2011/03/08 - 해당되는 글 1건

Explanation of parameters

Gabor filtering

This block implements one or multiple convolutions of an input image with a two-dimensional Gabor function:

equation 1.1

To visualize a Gabor function select the option "Gabor function" under "Output image". The Gabor function for the specified values of the parameters "wavelength", "orientation", "phase offset", "aspect ratio", and "bandwidth" will be calculated and displayed as an intensity map image in the output window. (Light and dark gray colors correspond to positive and negative function values, respectively.) The image in the output widow has the same size as the input image: select, for instance, input image octagon.jpg to get an output image of size 100 by 100. If lists of values are specified under "orientation(s)" and "phase offset(s)", only the first values in these lists will be used.

Two-dimensional Gabor functions were proposed by Daugman [1] to model the spatial summation properties (of the receptive fields) of simple cells in the visual cortex. They are widely used in image processing, computer vision, neuroscience and psychophysics. The parametrisaton used in Eq.(1) follows references [2-7] where further details can be found.



Wavelength (λ)

This is the wavelength of the cosine factor of the Gabor filter kernel and herewith the preferred wavelength of this filter. Its value is specified in pixels. Valid values are real numbers equal to or greater than 2. The value λ=2 should not be used in combination with phase offset φ=-90 or φ=90 because in these cases the Gabor function is sampled in its zero crossings. In order to prevent the occurence of undesired effects at the image borders, the wavelength value should be smaller than one fifth of the input image size.


The images (of size 100 x 100) on the left show Gabor filter kernels with values of the wavelength parameter of 5, 10 and 15, from left to right, respectively. The values of the other parameters are as follows: orientation 0, phase offset 0, aspect ratio 0.5, and bandwidth 1.


Orientation(s) (θ)

This parameter specifies the orientation of the normal to the parallel stripes of a Gabor function. Its value is specified in degrees. Valid values are real numbers between 0 and 360.



The images (of size 100 x 100) on the left show Gabor filter kernels with values of the orientation parameter of 0, 45 and 90, from left to right, respectively. The values of the other parameters are as follows: wavelength 10, phase offset 0, aspect ratio 0.5, and bandwidth 1.

For one single convolution, enter one orientation value and set the value of the last parameter in the block "number of orientations" to 1. 
If "number of orientations" is set to an integer value N, N >= 1, then N convolutions will be computed. The orientations of the corresponding Gabor functions are equidistantly distributed between 0 and 360 degrees in increments of 360/N, starting from the value specified under "orientation(s)". An alternative way of computing multiple convolutions for different orientations is to specify under "orientation(s)" a list of values separated by commas (e.g. 0,45,110). In this case, the value of the parameter "number of orientations" is ignored. 


Phase offset(s) (φ)

The phase offset φ in the argument of the cosine factor of the Gabor function is specified in degrees. Valid values are real numbers between -180 and 180. The values 0 and 180 correspond to center-symmetric 'center-on' and 'center-off' functions, respectively, while -90 and 90 correspond to anti-symmetric functions. All other cases correspond to asymmetric functions.

T

he images (of size 100 x 100) on the left show Gabor filter kernels with values of the phase offset parameter of 0, 180, -90 and 90 dgerees, from left to right, respectively. The values of the other parameters are as follows: wavelength 10, orientation 0, aspect ratio 0.5, and bandwidth 1.

If one single value is specified, one convolution per orientation will be computed. If a list of values is given (e.g. 0,90 which is default), multiple convolutions per orientation will be computed, one for each value in the phase offset list. 


Aspect ratio (γ)

This parameter, called more precisely the spatial aspect ratio, specifies the ellipticity of the support of the Gabor function. For γ = 1, the support is circular. For γ < 1 the support is elongated in orientation of the parallel stripes of the function. Default value is γ = 0.5.



The images (of size 100 x 100) on the left show Gabor filter kernels with values of the aspect ratio parameter of 0.5 and 1, from left to right, respectively. The values of the other parameters are as follows: wavelength 10, orientation 0, phase offset 0, and bandwidth 1.


Bandwidth (b)

The half-response spatial frequency bandwidth b (in octaves) of a Gabor filter is related to the ratio σ / λ, where σ and λ are the standard deviation of the Gaussian factor of the Gabor function and the preferred wavelength, respectively, as follows:

equation 2.1

The value of σ cannot be specified directly. It can only be changed through the bandwidth b. The bandwidth value must be specified as a real positive number. Default is 1, in which case σ and λ are connected as follows: σ = 0.56 λ. The smaller the bandwidth, the larger σ, the support of the Gabor function and the number of visible parallel excitatory and inhibitory stripe zones.


The images (of size 100 x 100) on the left show Gabor filter kernels with values of the bandwidth parameter of 0.5, 1, and 2, from left to right, respectively. The values of the other parameters are as follows: wavelength 10, orientation 0, phase offset 0, and aspect ratio 0.5.


Number of orientations

Default value is 1. If an integer value N, N >= 1, is specified then N convolutions will computed. The orientations of the corresponding Gabor functions are equidistantly distributed between 0 and 360 degrees, with increments of 360/N, starting from the value specified in "orientation(s)". For this option to work, one single value (without a comma present) must be specified for the parameter "orientation(s)".

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