TEXTURE GRADIENT FROM IMAGES FOR SEGMENTATION

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1 International Journal of Computer Science and Communication Vol., No. 1, January-June 011, pp TEXTURE GRADIENT FROM IMAGES FOR SEGMENTATION Roshni V.S.1, Raju G. and Ravindra Kumar3 1, 3 C DAC, Trivandrum, Kerala, India, roshnivs@cdactvm.in, ravi@cdactvm.in Kannur University, Kannur, Kerala, India, kurupgraju@rediffmail.com. ABSTRACT Texture description is important for segmentation, the process of splitting the image into regions which are visually distinct and uniform with respect to some property, such as texture or color. In order to properly segment texture images, texture gradient combined with intensity gradient is input to the segmentation algorithm. Texture information is extracted using a combination of complex and wavelet packet transform. To smoothen the computation of gradients, directional weighted median filtering is applied to the texture features. Experiments are performed with Brodatz texture database and nature images that have significant amount of texture information to investigate the efficiency of our texture description algorithm. Keywords: Wavelet Transforms, Complex Transforms, Packet Transforms, Texture Gradient, Intensity Gradient. 1. INTRODUCTION Efficient analysis on images as classification, segmentation, recognition, etc. is ultimately dependent on the features used for data annotation. Natural scenes are rich in color and texture. Many texture segmentation algorithms require the estimation of texture model parameters. Recently developed texture based features have proved to be one of the effective descriptions of content [1, ]. Spatial-frequency analysis techniques using Gabor filters and wavelets have provided good characterization of textures in controlled environments [3 8]. However, in order to better characterize textures, extracted features must capture the nature of the texture invariant to rotational, shift and scale transformations [9, 10]. There is evidence that human visual system (HVS) is able to distinguish between contour of objects and edges originating from textured regions in its early stages of visual information processing. The goal of our work is to introduce the idea of local spatial frequency analysis performed by HVS into computational model that identifies perceptually homogenous region boundaries. Considering nearly constant values of texture features in any perceptually homogeneous region, the proposed method is developed based on detecting significant changes in texture features. The gradient of each texture feature clearly highlights the edge of the textured regions. These gradients are suited to the detection of texture boundaries. In order to preserve the ability of the model to detect intensity changes, these gradients are also combined with an intensity gradient. The gradients of texture features and intensity values are combined into a region gradient which highlights the object boundaries [11, 1, and 13]. The choice of highly discriminating texture features is the most important factor for success in texture segmentation. In the early approaches attention was on analysis of the first-order or second-order statistics of textures [14]. Later multiresolution texture models with methods as Gabor filters, Wigner distribution and wavelets have been proposed, and successful results have been reported in [15 ]. The Dual Tree Complex Wavelet Transform (DTXWT) provides both good shift invariance and directional selectivity over the DWT and is computationally faster than the Gabor transform [3 5]. However, it is not suitable for textured images where the dominant frequency channels are located in the middle frequency channels. Therefore the packet transform in combination with complex transform or the dual tree complex wavelet packet transform has been taken in this work for feature extraction [6 8]. This paper is organized as follows. In Section 1 we discuss the methodology of texture feature extraction using dual tree complex wavelet packet. Section explains the applicability of the oriented weighted median filter for post processing of the extracted features. Texture gradient computation is explained in Section 3 followed by experimental results in Section 4. Section 5 concludes with future works.. TEXTURE REPRESENTATION.1 Dual Tree Complex Wavelet Transform (DTXWT) The human visual system can pre attentively segment textures in an efficient manner. This realisation has motivated extensive studies and has lead to a promising theory of human texture perception. This theory supported by much psycho physical and neurophysiological data, holds that the human visual system

