TEXTURE SEGMENTATION USING AREA MORPHOLOGY LOCAL GRANULOMETRIES

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1 TEXTURE SEGMENTATION USING AREA MORPHOLOGY LOCAL GRANULOMETRIES Neil D Fletcher and Adrian N Evans Department of Electronic and Electrical Engineering University of Bath, BA2 7AY, UK N.D.Fletcher@bath.ac.uk A.N.Evans@bath.ac.uk Abstract Texture segmentation based on local morphological pattern spectra provides an attractive alternative to linear scale spaces as the latter suffer from blurring and does not preserve the shape of image features. However, for successful segmentation, pattern spectra derived using a number of structuring elements, often at different orientations, are required. This paper addresses this problem by the use of area morphology to generate a single pattern spectra, consisting of a local granulometry and anti-granulometry, at each pixel position. As only one spectrum is produced, segmentation is performed by using the entire spectrum as the feature vector instead of taking pattern spectrum moments. Supervised and unsupervised segmentation results for a simulated image of Brodatz textures confirm the advantages of this new approach. Keywords: Texture analysis, granulometries, area morphology Introduction Automated texture classification and segmentation remains a challenging task for computer vision algorithms. Texture refers to the variation of intensity in a local neighbourhood and therefore cannot be defined by a single pixel [8]. In supervised texture classification schemes a feature vector, consisting of a number of textural features, is evaluated against a selected library of feature vectors for particular textures. Alternatively, if an a priori library is not available clustering techniques can be used to classify the feature vectors into an appropriate number of classes [10]. As texture can be said to consist of a distribution of image features at different scales, multiscale texture analysis schemes are an attractive alternative to the traditional fixed scale approach. In practice, multiscale feature vectors can be found by decomposing the signal into elements of different resolutions with a linear filterbank and then extracting the structural information in each sub-band. Popular methods include Ga-

2 2 Texture Segmentation Using AreaMorphology Local Granulometries bor filtering [9] and, more recently, wavelet analysis [11]. However, despite its popularity, linear image analysis suffers from a number of drawbacks including the shifting and blurring of image features, a scale parameter that is not related to a size-based definition of scale and it produces filtered images that do not correspond to the shape of image features [12]. An alternative method of decomposition uses mathematical morphology operators to produce an improved representation both in terms of scale and the position of sharp edged objects. In practice, this can be achieved by differencing a series of openings and closings by increasing scale structuring elements to produce a granulometric size distribution for greyscale images, termed a pattern spectrum [12], that has its roots in the binary granulometries of Matheron and Serra [13, 16]. Feature vectors are formed by taking moments of the local pattern spectra produced by a number of different structuring elements, where the term local refers to a window centred on the pixel of interest [7]. In terms of texture classification, morphological scale spaces obtained using standard standard open and close filters suffer from two disadvantages. Firstly, the shape of the structuring produces edge movement such as corner rounding and, secondly, the number of structuring elements required to capture textual features can be relatively large. The second point is further exacerbated when linear features are present in the texture at different orientations. Consequently, many pattern spectra are required at each image point and this explains in part why only moments of the spectra are used to form the feature vectors. Area morphology operators [17, 15] address both these problems. The scale spaces resulting from increasing area open-close (AOC) and area close-open (ACO) operations exhibit the property of strong causality thus guaranteeing the preservation of edge positions through scale [1]. In addition, as area operations can be considered as the be the maximum (resp. minimum) of openings (resp. closings) with all possible connected structuring elements with a given number of elements [5], the need for a set of differently orientated structuring elements is removed. An area morphology scale space classification scheme using a feature vector whose elements are the intensities of a particular pixel at a given set of scales is described in [1]. Here, a new local granulometric texture analysis technique is proposed that combines the advantageous properties of area morphology scale spaces with a local pattern spectra approach. This paper is arranged as follows. Section 1 discusses local granulometric texture analysis in more detail and the new area morphology local granulometric method is described in section 2. Experimental results for a compound image consisting of a number of Brodatz textures are given in section 3 and conclusions are drawn in section 4.

