Comparison of texture features based on Gabor filters
Summary (2 min read)
- At this point, the question arises of how to measure the usefulness of different features.
- None of the aforementioned evaluation methods can be generally considered as superior because each of them is informative in its own way and each has its limitations.
- In Section IV, a number of texture segmentation experiments are carried out and the properties of the considered operators are assessed using the classification result comparison method.
B. Gabor Energy Features
- The outputs of a symmetric and an antisymmetric kernel filter in each image point can be combined in a single quantity that is called the Gabor energy.
- This feature is related to the model of a specific type of orientation selective neuron in the primary visual cortex called the complex cell  and is defined in the following way: (3) where and are the responses of the linear symmetric and antisymmetric Gabor filters, respectively.
- The Gabor energy is closely related to the local power spectrum.
- The local power spectrum associated with a pixel in an image is defined as the squared modulus of the Fourier transform of the product of the image function and a window functio that restricts the Fourier analysis to a neighborhood of the ixel of interest.
- Using a Gaussian windowing function as the one used in (2) and taking into account (1) and (3) the following relation between the local power spectrum and the Gabor energy features can be proven: (4).
C. Complex Moments Features
- In  and , the real and imaginary parts of the complex moments of the local power spectrum were proposed as features that give information about the presence or absence of dominant texture orientations.
- In , the authors discuss the advantages of using the real and imaginary parts of the complex moments as features instead of their moduli and arguments.
- In their experiments, the authors use as features the nonzero real and imaginary parts of the complex moments of the local power spectrum.
- This amounts to 43 nonzero real values out of which only 24 are linearly independent because .
- Such a step can improve the separability of the feature clusters, but then this step should also be applied to the other features.
D. Grating Cell Operator Features
- Grating cells are selective for orientation but differ from the majority of orientation selective cells found in the mentioned cortical areas in that they do not react to single lines or edges, as for instance simple cells (modeled by Gabor filters) or complex cells (modeled by Gabor energy operators) do.
- The response increases with the number of bars that cross the receptive field of the cell and saturates at about ten bars.
- The grating cell operator was conceived to reproduce the properties of grating cells as known from electrophysiological researches –.
- Essentially, this operator signals the presence of one-dimensional (1-D) periodicity of certain preferred spatial frequency and orientation in 2-D images.
A. Comparison Method
- The feature vectors computed in different points of a texture image are not identical; they rather form a cluster in the multidimensional feature space.
- A linear transform that, under certain conditions, realizes such a projection was first introduced by Fisher  and is called the Fisher linear discriminant function.
- This projection of the feature vectors into the 1-D space maximizes theFisher criterion, which measures the separability of the two concerned clusters in the reduced space (7) where and are the standard deviations of the distributions of the projected feature vectors of the two clusters andand are the projections of the meansand , respectively.
- Strictly speaking, the transform given by (6) need not necessarily maximize the value of according to (7) for arbitrary distributions.
- Only recently, this criterion has been applied to the evaluation of texture feature extraction operators .
- The authors evaluated the performance of the operators presented in Section II according to the Fisher criterion by looking at the pair-wise separability of the feature clusters corresponding to nine test textures (Fig. 1).
- The separability achieved for the complex moments features is smaller than the one achieved with the Gabor energy features.
- Similarly, in , the authors stress that the grating cell operator was conceived to respond only to a given orientation and frequency of the input stimuli.
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Cites background from "Comparison of texture features base..."
...Gabor .lters [Grigorescu et al. 2002] and other steerable .lters [Freeman and Adelson 1991] typically employ a set of oriented, elliptic kernels to help analyze parallel structures or texture patterns....
...Gabor filters [Grigorescu et al. 2002] and other steerable filters [Freeman and Adelson 1991] typically employ a set of oriented, elliptic kernels to help analyze parallel structures or texture patterns....
...) Ó Ô Â - Â 3 Ô Õ Z 3 Z 3 3 where S [ and S b are the standard deviations...
"Comparison of texture features base..." refers methods in this paper
...If needed, scale and orientation invariance can be added to the methods in a way similar to the one used in other applications , ....
...frequency domain ....
...compares them with the linear Gabor features or with the thresholded Gabor features , ....
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Frequently Asked Questions (8)
Q1. What is the reason why the grating cell features are spatially more extended?
One should note that the grating cell features are spatially more extended, a property that is due to the weighted averaging step.
Q2. Why did the authors not include textures at different scales and orientations?
The authors did not include textures at different scales and orientations because the operators compared here are not scaling and rotation invariant, a property that is mainly due to the frequency and orientation selectivity of the Gabor filters.
Q3. What is the Fisher criterion for determining the distance between two clusters of feature?
In order to determine the distance between two clusters of feature vectors, it is sufficient to look at their projections onto a 1-D space, i.e., a line, under the assumption that this projection maximizes the separability of the clusters in the 1-D space.
Q4. What is the effect of local averaging on the texture operators?
the texture operators were also tested for their ability to detect texture in an image and to separate texture information from other image features like edges and contours of objects.
Q5. Why was the weighted local averaging part included in the grating cell operator?
It has been included in the model in order to reproduce a specific property of grating cells, namely, that a grating cell starts to respond when at least three parallel bars are present in its receptive field and that its response grows linearly with the addition of further bars to the grating, reaching saturation at about ten bars , .
Q6. What is the Fisher criterion for determining the separability of two clusters?
The authors evaluated the performance of the operators presented in Section II according to the Fisher criterion by looking at the pair-wise separability of the feature clusters corresponding to nine test textures (Fig. 1).While thenumberof test imagesusedis limited,onehastopoint out that the only aspect that was taken into account in selecting them is that the textures show a certain degree of “orientedness” which is to guarantee that (some of) the Gabor filters employed will respond.
Q7. How many linearly independent values are used for each point in the image?
The authors use this set of 24 linearly independent values computed for each point in the image as a feature vector associated with that point.
Q8. How was the interclass texture discrimination evaluated?
The interclass texture discrimination properties of different features were assessed by Fisher linear discriminant analysis and by the (classical) classification result comparison method.