Brain Tumor Texture Analysis – Using Wavelets and Fractals

: Brain tumor segmentation is quite popular area of research but detection of its surface texture is challenging for researchers. Normally, MRI datasets have very low resolution. This paper utilizes image enhancement technique based on wavelet. It is used to scale the low resolution image to a suitable resolution without loss. Secondly the proposed method is focused on implementation of a trained classifier using features: fractal dimension, fractal area, and wavelet average to classify type of texture present in brain tumor.


Introduction
Automatic image analysis has a lot of scope for implementation, from image classification to image retrieval. Semantic gap problem [1,2], which corresponds to the alteration between the user image perception and automatic extracted features. An important aspect of feature extraction task is to obtain a set of features (i.e. a feature vector) for representing the visual content of an image. In many applications texture features are used for maintaining orthogonal nature among different classes. On the other hand, it can be effectively implemented to address the semantic gap problem. As a result, research on texture classification is focused on improving the distinguish-ability of the algorithm.
In the paper the problem of identifying the type of texture in tumor of brain from MRI is addressed. Segmentation technique is utilized to visually extract the position and size of the tumor. Wavelet transform is established as a very efficient tool for analyzing an image's frequency components in a localized manner. The popular SFTA algorithm, is used along with the features extracted from wavelet transform.
The input MR Image is first subdivided in small blocks of pixel. Next, texture of each sub block is obtained in order to identify the texture of the tumor. Multi resolution wavelet transform is implemented to get the details of input image including energy and frequency details. The feature vector thus obtained is easily achievable in terms of complexity. The feature vector is 1x26 array consisting of multi resolution wavelet detail of different wavelet families.

Related Works
In image processing textural information plays a key role to identify the type of object present in the images. It dominates in the field of remote sensing, quality control & medical imaging due to its close relation to the underlying semantics.
Texture features captures the granularity and the repetitive pattern in the image. From statistical point of view texture information can be termed as fractal whose Area, Mean, Dimension can be accepted as Fractals features. Fractals [3] are small pictorial patterns those tend to repeat in a textured surface.
Another widely accepted approach is to use grayscale cooccurrence matrices (GLCM) by counting the number of occurrences of the gray levels at a given displacement and angle. Statistical quantities such as contrast, energy, entropy are computed from the GLCM to obtain the texture features as proposed by Haralick et al.
Filter Bank [4,5] approach is a widely accepted method for texture classification and segmentation. Gabor filters is among the popular filter banks known for its invariance with respect to scale, rotation and displacement. Where θ is the filter orientation, σ the standard deviation and λ the wavelength of the sinusoid, Equation shows the formal representation of the Gabor filter, The pixel position is given by x, y. Fractal dimension measurements can be used to estimate and quantify the complexity of the shape or texture of objects. The most common is the Hausdorff's dimension. An object with a Euclidean Dimension E, Hausdorff's fractal dimension D 0 computed by the following equation: where N (E) is the counting of hyper-cubes of dimension E and length that fill the object.
Hausdorff's dimension [7,8] is an important feature describing the fractal structure. The algorithm for obtaining the dimension value can be described as follows, if an object is described using a binary image I b then an approximate Dimension value van be calculated using box counting algorithm. The image is divide into small sub matrix of size e x e. By varying the size, it is possible to generate an approximated straight line curve using 123 4 , 123 , 56 . The slope of the line gives Hausdorff dimension.
Another prior art is FFS [9] (Fast Fractal Stack) in which the fractal dimension is computed from a set of binary images obtained from the input grayscale image using the binary stack decomposition algorithm. The image is decomposed by applying successive operation using threshold value. Depending on the number of threshold value, image forms a binary image stack. The main disadvantage of this method since threshold intensities are chosen at an equal interval hence a lot of information gets lost during the operation.
The above algorithm proves to have an efficiency of 76% when implemented with a Knn classifier [10,11] and 80% when trained with a discriminant based classifier. It is time consuming algorithm. For achieving higher classifier efficiency number of operation needs to be increased, hence there is a tradeoff between the classifier efficiency and the speed of the algorithm.
The thresholding using multilevel Otsu algorithm improves the intra class variance between the binary stack images is least.