3 < < < Morphological Texture Analysis 3 1. Morphological Texture Analysis The granulometric size distributions first proposed by Matheron [13] provide a morphological description of the granularity or texture in an image, see also chapter 8 of [6]. Granulometries are obtained by the repeated application of multiscale non-linear filters. For example, consider the opening of a binary image image with a binary structuring element. As the opening operator is increasing, when is a subimage of then is a subimage of. Therefore if is an increasing sequence of structuring elements, the filtered images will form the decreasing sequence (1) The total number of pixels remaining in each successive opening results in the decreasing function "! where, for a given value of #, "!%$'& for )(*#. Various textural information can be extracted from "! depending on the shape of the structuring element. The sequence of images given by $,+.- 0/1&324526#8769;: (2) defines the granulometry and the resulting function "! is known as the size distribution [7]. Since "! is a decreasing function its normalisation yields the probability distribution function (pdf) "!=$>9?7 (3) The discrete derivative of (3) produces the discrete density function B < "!=$,+ "!=7 769A!C/"924526#8769;: (4) that defines the discrete pattern spectrum. The pattern spectrum for greyscale images, D?EGF, can be described by the decreasing sequenceh0i FJK!=$MLN O7 QP (5) where is now a greyscale opening, is the size parameter, the structuring element defines the shape parameter and LRN P $>SUTV XẄ ZY[! [12]. Keeping fixed produces a decreasing sequence of greyscale openings reminiscent of (1) and the result is a size histogram of relative to. The pattern spectrum can be extended to contain negative values by replacing the greyscale opening in (5) with a greyscale closing giving H0I ] FJK 0\!=$MLN O7 ] ^\ QP (6)

4 4 Texture Segmentation Using AreaMorphology Local Granulometries If local pattern spectra of (5) and (6) are normalised by the total energy in the original image, this defines a size density F1 "!=$ 9 LRN P LRN ] LRN 7 7 =5(6& =527 9 This density is equivalent to the pattern spectrum for binary images of (4) with the discrete differentiation being replaced by a point-wise difference of functions. To obtain the full shape-size classification for XW ZY"! using either the binary or the greyscale approach an appropriate set of the structuring elements is required and, for each, the size parameter is varied over its range, producing a discrete pattern spectrum for each structuring element. Ganulometric-Based Texture Segmentation Granulometric size distributions can be used as features for texture-based classification schemes. However, if the overall aim is the segmentation of images containing more than one texture the classification needs to be performed at pixel-level and the features should reflect the local size distribution. This is the notion behind the local pattern spectrum methods of [7, 6] that compute local size distributions centred on a pixel of interest. For binary images, local granulometric size distributions can be generated by placing a window T at each image pixel position W and, after each opening operation, counting the number of remaining pixels within (7) T. This results in a local size distribution, T, that can be normalised in the same manner as the global granulometry to give the local pdf < T "!. Differentiating gives the density B < T that yields the local pattern spectrum at pixel W, providing a probability density which contains textural information local to each pixel position. As acknowledged in [7], the reason for calculating local pattern spectra on binary images is computational complexity. The analysis of grey-scale images is preferable as more image information is available for the classification algorithm and can be achieved by replacing the density B < T with a local greyscale size density calculated by applying (7) within a local window T. Textural feature extraction can be achieved by employing several structuring elements to generate a number of granulometries, each providing different texture qualities, to produce in a more robust segmentation. Supervised classification schemes compare the observed pattern spectra moments at each pixel position to a database of texture moments [7]. For every pixel the distance between the local size density and every entry in the database of codevectors is calculated. The texture class with the minimum distance is then assigned to the pixel position, resulting in a texture class map.

