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Feature analysis for scaled and rotated texture segmentation
Computers ind. Engng Vol. 33, Nos 1-2, pp. 445-448, 1997 0 1997 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0360°8352/97 $17.00 + 0.00
Pergamon PIh S0360-8352(97)00133-2
FEATURE ANALYSIS FOR SCALED AND ROTATED TEXTURE SEGMENTATION V. Manian and R . V~isquez Department of Electrical and Computer Engineering University of Puerto Rico, Mayagnez, PR 00681-5000
ABSTRACT In this paper a class of spatial and spectral features obtained from the most popular methods for texture classification are analyzed for their ability to segment scaled and rotated textures. The features are defined from: the co-occurrence matrix using spatial-gray level dependence method, the gray level run length method, the spatial gray level difference method, the Fourier spectrum and the Gabor transform. Several experimental results are presented and discussed. The Gabor features and the co-occurrence matrix features give best results followed by the pixel-based, Fourier and spatial gray level difference features. The run length features perform poorly. The feature analysis shows that the angle at which the second order statistical features such as the co-occurrence features and gray level difference features are obtained, control the performance of the features. The Gabor features gives best results when the filter is tuned well to the orientation of the textured images. The features can be used for segmenting images obtained at different resolutions and transformations by augmenting the statistical invariance of the features to scale and rotation. Contrary to earlier conclusions, the analysis of these feature sets for scaled and rotated texture segmentation proves that some of the features can very well be applied to practical situations and further enhanced for better performance. © 1997 Elsevier Science Ltd
KEYWORDS Invariant texture segmentation, co-occurrence method, Gabor, Fourier and statistical methods
INTRODUCTION
Texture segmentation is the process by which a method is used to extract features from a set of texture classes. Training samples are used to train a classifier to recognize other samples (test samples) of the texture images and label them as belonging to a particular class. Most work in texture classification has been done without much attention to the recognition of scaled and rotated textures in spite of the fact that many practical applications require scale and rotation invariant classification methods. Tan (1994) gives a good summary of the work done in texture classification. Model based methods (Kashyap and Khotanzaed, 1986), mental transformation approaches (Leung and Peterson, 1992), multi-channel methods, random field models (Wu and Yoshida, 1995), and methods using tuned masks (You and Cohen, 1993), have been proposed for invariant texture segmentation. But, most of the prevalent features have been used in classifications where the test samples have the same scale and orientation as the original training texture sample. While many new methods have been proposed, the existing methods have not been studied or compared clearly for scaled and rotated texture segmentation. This
445
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21st International Conference on Computers and Industrial Engineering
paper is the first effort to provide an extensive study of the existing texture features for their invariance property.
FEATURE ANALYSIS FRAMEWORK The textures from the Brodatz (1966) album are first scaled and rotated. The textured mosaics are constructed with these transformed textured images. A classifier is trained with features extracted from original texture samples from each class of texture. These original textures are with scale 1 and 0 ° orientation (i.e., without any transformation). Six feature sets with spatial and spatial/frequency based features are used and each of them are described below. A classifier is then used to segment the scaled and rotated textured images by using each of the six feature sets. Pixel based first-order statistical features are used. The features are gray level mean, variance and standard deviation. The other features that are tested are the average deviations of: pixel gradient magnitude, residual, horizontal directional residual and vertical directional residual. The features entropy, correlation, contrast, angular second moment, sum squares, sum average, sum variance, sum entropy, difference variance, difference entropy, inverse difference moment and information measures of correlation defined (Haralick et al., 1973) using the second-order spatial gray level dependence method (SGLDM) are used for segmenting the scaled and rotated textured image. The features used from the spatial gray level difference method (SGDM) (Weska et al., 1976) are contrast, angular second moment, entropy and mean. The features obtained from the higher order statistical method called the spatial gray level run length method (SGLRLM) is also used for analysis (Weska et al., 1976). The features include long runs emphasis, short runs emphasis, run length distribution, gray level distribution and run percentage. Features obtained from the real-valued Fourier power spectrum include ring and wedge-shaped features, maximum magnitude, average magnitude, energy and variance of the magnitude. Gabor coefficients of the texture samples are computed using the auxiliary function to the Gaussian window function. The 2-D auxiliary window function are assumed to be separable and are computed as the products of the 1-D sequences (Wang et al., 1994). Gabor features include the average absolute deviation which measures the energy of the filtered image, the mean and variance of the filtered image.
