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Merge pull request #1119 from ikajic/filter-docu
Gabor filter docstrings
This commit is contained in:
Emmanuelle Gouillart
@@ -194,3 +194,6 @@
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- Alexey Umnov
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skimage.draw.ellipse bug fix and tests.
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- Ivana Kajic
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Updated description and examples in documentation for gabor filters
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+72
-20
@@ -13,27 +13,33 @@ def _sigma_prefactor(bandwidth):
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def gabor_kernel(frequency, theta=0, bandwidth=1, sigma_x=None, sigma_y=None,
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offset=0):
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n_stds=3, offset=0):
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"""Return complex 2D Gabor filter kernel.
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Frequency and orientation representations of the Gabor filter are similar
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to those of the human visual system. It is especially suitable for texture
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classification using Gabor filter banks.
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Gabor kernel is a Gaussian kernel modulated by a complex harmonic function.
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Harmonic function consists of an imaginary sine function and a real
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cosine function. Spatial frequency is inversely proportional to the
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wavelength of the harmonic and to the standard deviation of a Gaussian
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kernel. The bandwidth is also inversely proportional to the standard
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deviation.
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Parameters
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----------
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frequency : float
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Frequency of the harmonic function.
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theta : float
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Spatial frequency of the harmonic function. Specified in pixels.
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theta : float, optional
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Orientation in radians. If 0, the harmonic is in the x-direction.
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bandwidth : float
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bandwidth : float, optional
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The bandwidth captured by the filter. For fixed bandwidth, `sigma_x`
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and `sigma_y` will decrease with increasing frequency. This value is
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ignored if `sigma_x` and `sigma_y` are set by the user.
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sigma_x, sigma_y : float
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sigma_x, sigma_y : float, optional
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Standard deviation in x- and y-directions. These directions apply to
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the kernel *before* rotation. If `theta = pi/2`, then the kernel is
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rotated 90 degrees so that `sigma_x` controls the *vertical* direction.
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n_stds : scalar, optional
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The linear size of the kernel is n_stds (3 by default) standard
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deviations
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offset : float, optional
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Phase offset of harmonic function in radians.
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@@ -47,13 +53,29 @@ def gabor_kernel(frequency, theta=0, bandwidth=1, sigma_x=None, sigma_y=None,
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.. [1] http://en.wikipedia.org/wiki/Gabor_filter
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.. [2] http://mplab.ucsd.edu/tutorials/gabor.pdf
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Examples
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--------
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>>> from skimage.filter import gabor_kernel
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>>> from skimage import io
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>>> from matplotlib import pyplot as plt # doctest: +SKIP
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>>> gk = gabor_kernel(frequency=0.2)
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>>> plt.figure() # doctest: +SKIP
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>>> io.imshow(gk.real) # doctest: +SKIP
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>>> io.show() # doctest: +SKIP
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>>> # more ripples (equivalent to increasing the size of the
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>>> # Gaussian spread)
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>>> gk = gabor_kernel(frequency=0.2, bandwidth=0.1)
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>>> plt.figure() # doctest: +SKIP
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>>> io.imshow(gk.real) # doctest: +SKIP
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>>> io.show() # doctest: +SKIP
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"""
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if sigma_x is None:
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sigma_x = _sigma_prefactor(bandwidth) / frequency
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if sigma_y is None:
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sigma_y = _sigma_prefactor(bandwidth) / frequency
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n_stds = 3
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x0 = np.ceil(max(np.abs(n_stds * sigma_x * np.cos(theta)),
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np.abs(n_stds * sigma_y * np.sin(theta)), 1))
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y0 = np.ceil(max(np.abs(n_stds * sigma_y * np.cos(theta)),
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@@ -72,49 +94,79 @@ def gabor_kernel(frequency, theta=0, bandwidth=1, sigma_x=None, sigma_y=None,
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def gabor_filter(image, frequency, theta=0, bandwidth=1, sigma_x=None,
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sigma_y=None, offset=0, mode='reflect', cval=0):
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sigma_y=None, n_stds=3, offset=0, mode='reflect', cval=0):
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"""Return real and imaginary responses to Gabor filter.
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The real and imaginary parts of the Gabor filter kernel are applied to the
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image and the response is returned as a pair of arrays.
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Frequency and orientation representations of the Gabor filter are similar
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to those of the human visual system. It is especially suitable for texture
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classification using Gabor filter banks.
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Gabor filter is a linear filter with a Gaussian kernel which is modulated
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by a sinusoidal plane wave. Frequency and orientation representations of
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the Gabor filter are similar to those of the human visual system.
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Gabor filter banks are commonly used in computer vision and image
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processing. They are especially suitable for edge detection and texture
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classification.
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Parameters
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----------
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image : array
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image : 2-D array
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Input image.
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frequency : float
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Frequency of the harmonic function.
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theta : float
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Spatial frequency of the harmonic function. Specified in pixels.
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theta : float, optional
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Orientation in radians. If 0, the harmonic is in the x-direction.
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bandwidth : float
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bandwidth : float, optional
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The bandwidth captured by the filter. For fixed bandwidth, `sigma_x`
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and `sigma_y` will decrease with increasing frequency. This value is
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ignored if `sigma_x` and `sigma_y` are set by the user.
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sigma_x, sigma_y : float
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sigma_x, sigma_y : float, optional
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Standard deviation in x- and y-directions. These directions apply to
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the kernel *before* rotation. If `theta = pi/2`, then the kernel is
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rotated 90 degrees so that `sigma_x` controls the *vertical* direction.
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n_stds : scalar, optional
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The linear size of the kernel is n_stds (3 by default) standard
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deviations.
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offset : float, optional
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Phase offset of harmonic function in radians.
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mode : string, optional
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Mode used to convolve image with a kernel, passed to `ndimage.convolve`
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cval : scalar, optional
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Value to fill past edges of input if `mode` of convolution is
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'constant'. The parameter is passed to `ndimage.convolve`.
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Returns
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-------
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real, imag : arrays
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Filtered images using the real and imaginary parts of the Gabor filter
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kernel.
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kernel. Images are of the same dimensions as the input one.
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References
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----------
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.. [1] http://en.wikipedia.org/wiki/Gabor_filter
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.. [2] http://mplab.ucsd.edu/tutorials/gabor.pdf
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Examples
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--------
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>>> from skimage.filter import gabor_filter
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>>> from skimage import data, io
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>>> from matplotlib import pyplot as plt # doctest: +SKIP
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>>> image = data.coins()
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>>> # detecting edges in a coin image
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>>> filt_real, filt_imag = gabor_filter(image, frequency=0.6)
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>>> plt.figure() # doctest: +SKIP
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>>> io.imshow(filt_real) # doctest: +SKIP
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>>> io.show() # doctest: +SKIP
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>>> # less sensitivity to finer details with the lower frequency kernel
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>>> filt_real, filt_imag = gabor_filter(image, frequency=0.1)
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>>> plt.figure() # doctest: +SKIP
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>>> io.imshow(filt_real) # doctest: +SKIP
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>>> io.show() # doctest: +SKIP
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"""
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assert_nD(image, 2)
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g = gabor_kernel(frequency, theta, bandwidth, sigma_x, sigma_y, offset)
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g = gabor_kernel(frequency, theta, bandwidth, sigma_x, sigma_y, n_stds,
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offset)
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filtered_real = ndimage.convolve(image, np.real(g), mode=mode, cval=cval)
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filtered_imag = ndimage.convolve(image, np.imag(g), mode=mode, cval=cval)
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