5 Area Morphology Local Granulometries 5 Feature vectors that posses common attributes will form clusters in the feature space. The distances between points inside a cluster are smaller than those to points which are members of different cluster and therefore the clusters can be regarded as texture classes. In this manner, popular clustering algorithms such as the -means [10] can be employed to provide an unsupervised texture segmentation scheme. This was the approach used to cluster granulometric moments for segmenting grey-scale mammogram images [2]. 2. Area Morphology Local Granulometries Morphological area openings and closings [17, 15] remove connected components less than a given area and can be used to generate a scale space in which area provides a scale parameter equivalent to structuring element size in standard morphology. Area openings and closings can be defined by operations on a threshold decomposition or, alternatively, by and!=$ F! $ F ] 3! (8) 3! (9) respectively where L is the set of connected subsets with area greater or equal to [5]. This alternative definition illustrates the fact that area operators select the most appropriately shaped structuring at each pixel, the only constraint being its area. therefore, the operations adapt to the underlying image structure and eliminate any shape bias and artificial patterns associated with fixed structuring elements. In terms of texture classification, area morphology scale spaces are attractive as they can capture all the structures contained in an image. This is advantageous as textured images generally contain far more structures that can be described by a family of fixed structuring elements. In addition, area scale spaces have the property of strong causality which ensures that edge positions are preserved through scale [1, 3]. Computational complexity issues have also been greatly reduced with the development of fast area opening and pattern spectra algorithms [14]. Successful feature classification was demonstrated by Acton and Mukherjee using a scale space vector containing the intensity of each pixel at a selected set of scales [1]. To extend the use of area morphology operators to texture segmentation a new approach based on local area morphology granulometries is proposed. The area operators are applied to a local window to produce a single pattern spectrum containing information of all shapes at each scale, given

$6 Texture Segmentation Using AreaMorphology Local Granulometries Figure 1. Test image. by F! $ 9 LN P LN! 7! P (M9 LN \! 7 \!$

6 6 Texture Segmentation Using AreaMorphology Local Granulometries Figure 1. Test image. by F! $ 9 LN P LN! 7! P (M9 LN \! 7 \! P 27 9 (10) As the size of the local window is kept relatively small to ensure it captures the texture at a particular pixel, the number of elements in the pattern spectra, being directly related to the maximum area, is considerably lower than for a global scale space. For example, an area of 81 is sufficient for a window. In practice a smaller maximum area size can be chosen, above which features are considered too large to contain textural information. This approach is computationally simpler than the scale space sampling of [1]. In addition, as the single pattern spectrum produced by this approach containins a limited number of elements it can be used directly to provide a feature vector for classification purposes, instead of indirectly through pattern spectra moments [7]. 3. Experimental Results A simulated image created from five natural textures from the Brodatz album [4], see figure 1, was used to quantify the performance of the new local area granulometry texture segmentation technique. To provide a set of comparative results the test image was first segmented using binary and greyscale versions of the local granulometry segmentation scheme described in [7, 6]. The binary test image was created by thresholding figure 1 so that equal numbers of pixels were assigned to each value. For both the binary and greyscale methods five structuring elements, four linear (vertical, horizontal, positive diagonal and negative diagonal) and one circular, were used to create local size distributions using a window. The first 3 central moments of the local pattern spectra were used as textural features, augmented by two additional features, W and QY, giving a 17 element feature vector. The W feature finds the maximum linear dimen-

Experimental Results 7 True Classified as: class: D77 D84 D55 D17 D24 D77 61.91% 24.73% 0.13% 5.34% 7.90% D84 0.00% 97.44% 1.20% 0.00% 1.36% D55 0.00% 18.86% 80.74% 0.00% 0.40% D17 0.00% 26.18% 1.