2 166 International Journal of Computer Science and Communication (IJCSC) is performing some form of local spatial frequency analysis on the retinal image and this analysis is done by a bank of tuned band pass filters. The concept of local spatial frequency or local frequency, had been put forth in the context of communication systems, many years earlier by Gabor. Classically, images are viewed as either a collection of pixels (in spatial domain) or the sum of sinusoids of infinite extent (in spatial frequency domain). Gabor, however, observed that the spatial representation and the spatial frequency representation are just opposite extremes of a continuum of possible joint space/spatial frequency representations. In a joint space/spatial frequency representation for images, frequency is viewed as a local phenomena (i.e., as a local frequency) that can vary with position throughout the image. Using this paradigm within the framework of human vision, perceptually significant texture differences presumably correspond to differences in local spatial frequency content. Texture segmentation thus involves decomposing a retinal image into a joint space/spatial frequency representation (by using a bank of Band pass filters) and then using this information to locate regions of similar local spatial frequency content. Motivated by the fact that a Gabor filter produces different outputs (called texture signatures) for distinct textured regions in an image, a number of studies has been performed on segmentation capabilities of Gabor filters. The DTXWT introduced by Kingsbury [4, 5] known for its properties of approximate shift invariance and good directional selectivity offer a computationally attractive alternative to Gabor functions for texture analysis. Unlike the Gabor decomposition, the complex wavelet filter bank is comprises of two parallel wavelet filter bank trees that contain carefully designed filters of different delays that minimize the aliasing effects due to down sampling (Fig. 1). normal wavelet decomposition for two levels using the above complex filters will result in a tiling of the frequency space as shown in Fig. 3. The analysis of frequency content in octave bands can be continued to further levels is explanatory of Fig. 3. The DTXWT therefore mirrors a common spread of Gabor analysis filters. Advantage of using a spatial filtering method such as the DTXWT is that the basis functions are spatially limited which contributes to localized texture characterization. Secondly there is no windowing as required with frequency domain filtering techniques. Frequency domain filtered images are found to have significant edge artifacts. The most important consideration for the use of a complete DTXWT decomposition is that it is less computationally complex compared to an equivalent Gabor analysis. Figure 4 shows the magnitude of a single, orientated, second scale subband [Fig. 4 (b)] from a DTXWT of the cameraman test image [Fig. 4 (a)].. Wavelet Packet Transform The wavelet transform decomposes a signal into a set of frequency channels that have narrower bandwidths in the lower frequency region. The transform is suitable for Fig. : Plot of the Complex Wavelet Impulse Response at Level 4 Fig. 1: The DTXWT Implemented using two Wavelet Filter Banks Operating in Parallel The vertical and horizontal complex and imaginary parts of the filtering process are treated separately. The DTXWT therefore results in six differently oriented complex valued subbands at each scale as shown in Fig.. The similarity of the basis functions to that of two dimensional Gabor functions is well understandable from Fig.. The Fig. 3: Tiling of the Frequency Space for the First two Levels of DTXWT Decomposition

3 Texture Gradient from Images for Segmentation 167 Fig. 4: (a) Original Image and (b) Complex Wavelet Subband signals consisting primarily of smooth components so that their information is concentrated in the low frequency regions. However, it may not be suitable for quasi-periodic signals such as speech signals or textures whose dominant frequency channels are located in the middle frequency region. This concept can be illustrated in Fig. 5 where the wavelet transform is applied to two different kinds of images. We use the Lenna image as a representative for an ordinary image. The image [Fig. 5 (a)] and the wavelet transformed subbands [Fig. 5 (b)] for level decomposition are shown below. The textured image Texmos (from the Brodatz s album [31]) and its pyramidstructured wavelet transform are shown in Fig. 5 (c) and (d) for comparison. By examining the wavelet-transformed image in Fig. 5 (b), we recognize the Lenna image clearly from its low frequency channel (the upper left corner). In contrast, we are not able to recognize a similar texture pattern in the same low frequency channel for Fig. 5 (d). Instead, we observe some horizontal and vertical dot patterns clearly in the middle frequency region. The simple experiment implies that the low frequency region of textures may not necessarily contain significant information. Thus, an appropriate way to perform the wavelet transform for textures is to detect the significant frequency channels and then to decompose them further. The (full) discrete wavelet packet transform (DWPT), obtained by iterating a perfect reconstruction filter bank on both its low-pass and high-pass output results in a larger binary tree decomposition that generates two branches from each node as shown in Fig. 6. It provides a frequency-domain analysis as illustrated in Fig. 7 (for a four-level DWPT). However, like the DWT, the DWPT is also shift-variant and mixes perpendicular orientations in multiple dimensions..3 Dual Tree Complex Wavelet Packet Transform (DTXWPT) The easiest way to generate a complex dual-tree form of the DWPT is to convert each of the two DWTs used to Fig. 5: (a) Lenna Image, (b) Wavelet Transformed Image, (c) Texture Image Texmos, and (d) Wavelet Transformed Image Fig. 6: Full Wavelet Packet Binary Tree for two Levels Fig. 7: Frequency Domain Analysis of DWPT construct the DTXWT into packets themselves using the same set of filters. But as illustrated in Fig. 8, for several subbands in this construction, significant energy leaks into the negative frequency band. Therefore the requirement of being approximately analytic is not met by the subbands taken into consideration. Hence, this construction does not fully possess the desired properties of a DTXWPT. To generate the required packet form of the DTXWT, each of the subbands should be repeatedly decomposed