EXPERIMENTAL RESULTS Three sets of scaled and rotated textured mosaics are used for the experiment. Mosaic 1 is shown in Fig. l(a) which has textures D l l , D103, D55 and D105 (Brodatz, 1966) at a scale of 0.33 and rotated by an angle of 90 °, (b) mosaic 2 has textures D93, D28, D101 and D20 at a scale of 2 and orientation of 120 °, (c) mosaic 3 has textures D6, D19, D36 and D68 at a scale of 0.5 and orientation of 30 °. Features extracted from samples of the original texture with a scale of 1 and 0 ° orientation are used to train a Mahalanobis distance classifier. A moving window of size 16 x 16 pixels is used to extract features from the transformed texture mosaics. The classifier computes the distance between the features for each window and that of the texture classes and assigns the unknown sample to the texture class with the shortest distance. A gray color is then assigned to the sample as per the class it is being recognized and the texture mosaic is segmented. An example segmented image using the Gabor features and SGLDM features for mosaic 1 are shown in Fig. 2 (a) and (b) respectively. The classification results for each of the six feature set is shown in Table 1. As seen from the Table the Gabor features, the SGLDM features and the pixel based features have performed well compared to the others. The next performance is shown by Fourier features followed by the SGDM features and finally the SGLRLM features.
21st International Conference on Computers and Industrial Engineering
447
m mm (a) Mosaic 1
(b) Mosaic 2 (c) Mosaic 3 Fig. 1. Original texture mosaics
Fig. 2. (a) and (b). Segmented images
Table 1. Classification results for each feature set Feature Sets
Gabor features SGLDM features Pixel based features FPS features SGDM features SGLRLM features
Percentage of Correct Classifications for Mosaic 1 Mosaic 2 Mosaic 3 100 89.06 90.63 78.12 79.69 67.19
75.00 75.00 75.00 68.75 71.88 56.25
100 84.38 75.00 76.56 70.31 73.44
DISCUSSION The SGLRLM features performed poorly and this is justifiable since as per previous results by Weszka et al., (1976), the features did not give good results even for the textures with the same scale and orientation as the original textures. Only the short runs emphasis and run percentage gave better results than other features. The SGDM features obtained at angles of 135 ° and 45 ° performed better than those at 0 ° and 90 °. Best results for the Fourier method were obtained from the maximum magnitude, average magnitude and energy of magnitude which are statistical features defined on the power spectrum. The gray-level statistics of mean, variance and average residual showed good results while the average horizontal and average vertical residual degraded the performance. SGLDM feature at angles of 0 ° and 90 ° performs poorly. Best features were contrast, correlation, homogeneity, entropy and inverse difference moment computed at angles of 45 ° and 135 ° at a distance of 1. The best features in Gabor method were the average of the filtered image, variance and average residual of the coefficients. In this case, the length of the Gabor feature vector is only 3 compared to that of 256 in (Leung and Peterson, 1992). The statistical properties of the features plays significant role in the performance. Also, the
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21st International Conference on Computers and Industrial Engineering
orientation at which the second order statistics are obtained affects the performance of the SGLDM and SGDM methods.
CONCLUSIONS As seen from the results, several of the features used perform well for invariant texture segmentation and the statistical properties of the features, are important in the discrimination of transformed textures. As opposed to the current belief (You and Cohen, 1993) the existing features can be used for invariant texture classification and their performance can be considerably enhanced by statistically adding invariant characteristics and transformation (scale and orientation) selectivity to the features. This work presents useful results which have not been provided so far for applying the existing features for scaled and rotated texture segmentation.
ACKNOWLEDGMENT This work was partially supported by NSF grant CDA 9417659, NASA grant NCCW-0088 and the Department of Electrical and Computer Engineering at the University of Puerto Rico at Mayagiiez.
REFERENCES Tan, T. N. (1994). Scale and rotation invariant texture classification. Proceedings oflEE Colloquium on texture classification: theory and applications, 3/1-3/3. Kashyap, R. L. and A. Khotanzaed (1986). A model-based method for rotation-invariant texture classification," IEEE trans. PAMI, 8, 472-481. Leung, M. M. and A. M. Peterson (1992). Scale and rotation invariant texture classification. Proc. 2~ h Asilomar Conf. Signals, Systems and Computers. 1, 461-465. Wu, Y. and Y. Yoshida (1995). An efficient method for rotation and scaling invariant texture classification. Proceedings of lCASSP'95, 4, 2519-2522. You, J. and H. A. Cohen (1993). Classification and segmentation of rotated and scaled textured images using texture tuned masks, Pattern Recognition, 26, 245-258. Brodatz, P (1966). Textures-A photographic album for artists and designers, Dover, New York. Haralick, R. M., K. Shanmugam and I. Distein (1973). Texture features for image classification, IEEE trans, systems, man and cybernetics, SMC-3, 610-621. Weszka, J.S., C. R. Dyer and A. Rosenfeld (1976). A comparative study of texture measures for terrain classification, IEEE trans, systems, man and cybernetics, SMC-6, 269-285. Wang K., C. T. Chen and W. C. Lin (1994). An efficient algorithm to compute the complete set of discrete Gabor coefficients, IEEE trans, image processing, 3, 87-92.