7 Experimental Results 7 True Classified as: class: D77 D84 D55 D17 D24 D % 24.73% 0.13% 5.34% 7.90% D % 97.44% 1.20% 0.00% 1.36% D % 18.86% 80.74% 0.00% 0.40% D % 26.18% 1.40% 59.30% 13.12% D % 2.67% 10.83% 0.00% 86.50% Figure 2. Supervised segmentation results using binary pattern spectra. sion regardless of direction while the QY feature differentiates between regions of large linear components and circular components with similar diameters. The database of codevectors used for the supervised classifier were obtained by generating the 17 feature images for homogeneous texture and then calculating the mean value of each feature image. The supervised segmentation results achieved by the binary and greyscale schemes using a minimum distance classifier are shown in figure 2 and figure 3 respectively. Comparison of these result shows the improved performance of greyscale spectra. The overall correct classification, given by the mean value of the diagonal for each confusion matrix, rises from 77.18% (binary) to 83.15% (greyscale). However, many intra-region classification errors are still present resulting, in part, from the introduction of new features with increasing scale [1]. The classification result for the supervised area morphology local granulometry scheme is given in figure 4. Here, the maximum area size was set to 78 pixels, a value equal to the area of the largest structuring element in the previous results, and the local window size was as before. The granulometry and anti-granulometry were found using (10) resulting in a 144 element local size density. The results are an improvement on the greyscale structuring element approach with an average correct classification of 87.71%. In texture segmentation, adjacent pixels are highly probable to belong to the same texture class and the incorporation of spatial information in the feature space has been shown to reduce misclassifications in regions of homogeneous

8 Texture Segmentation Using AreaMorphology Local Granulometries True Classified as: class: D77 D84 D55 D17 D24 D77 82.98% 3.94% 1.25% 11.26% 0.56% D84 0.00% 92.06% 0.04% 6.25% 1.64% D55 0.24% 37.

8 8 Texture Segmentation Using AreaMorphology Local Granulometries True Classified as: class: D77 D84 D55 D17 D24 D % 3.94% 1.25% 11.26% 0.56% D % 92.06% 0.04% 6.25% 1.64% D % 37.66% 60.27% 1.32% 0.51% D % 12.12% 0.01% 87.27% 0.61% D % 5.07% 1.59% 0.17% 93.17% Figure 3. Supervised segmentation results using greyscale pattern spectra. texture and at texture boundaries [9]. In practice, this can be achieved by including the spatial co-ordinates of each pixel as two extra features. As no a priori information about the co-ordinates of each texture class is available this approach is incompatible with a supervised segmentation scheme. Instead a -means clustering algorithm can be used to provide an unsupervised segmentation. The result achieved by this approach is presented in figure 5 and achieves an overall correct classification of 93.26%. Inspection of the figure shows that intra-region classification errors are virtually eliminated with the only misclassifications occurring at region boundaries. 4. Conclusions A new approach to morphological texture segmentation using area morphology local granulometries has been presented that combines the advantages of area morphology with a local granulometry approach. Pixel-wise classification is achieved using a feature vector consisting of a local area morphology size density. Segmentation results on a simulated image show the supervised scheme to out-perform supervised fixed structuring element segmentation for both binary and greyscale operations. An unsupervised area granulometry texture segmentation scheme has also been presented that produces improved results by virtue of incorporating the spatial co-ordinates as additional feature vector elements. Results show that this unsupervised technique produces the best performance in terms of overall

Conclusions 9 True Classified as: class: D77 D84 D55 D17 D24 D77 95.67% 0.02% 0.00% 0.74% 3.56% D84 0.44% 91.38% 2.25% 0.91% 5.02% D55 0.59% 5.06% 83.81% 2.64% 7.90% D17 20.85% 4.46% 2.27% 69.86% 2.