4 International Journal of Computer Science and Communication (IJCSC) 168 using low-pass/highpass perfect reconstruction filter banks (PR FBs). The PR FBs should be chosen so that the response of each branch of the second wavelet packet FB is the discrete Hilbert transform of the corresponding branch of the first wavelet packet FB. Then each subband of the DTXWPT will be analytic as illustrated in Fig. 9. Accordingly three PR filter sets would be required for implementing a tree of the DTXWPT (Fig. 10). Table 1 lists the Stage 1 filters for Trees 1 and respectively. These filters are related by a unit shift. Table provide the values for the half shift filters used in the next stage and Table 3 the remaining filters which are Daubechies filters with 5 and 6 vanishing moments. Note that it is usually unnecessary and expensive to decompose all subsignals in each scale to achieve a full decomposition. To avoid a full decomposition, we may consider a criterion to decide whether a decomposition is needed for a particular output. The best basis selection algorithm [9, 30] decides a decomposition structure among the library of possible bases, by measuring a data dependent cost function. MSE or entropy has been some of the choices for cost function. We have chosen. Table 1 Fig. 8: Frequency Domain Analysis of Non-analytic DTXWPT Tree 1 H0(1) Fig. 9: Frequency Domain Analysis of Analytic DTXWPT Fig. 10: First Wavelet Packet FB of a 3 Stage DTXWPT Tree H1(1) H0(1) H1(1)

5 Texture Gradient from Images for Segmentation TEXTURE POST PROCESSING Table Tree 1 Tree H H1 H H Table 3 Tree 1 and Tree Tree 1 and Tree F0 F1 F F The aim of our work is to compute the texture gradient from images which can later be used for classification and segmentation. A simple solution would be the integration of the gradient of the selected subbands. But usually the texture feature extraction methods will give high energy values over simple intensity boundaries found in nontextured image regions and the gradient of the subband magnitudes will give a double edge at such intensity boundaries. The gradient of each subband should therefore aim at step detection rather than edge detection. The solution is to median filter the texture subband magnitude before the application of the gradient operator. Median filtering is well known as a nonlinear edgepreserving smoothing or noise removal technique. In this case, the noise in question is any wavelet response with a small spatial extent-indicating a local edge rather than an extended area of texture. Directional weighted median filter has been applied in our work since it is found to preserve more details along with noise removal. We consider coordinates along the directions shown in Fig Shannon Entropy as the cost function for the above algorithm in our application Table 4 lists typical entropy values obtained for various images for the parent as well as the subbands of a first level decomposition of images used in the various illustrations in this paper. Table 4 Typical Entropy Values for Images First level Image Parent LL LH HL HH Coin Ricee Lenna Cameraman Fig. 11: Directions for Detection of Noise The second order difference (SOD) among pixels in a test window is used to determine the noise status of the centre pixel. The SODs have a stronger response to fine details, such as thin lines and isolated points. Consider a 3 3 window W, symmetrically surrounding the test pixel x (i, j) as W = {x (i + s; j + t) 1 s, t 1}. For each direction shown in Fig. 11, the SODs are found as dk = x (i + u; j + v) + x (i u; j v) x (i; j) where u, v correspond to the neighborhoods in the directions. The minimum of dk is computed as d = min {dk : 1 k 4}. The pixel under consideration is treated as a noisy pixel if d exceeds a defined threshold since it will have large SOD in all directions resulting in a larger value of