Pergamon PIh S0360-8352(97)00133-2
FEATURE ANALYSIS FOR SCALED AND ROTATED TEXTURE SEGMENTATION V. Manian and R . V~isquez Department of Electrical and Computer Engineering University of Puerto Rico, Mayagnez, PR 00681-5000
ABSTRACT In this paper a class of spatial and spectral features obtained from the most popular methods for texture classification are analyzed for their ability to segment scaled and rotated textures. The features are defined from: the co-occurrence matrix using spatial-gray level dependence method, the gray level run length method, the spatial gray level difference method, the Fourier spectrum and the Gabor transform. Several experimental results are presented and discussed. The Gabor features and the co-occurrence matrix features give best results followed by the pixel-based, Fourier and spatial gray level difference features. The run length features perform poorly. The feature analysis shows that the angle at which the second order statistical features such as the co-occurrence features and gray level difference features are obtained, control the performance of the features. The Gabor features gives best results when the filter is tuned well to the orientation of the textured images. The features can be used for segmenting images obtained at different resolutions and transformations by augmenting the statistical invariance of the features to scale and rotation. Contrary to earlier conclusions, the analysis of these feature sets for scaled and rotated texture segmentation proves that some of the features can very well be applied to practical situations and further enhanced for better performance. © 1997 Elsevier Science Ltd
KEYWORDS Invariant texture segmentation, co-occurrence method, Gabor, Fourier and statistical methods
INTRODUCTION
Texture segmentation is the process by which a method is used to extract features from a set of texture classes. Training samples are used to train a classifier to recognize other samples (test samples) of the texture images and label them as belonging to a particular class. Most work in texture classification has been done without much attention to the recognition of scaled and rotated textures in spite of the fact that many practical applications require scale and rotation invariant classification methods. Tan (1994) gives a good summary of the work done in texture classification. Model based methods (Kashyap and Khotanzaed, 1986), mental transformation approaches (Leung and Peterson, 1992), multi-channel methods, random field models (Wu and Yoshida, 1995), and methods using tuned masks (You and Cohen, 1993), have been proposed for invariant texture segmentation. But, most of the prevalent features have been used in classifications where the test samples have the same scale and orientation as the original training texture sample. While many new methods have been proposed, the existing methods have not been studied or compared clearly for scaled and rotated texture segmentation. This
445
446
21st International Conference on Computers and Industrial Engineering
paper is the first effort to provide an extensive study of the existing texture features for their invariance property.
FEATURE ANALYSIS FRAMEWORK The textures from the Brodatz (1966) album are first scaled and rotated. The textured mosaics are constructed with these transformed textured images. A classifier is trained with features extracted from original texture samples from each class of texture. These original textures are with scale 1 and 0 ° orientation (i.e., without any transformation). Six feature sets with spatial and spatial/frequency based features are used and each of them are described below. A classifier is then used to segment the scaled and rotated textured images by using each of the six feature sets. Pixel based first-order statistical features are used. The features are gray level mean, variance and standard deviation. The other features that are tested are the average deviations of: pixel gradient magnitude, residual, horizontal directional residual and vertical directional residual. The features entropy, correlation, contrast, angular second moment, sum squares, sum average, sum variance, sum entropy, difference variance, difference entropy, inverse difference moment and information measures of correlation defined (Haralick et al., 1973) using the second-order spatial gray level dependence method (SGLDM) are used for segmenting the scaled and rotated textured image. The features used from the spatial gray level difference method (SGDM) (Weska et al., 1976) are contrast, angular second moment, entropy and mean. The features obtained from the higher order statistical method called the spatial gray level run length method (SGLRLM) is also used for analysis (Weska et al., 1976). The features include long runs emphasis, short runs emphasis, run length distribution, gray level distribution and run percentage. Features obtained from the real-valued Fourier power spectrum include ring and wedge-shaped features, maximum magnitude, average magnitude, energy and variance of the magnitude. Gabor coefficients of the texture samples are computed using the auxiliary function to the Gaussian window function. The 2-D auxiliary window function are assumed to be separable and are computed as the products of the 1-D sequences (Wang et al., 1994). Gabor features include the average absolute deviation which measures the energy of the filtered image, the mean and variance of the filtered image.