9 Conclusions 9 True Classified as: class: D77 D84 D55 D17 D24 D % 0.02% 0.00% 0.74% 3.56% D % 91.38% 2.25% 0.91% 5.02% D % 5.06% 83.81% 2.64% 7.90% D % 4.46% 2.27% 69.86% 2.55% D % 0.23% 1.92% 0.00% 97.84% Figure 4. Supervised segmentation results using local area pattern spectra. correct classifications. The approach has the additional advantage of eliminating the need of a training stage to calculate texture codevectors. An area of future work is the application of the new supervised and unsupervised segmentation schemes to synthetic aperture radar images, where there may be limited a priori information on the number of textures classes. Acknowledgements Neil Fletcher supported by an EPSRC CASE award in conjunction with QinetiQ. References [1] S.T. Acton and D.P. Mukherjee. Scale space classification using area morphology. IEEE Trans. on Image Processing, 9(4): , April [2] S. Baeg, A.T. Popov, V.G. Kamat, S. Batman, K. Sivakumar, N. Kehtarnavaz, E.R. Dougherty, and R.B. Shah. Segmentation of mammograms into distinct morphological texture regions. In Proc. 11th IEEE Symposium on Computer Based Medical Systems, pages 20 25, [3] J.A. Bangham, R. Harvey, P.D. Ling, and R.V. Aldridge. Morphological scale-space preserving transforms in many dimensions. Journal of Electronic Imaging, 5(3): , July [4] P. Brodatz. A Photographic Album for Artists and Designers. Dover, New York, [5] F. Cheng and A.N. Venetsanopoulos. An adaptive morphological filter for image processing. IEEE Trans. on Image Processing, 1(4): , 1992.

10 Texture Segmentation Using AreaMorphology Local Granulometries True Classified as: class: D77 D84 D55 D17 D24 D77 99.94% 0.06% 0.00% 0.00% 0.00% D84 5.45% 88.34% 0.00% 2.49% 3.73% D55 5.81% 0.

10 10 Texture Segmentation Using AreaMorphology Local Granulometries True Classified as: class: D77 D84 D55 D17 D24 D % 0.06% 0.00% 0.00% 0.00% D % 88.34% 0.00% 2.49% 3.73% D % 0.00% 89.35% 3.20% 1.64% D % 0.03% 2.03% 97.94% 0.00% D % 0.71% 1.38% 2.20% 90.74% Figure 5. Unsupervised segmentation results using local area pattern spectra. [6] E.R. Dougherty and R.A. Lotufo. Hands-on Morphological Image Processing. SPIE Press, [7] E.R. Dougherty, J.T. Newell, and J.B. Pelz. Morphological texture-based maximum likelihood pixel classification based on local granulometric moments. Pattern Recognition, 25(10): , [8] R.M. Haralick. Statistical and structural approaches to texture. Proceedings of the IEEE, 67(5): , May [9] A.K. Jain and F. Farrokhnia. Unsupervised texture segmentation using Gabor filters. Pattern Recognition, 24(12): , [10] T. Kohonen. The self-organizing map. Proceedings of the IEEE, 78(9): , [11] A. Laine and J. Fan. Texture classification by wavelet packet signatures. IEEE Trans. on Pattern Analysis and Machine Intelligence, 15(11): , [12] P. Maragos. Pattern spectrum and multiscale shape representation. IEEE Trans. on Pattern Analysis and Machine Intelligence, 11(7): , [13] G. Matheron. Randon Sets and Integral Geometry. Wiley, [14] A. Meijster and M.H.F. Wilkinson. A comparison of algorithms for connected set openings and closings. IEEE Trans. on Pattern Analysis and Machine Intelligence, 24(4): , April [15] P. Salembier and J. Serra. Flat zones filtering, connected operators, and filters by reconstruction. IEEE Trans. on Image Processing, 4(8): , August [16] J. Serra. Image Analysis and Mathematical Morphology. Academic Press, [17] L. Vincent. Morphological area openings and closings for grey-scale images. In Shape in Picture: Mathematical Description of Shape in Grey-level Images, pages , 1993.

A Miniature-Based Image Retrieval System

A Miniature-Based Image Retrieval System Md. Saiful Islam 1 and Md. Haider Ali 2 Institute of Information Technology 1, Dept. of Computer Science and Engineering 2, University of Dhaka 1, 2, Dhaka-1000,