6 International Journal of Computer Science and Communication (IJCSC) 170 d. The replacement is computed using a weighted median filter supported with the four directional information. The gray level difference between two neighboring pixels of the pixel under consideration, in the four directions is computed. Let the minimum of these differences be Sk and the respective direction Dk. It signifies that the pixels aligned along Dk are close to each other and the reference pixel value also should be close to these values. Hence when computing the median more weightage is given to the neighboring pixels in the identified direction. texture gradient is then added, the combined result will be dominated by intensity gradient in smooth regions and texture gradient in textured regions, as required. The intensity gradient of the input image is obtained using the Gaussian derivative function and normalized by its l norm energy. Scaling as required for increasing the dynamic range of the values to suit the texture gradient values is done before summing the intensity gradient and texture gradient. Figure 13 gives a good illustration of this process. Fig. 1: Median Filtered Subband 4. TEXTURE GRADIENT COMPUTATION The median filtered texture subband images are now suitable for gradient extraction. The gradient operator approximation used is the commonly used Gaussian derivative function. The gradient magnitude of each subband is given by TGi,θ ( x, y ) = (S ( x, y ) * Gx ) Si, θ ( x, y ) i, θ ( + Si, θ ( x, y ) * Gy ) where G x and G y are the Gaussian partial derivative filters in the x and y directions and * denotes convolution. To obtain the combined gradient within the multidimensional feature space, sum the gradients obtained for each of the individual subbands, i.e. n TG (x, y) = i=1 TGi ( x, y ) Fig. 13: (a) Complex Subband (b) Texture Gradient 5. RESULTS The Brodatz image database with 116 images that have significant amount of texture information were chosen for performance evaluations. We used 40 textures, as shown in Fig. 14. Every original image is of size pixels with 56 gray levels. l ( TGi ) where TG (x, y) is the magnitude of the texture gradient. Each median filtered subband gradient normalized by its l norm energy contributes to the total gradient. In smooth regions, texture gradient may not give satisfactory results as intensity gradient dominates texture gradient. So intensity gradient modulated by a measure of texture activity also has to be taken into account. The aim is to suppress the intensity gradient in textured areas but leave it unmodified in smooth regions. When the Fig. 14

7 Texture Gradient from Images for Segmentation To analyze the performance of the method, we present a comparison of segmentation results applied on texture gradient images and plain intensity gradient images. In the experiments, the feature of DTXWPT is extracted from the energy of all selected frequency regions in the third scale, three middle and high frequency regions in the second scale and three middle and high frequency regions in the first scale. The number of segments obtained in each case is tabulated in Table 5. Segmented outputs for samples of textured images (D1, D, D3, and D4) using both texture gradient and intensity gradient are shown in Table 6. All 171 the images exhibit better performance when segmented using the texture gradient rather than the plain intensity gradient images. To highlight the effect of texture gradient on segmentation, we perform segmentation using the above gradients on non textured images also (E1, E, E3 and E4). Table 7 illustrates the segmentation results for the above case. Clearly the texture gradient is found to exhibit substantially lesser performance in this case when compared to the first case. For textured images the effect of smoothing the scaled subbands using the directional weighted median filter adds to better performance results. Table 7 Segmented Non-textured Images Table 5 No. of Regions Textured images Image Texture gradient method Intensity gradient method D1 60 D 14 D D Non-Textured images Image Intensity gradient method Texture gradient method E1 5 E 1 55 E E Table 6 Segmented Textured Images 6. CONCLUSION This work focuses on the role of texture gradient in the segmentation of textured images. It has used the concept of region gradients to produce effective segmentation for natural and textured images. The first stage is the use of the combined complex wavelets and packet wavelets for feature extraction. The second stage proposes oriented weighted median filtering to correctly treat edgeresponses in the texture features followed by computation of texture gradient. Using these algorithms with a usual image gradient will often lead to effective segmentation for textured and non-textured images.

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