EXPERIMENTAL RESULTS Three sets of scaled and rotated textured mosaics are used for the experiment. Mosaic 1 is shown in Fig. l(a) which has textures D l l , D103, D55 and D105 (Brodatz, 1966) at a scale of 0.33 and rotated by an angle of 90 °, (b) mosaic 2 has textures D93, D28, D101 and D20 at a scale of 2 and orientation of 120 °, (c) mosaic 3 has textures D6, D19, D36 and D68 at a scale of 0.5 and orientation of 30 °. Features extracted from samples of the original texture with a scale of 1 and 0 ° orientation are used to train a Mahalanobis distance classifier. A moving window of size 16 x 16 pixels is used to extract features from the transformed texture mosaics. The classifier computes the distance between the features for each window and that of the texture classes and assigns the unknown sample to the texture class with the shortest distance. A gray color is then assigned to the sample as per the class it is being recognized and the texture mosaic is segmented. An example segmented image using the Gabor features and SGLDM features for mosaic 1 are shown in Fig. 2 (a) and (b) respectively. The classification results for each of the six feature set is shown in Table 1. As seen from the Table the Gabor features, the SGLDM features and the pixel based features have performed well compared to the others. The next performance is shown by Fourier features followed by the SGDM features and finally the SGLRLM features.
21st International Conference on Computers and Industrial Engineering
447
m mm (a) Mosaic 1
(b) Mosaic 2 (c) Mosaic 3 Fig. 1. Original texture mosaics
Fig. 2. (a) and (b). Segmented images
Table 1. Classification results for each feature set Feature Sets
Gabor features SGLDM features Pixel based features FPS features SGDM features SGLRLM features
Percentage of Correct Classifications for Mosaic 1 Mosaic 2 Mosaic 3 100 89.06 90.63 78.12 79.69 67.19
75.00 75.00 75.00 68.75 71.88 56.25
100 84.38 75.00 76.56 70.31 73.44
DISCUSSION The SGLRLM features performed poorly and this is justifiable since as per previous results by Weszka et al., (1976), the features did not give good results even for the textures with the same scale and orientation as the original textures. Only the short runs emphasis and run percentage gave better results than other features. The SGDM features obtained at angles of 135 ° and 45 ° performed better than those at 0 ° and 90 °. Best results for the Fourier method were obtained from the maximum magnitude, average magnitude and energy of magnitude which are statistical features defined on the power spectrum. The gray-level statistics of mean, variance and average residual showed good results while the average horizontal and average vertical residual degraded the performance. SGLDM feature at angles of 0 ° and 90 ° performs poorly. Best features were contrast, correlation, homogeneity, entropy and inverse difference moment computed at angles of 45 ° and 135 ° at a distance of 1. The best features in Gabor method were the average of the filtered image, variance and average residual of the coefficients. In this case, the length of the Gabor feature vector is only 3 compared to that of 256 in (Leung and Peterson, 1992). The statistical properties of the features plays significant role in the performance. Also, the
448
21st International Conference on Computers and Industrial Engineering
orientation at which the second order statistics are obtained affects the performance of the SGLDM and SGDM methods.
CONCLUSIONS As seen from the results, several of the features used perform well for invariant texture segmentation and the statistical properties of the features, are important in the discrimination of transformed textures. As opposed to the current belief (You and Cohen, 1993) the existing features can be used for invariant texture classification and their performance can be considerably enhanced by statistically adding invariant characteristics and transformation (scale and orientation) selectivity to the features. This work presents useful results which have not been provided so far for applying the existing features for scaled and rotated texture segmentation.
ACKNOWLEDGMENT This work was partially supported by NSF grant CDA 9417659, NASA grant NCCW-0088 and the Department of Electrical and Computer Engineering at the University of Puerto Rico at Mayagiiez.
REFERENCES Tan, T. N. (1994). Scale and rotation invariant texture classification. Proceedings oflEE Colloquium on texture classification: theory and applications, 3/1-3/3. Kashyap, R. L. and A. Khotanzaed (1986). A model-based method for rotation-invariant texture classification," IEEE trans. PAMI, 8, 472-481. Leung, M. M. and A. M. Peterson (1992). Scale and rotation invariant texture classification. Proc. 2~ h Asilomar Conf. Signals, Systems and Computers. 1, 461-465. Wu, Y. and Y. Yoshida (1995). An efficient method for rotation and scaling invariant texture classification. Proceedings of lCASSP'95, 4, 2519-2522. You, J. and H. A. Cohen (1993). Classification and segmentation of rotated and scaled textured images using texture tuned masks, Pattern Recognition, 26, 245-258. Brodatz, P (1966). Textures-A photographic album for artists and designers, Dover, New York. Haralick, R. M., K. Shanmugam and I. Distein (1973). Texture features for image classification, IEEE trans, systems, man and cybernetics, SMC-3, 610-621. Weszka, J.S., C. R. Dyer and A. Rosenfeld (1976). A comparative study of texture measures for terrain classification, IEEE trans, systems, man and cybernetics, SMC-6, 269-285. Wang K., C. T. Chen and W. C. Lin (1994). An efficient algorithm to compute the complete set of discrete Gabor coefficients, IEEE trans, image processing, 3, 87-92.