(color) [5 5] 45 642
Laws MasksImage mask time(in secs)
PingPong(gray) [3 3] 0.22 ' ' [3 3] 0.73
PingPong(color) [5 5] 0.45 ' ' [5 5] 0.8
6. Conclusion The key idea behind getting a good understanding of the texture analysis was pretty healthy and good start towards image segmentation and pattern recognition. The texture plays a vital role in the abstraction of key features of an image and makes the segmentation part more robust with this classification. We were given to study different images for the texture analysis using descriptors like GLCM and Laws masks. Not all, but few better classified the image on the basis of their texture. GLCM gave more better results with its statistical parameters energy and entropy when taken for different orientations and distances. We conclude that the mask size with [3 3] gave better result because as we increased the mask size we got some blurred which destroyed the actual texture of the image. With Laws Masks, it was very efficient but all the laws masks didn't showed good result. So, the selection of the mask was the crucial thing in this. Overall, it gave some good results for statistical parameters absolute mean and standard deviation.
References1. Joan Marti, Jordi Freixenet Lecture Slides on “Texture Characterization”2. Christian Mata Miquel, “MSc. Thesis VIBOT Texture Descriptors applied to Digital Mammography”
3. A.N.Tassetti, E.S.Malinverni,M. Hahn,”Texture Analysis to improve supervised Classification in Ikonos Imagery”4. A. Karahaliou, MSC, S Skiadopoulos, PHD, L Boniatis, MSC, P Sakellaropoulos, PHD, E Likaki, MD, G Panayiotakis, PHD and L Costaridou, PHD “Texture analysis of tissue surrounding microcalcifications on mammograms for breast cancer diagnosis”
