Related Works

1.3.1 Texture Analysis

“Definition” of Texture

At first, we should give a definition to texture, but it is unfortunately that there is not a precise and identical definition to texture until now. Although there is not a best definition to texture, this feature is so obvious that we still can’t neglect it. This situation is analogic to the tone in sound. We can easily distinguish the sound between violin and piano, but it is also hard to give a physical meaning to tone.

Many people have proposed some descriptions about texture, and the

“definition” of texture is formulated depending on the particular application and that there is no generally agreed upon definition. We give some perceptually motivated examples here.

• “We may regard texture as what constitutes a macroscopic region. Its structure is simply attributed to the repetitive patterns in which elements or primitives are arranged according to a placement rule.” [5]

•“A region in an image has a constant texture if a set of local statistics or other local properties of the picture function are constant, slowly varying, or approximately periodic.” [6]

• “The notion of texture appears to depend upon three ingredients: (i) some local‘order’ is repeated over a region which is large in comparison to the order’s size,(ii) the order consists in the nonrandom arrangement of elementary parts, and (iii)the parts are roughly uniform entities having approximately the same dimensions everywhere within the textured region.” [7]

In this thesis we refer to descriptions which have been proposed, and simplify the situation:

1. Texture is characterized by properties of a local region and in this region there should adequate spatial-relationships between elements or primitives.

In this thesis spatial-relationships simply mean the orientation and frequency.

2. Here we discuss the homogeneous texture which means that there are similar features over all single texture patterns. In means that the size and orientation invariant problems which may not be discriminable are not considered in this thesis.

Filter Design

There have been many algorithms to cope with this topic, and these algorithms may generally be grouped into the following major classes: feature space clustering, statistical classification, multi-channel filtering approaches: texture gradient operators, optimal filtering technique, and toxton-based methods. Among the algorithms mentioned above, the multi-channel filtering approach appears to be one of successful one in texture segmentation. Here we will discuss some algorithms in this class.

Supervised methods

Bovic, Clark and Geisler [8], 錯誤! 找不到參照來源。 give a very detailed analysis of the Gabor function using localized spatial filters for texture feature extraction. Bovik mentioned three supervised approaches to select filter locations using empirical information based on the power spectrum characteristics of the individual textures. For strongly oriented textures, the most significant spectral peak

along the dominant orientation direction is used as a filter location. Picking the lower fundamental frequency identifies periodic textures. Finally, the non-oriented textures using the center frequencies of the two largest maxima are recommended. It is clear that an automated method is more attractive.

Dunn and Higgins [10] developed a method to select optimal filter parameters based on known samples of the textures. This is a totally supervised approach that focused mainly on using the minimum number of filters. Only the specific filter that separates two textures optimally is used to partition an image. The optimal filter responds strongly to one class and may express a lack of textural information of the other class. This other class is not identified to have a particular characteristic but lacking a characteristic of the other class. The more global solution to the problem is to spread filters throughout the frequency domain field to capture salient information.

Unsupervised methods

By providing near uniform coverage of the spatial-frequency domain with Gabor filters, the problem of selecting central frequencies is avoided. Jain and Farrokhnia [11] implemented real Gabor filters for texture segmentation using frequency bandwidth of one octave, center frequency spacing of one octave, angular bandwidth of 45°, and angular spacing of 45°.

The frequencies used in it for filters are:

2

1 , 2 2, 4 2, ……

(

)

For textures with distinct spectral peaks which correspond to some global regularities, T. N. Tan proposed a useful method [12] to design Gabor dilters automatically. The central step in the algorithm is spectral detection. It detects a global spectral peak a time, and repeatedly detects conspicuous peaks by erasing operation on the spatial frequency plane: the power spectrum of a small neighborhood (e.g. 7×7) around the detected peak is set to zero. The iteration of peak detection terminates when the ratio of the magnitude of current peak to that of the first (e.g., the highest) peak is less than a pre-specified value (e.g., 80%).

Feature Extraction

Filter outputs by default are not appropriate for identifying key texture features.

A number of feature extraction methods were proposed to extract useful information from the filter outputs. Clausi and Jernigan [13] reviewed some feature extraction methods. Some of which include:

1. Using the Magnitude Response, where the texture identification can be performed based on the magnitude of the output of the Gabor functions [8].

In the case of a filter that matches the particular texture the magnitude of the output is large to allow identification.

2. Applying the Spatial Smoothing where Gaussian smoothing is known to improve the performance of Gabor filters for texture analysis. Bovik et al [8]

recommended post filtering the channel amplitudes with Gaussian filters having the same shape as the corresponding channel filters, but wider spatial extents.

3. Using only the Real Component Jain and Farrohknia [11] used a bank of even symmetric Gabor filters to characterize the channels.

4. Using Pixel Adjacency Information Jain and Farrokhnia suggested in [11]

using this method as extra features due to the fact that pixels belonging to the same texture are close to each other, so they should be clustered together.

However, this will not perform well if there are some texture regions that are not adjacent in the image.

5. Using a Non Linear Sigmoidal function that saturates the output of the filter where each filter image was subjected to a Sigmoidal non linear transformation [11] that can be interpreted as a blob detector. It is indicated by:

Where a is an empirical constant, a = 0.25. Their explanation was that most textures can be characterized by blobs of different sized and orientations.

6. Applying Full Wave Rectification: many HVS models consider the evolvement of non linear behaviour [14]. Adding the absolute value of real and imaginary responses -full wave rectification- is a non linear method that is used to process the complex filter outputs [13].

1.3.2 Cellular Neural Networks

As we have mentioned above, there have been a lot of researches on texture based on the Gabor filter, but a drawback of Gabor filtering approaches is that they are computationally intensive.

Recently, a novel class of information-processing system called cellular neural networks (CNN) has been proposed [15], [16]. Cellular neural/nonlinear networks (CNN’s) show a strong resemblance to biological visual systems. It is therefore not surprising that several CNN models have been produced for the unraveling of the processing in some parts of the vertebrate visual pathway [18], and the Gabor-like filters also have been implemented on CNN [20].

The advantage of CNN’s is that they can be implemented in analog VLSI alongside photosensors which sense the image, and the filter outputs can be computed in less time than required by serial digital computer implementations and be read off the chip directly, relieving the computational bottleneck of preprocessing with Gabor filters.