Estudios de campo previos a la ejecución de acciones de mantenimiento.

Texture exhibits visual patterns which are properties of surfaces containing information about the structural arrangement. In the context of medical image processing, texture is used to describe tissue structures and functionality with terms such as smoothness, granulation, regularity, homogeneity, heterogeneity, etc. These parameters can be derived from local intensity variation by using texture matrices (201). Such matrices can be calculated by considering for example “grey-level patterns, pixel interrelationships and spectral properties of an image” within a region of interest (18).

Texture analysis was firstly introduced by Haralick et al. (202) and was applied in diversified applications from macroscopic satellite images (203) and material structures (204) to microscopic images of biological tissues (205). TA methods are broadly categorised into four main approaches namely structural, model-based, statistical and transform-based techniques (206, 207).

Structural-based methods, firstly presented by Haralick (205), symbolize texture by applying the principle of mathematical morphology to define a primitive (microtexture) to be placed at a particular location (spatial arrangement or macrotexture). These methods are more useful for producing new objects, by using approaches such as addition and subtraction between elements than quantifying surface arrangement. The natural textures of brain tumours, having variability of microstructure, macrostructure and limited information of separation lines between them, can be poorly defined by these methods (208).

Model-based methods represent image texture-based on mathematical models, such as fractal or stochastic method (209, 210). The fractal model (211) can be useful for discriminating some natural textures. However, it is less flexible to provide orientation selectivity and is not appropriate to describe local image structures (206). The stochastic model requires the computational complexity to estimate texture parameters.

Statistical techniques analyse the spatial distribution of images’ grey-levels. The methods can be classified as first-, second- or higher-order statistics according to the number of pixels used to define the local feature. In first-order statistics, local features are solely obtained from individual pixel values. Second-order statistics construct matrices based on

pixel pair relationships and higher-order statistics consider number of consecutive pixels at each grey-level.

The first-order statistics include mean, variance, skewness and the kurtosis. However, some of these parameters can be roughly estimated visually, while provide limited information about the relative position of pixels to each other. For example, a checkerboard pattern in Figure 3.5 (a) has an equal number of black and white pixels, and produces the same grey-level histogram as Figure 3.5 (b).

(a) (b)

Figure 3.5: Two images having the same textural features of first-order statistics. Image (a) and (b) have the number of black and white elements.

As a result, it is difficult to differentiate the two images using the first-order statistical analysis (212). The second- and higher-order statistical methods, constructed from grey- level co-occurrence matrices (GLCMs) and grey-level run-length matrices (GLRLMs) respectively, have a tendency to obtain higher discrimination indices than the first-order statistics and visual examination (23). Although GLCMs and GLRLMs can describe surface pattern better, their matrices are rotational-variant (213), i.e. the rotation of the same

object produces different texture matrices and can lead to misinterpretation of object’s pattern.

Transform-based TA methods employ time-frequency analysis based on Fourier (214), Gabor (215) or Wavelet transforms (216). These methods transform an image to another space, using particular mathematical functions. The texture characteristics of a transformed image space are commonly represented by energy and frequency. Fourier transform has the potential to capture an image’s global features, however, it can be insufficient to define local features (217) and to provide spatial localisation (206). Imaging features of intracranial lesions that vary in space and time may not be captured by the Fourier transform method. Gabor filters offer an improved spatial localisation, however, their non-orthogonality application produces redundant features at different scales and is difficult to localise a spatial structure of natural textures (218, 219). Wavelets are an extension of windowed Fourier analysis (220), decomposing an image into multi-scale of spatial resolutions. Wavelets provide several advantages over the other two transform approaches. For example, a multiresolution decomposition can represent natural texture at a suitable scale with lower computational cost than Gabor filters (216); an orthogonality property of certain wavelet families produces non-redundant feature maps from an original image to different scales. In spite of these advantages, wavelet transforms are translation-variant (221) which can lead to translation-variant textural features, reducing classification accuracy. However, they can possibly supply additional textural properties that may not be captured in GLCMs and GLRLMs. In addition, wavelet transform methods are often found in the medical image analysis literature, including image-based TA software, such as MaZda tool (222).

The statistical methods potentially provide better classification outcome than the structural or transform based methods (208, 223). In TA-based brain studies, the first- order statistics, GLCMs, absolute gradient matrices, GLRLMs and wavelets are the well- known techniques for the characterisation of healthy and pathological human cerebral tissues (23, 24, 224). Among these approaches, the first- and second-order statistical analysis outperform wavelet transforms in the classification of Alzheimer’s disease based on T2-weighted brain images (225), and the most popular texture analysis methods for MR images was voted to be the GLCMs (23). In addition, compared with features derived from Laws and Haar wavelet, GLCM-based features can achieve higher accuracy in differentiating between anaplastic/large cell and non-anaplastic/large cell medulloblastoma in children (226). Dange et al. compared texture classification based on four methods: GLCMs, Haar, Daubechies-4, Symlet-8 (213). The study showed that in the case of rotation, Haar wavelet was the most efficient method in terms of classification accuracy and computation time. Although GLCMs can provide relative similar classification accuracy, it performed badly when images are rotated.

As discussed above, GLCMs are generally preferable in several applications. However, GLCMs require higher computation time and yield less accuracy when rotation takes place. Wavelet transform based features has been reported a high classification rate of some types of brain tumours (227). Therefore, wavelet transform based features are recommended as complementary features and offer superior result when image rotation is considered. In order to summarise the discussion aforementioned, the advantages and disadvantages of TA methods for diagnosing brain tumours are shown in Table 3.2.

Table 3.2: Advantages and disadvantage of TA for defining brain tumours.

Textural Analysis Advantages Disadvantages

Structural method e.g. morphological processing

It is useful for representing an object by using addition and subtraction between elements.

Micro and macrostructure of brain tumours’ MR images and faint separation lines between them can be poorly defined. Model-based

method

e.g. Fractal and Stochastic method

It offers sophisticated models for defining brain tumours.

It requires high computation time and provides deficiency of orientation selectivity.

Statistical analysis e.g. first-order statistics, GLCM, GLRLM

The first-order statistic is simply calculated and can describe simple structures of biological tissues. The second- and higher-order statistics provide higher discriminative power and are found to be useful in various studies.

The first-order statistic can give the same textural features of two distinct objects having the same grey-level distribution. The second- and higher-order statistics require high

computation time and shift- variant.

Transform-based method

e.g. Fourier, Gabor and wavelet transforms

Wavelet transforms offer multiscale decomposition which can provide a suitable scale for brain tumours’ MR images with low computational cost.

Discrete wavelet transform is shift-variant and energy derived from wavelet coefficients can be shift- variant, resulting in low classification accuracy.

As critically reviewed, this thesis aims to combine the advantages of the most commonly used sets of textural features derived from statistical and wavelet transform approaches. The first-, second- and higher-order statistics as well as Haar, Daubechies and Symlet wavelets are selected for our study. The theoretical background of these texture analysis methods and their associated textural features are explained in the following sections and Appendix A.

First-Order Statistics Based Textural Features