Proposed Method
Wavelet Decomposition technique to the input image is firstly applying for obtaining the feature based on the decomposition. Secondly applying multilevel Otsu algorithm for finding threshold of the input image and then implementing box counting algorithm to obtain the features from it. The features obtained from both algorithms will serve as the feature set for the classifier. The trained classifier will then utilize it to predict texture of the new image.
Wavelet proves to be a very suitable and efficient method to obtain the localized frequency information of any signal. Previously frequency details were retrieved using Fast Fourier Transform. On the other hand, Wavelet based transform gives the localized information about the frequency content as feature.
Wavelet transform over the image generates two kind of features: ( Input image = A 3 + D 3 + D 2 + D 1 When the images are decomposed into further levels then approximate image (Ai) gets smoother and holds the information about low pass filter applied over the initial image. On the other hand, frequency domain details of the image (Di) preserves the high pass filter information.
These values use as a set for classifying texture. The decomposition Algorithm finds the Energy values and Detail values calculated using different types of wavelet packets. The Wavelet families are used for feature extraction (i) Haar (ii) Daubechious (iii) Bior (iv) Coiflet.
The following algorithm is used to find out feature vector using wavelet transform: I After the first set of features are obtained, second set of features are extracted from the fractal analysis. This Algorithm incorporates two basic algorithm (i) Multilevel Otsu Algorithm [12] (ii) Bounding box technique to obtain the fractal dimension [3] a) Multilevel Otsu Algorithm The Otsu algorithm takes a grayscale image I (x, y) as an input and calculate the user defined number of threshold points such that the intra class variance becomes minimum. It incorporates the gray level distribution function to generate the threshold levels. When the threshold points (T) are obtained the next task is to generate the binary images using two threshold segmentation levels from the equation.
where t l and t u denote, respectively, lower and upper threshold values. The set of binary images is obtained by applying the two threshold segmentation to the input image using all pairs of contiguous thresholds from T ∪ {nl} and all pairs of thresholds {t, nl}, t ∈ T, where n 1 corresponds to the maximum possible gray level in I (x, y). b) Box Counting Algorithm to compute the Fractal Dimension, Area, Mean After applying the Multilevel Otsu Algorithm to the input gray level image, the feature vector is constructed as the resulting binary images' size, mean gray level and boundaries' fractal dimension. The regions' boundaries of a binary image I b (x, y) denoted by border image ∆(x, y) and computed as follows: y)] denotes the set of pixels that are 8connected to (x, y). ∆ (x, y) has value 1 if the pixel at position (x, y) in the corresponding binary image I b (x, y) has the value 1 and having at least one neighboring pixel with value 0. Otherwise, ∆(x, y) takes the value 0. Hence, one can realize that the resulting borders are one-pixel wide. Fractal Dimension are extracted using Box Counting algorithm in which the binary image is divided in to small grid and for each sub grid part the fractal dimension is stored given by the number of instance a border is found. Mean and Area of the fractals are computed without much computational power.
Having described the basic processing tools used in the algorithm, the complete explanation of the algorithm goes in the following way.
Algorithm can be decomposed in two stages: A. Training a Discriminant classifier using some known datasets whose texture is known by the user. B. Using the Discriminant classifier on the segmented tumor image for detecting the texture type.      As the experiments reveal the wavelet energy and details efficiently describe a texture pattern and forms a highly uncorrelated feature sets. More over the Fractal analysis algorithm not on describe the texture completely but also forms an orthogonal set of feature. As mentioned in the prior work [3] SFTA Algorithm was implemented which gave an amazing texture classification but with 4 threshold level. In our algorithm we reduced the number of threshold, but reducing the threshold points decreases the strength of the feature sets. So along with reduction in the threshold points we introduced the wavelet based features which not only improve the classification efficiency but also reduced the classification time.       So from the Texture detail image [ Fig. 12] it can be seen that the tumor boundaries are slight rough whereas the center and rest portion are having very smooth textures.

Deployment Phase Algorithm
Gray Scale Values corresponding to different classes:

Conclusion
The proposed technology is useful to doctors as well as to the diagnostic center as it portrays the texture that tumor is having. Our algorithm defines the texture of tumor in reference to our daily known textures. The proposed state-ofthe-art algorithm utilizes both fractal analysis along with wavelet features to make the prediction much more firm in terms of accuracy. Generally, tumor appears as very smooth type and near the sides it becomes slight rough. The texture detail image will let medical practitioner know the type of texture of the tumor. This will help in diagnostics of the Brain tumor by correlating with other clinical tests and findings.