Module: filters  
skimage.filters.apply_hysteresis_threshold(…) Apply hysteresis thresholding to image.  
skimage.filters.correlate_sparse(image, kernel) Compute valid cross-correlation of padded_array and kernel.  
skimage.filters.difference_of_gaussians(…) Find features between low_sigma and high_sigma in size.  
skimage.filters.farid(image, *[, mask]) Find the edge magnitude using the Farid transform.  
skimage.filters.farid_h(image, *[, mask]) Find the horizontal edges of an image using the Farid transform.  
skimage.filters.farid_v(image, *[, mask]) Find the vertical edges of an image using the Farid transform.  
skimage.filters.frangi(image[, sigmas, …]) Filter an image with the Frangi vesselness filter.  
skimage.filters.gabor(image, frequency[, …]) Return real and imaginary responses to Gabor filter.  
skimage.filters.gabor_kernel(frequency[, …]) Return complex 2D Gabor filter kernel.  
skimage.filters.gaussian(image[, sigma, …]) Multi-dimensional Gaussian filter.  
skimage.filters.hessian(image[, sigmas, …]) Filter an image with the Hybrid Hessian filter.  
skimage.filters.inverse(data[, …]) Apply the filter in reverse to the given data.  
skimage.filters.laplace(image[, ksize, mask]) Find the edges of an image using the Laplace operator.  
skimage.filters.median(image[, selem, out, …]) Return local median of an image.  
skimage.filters.meijering(image[, sigmas, …]) Filter an image with the Meijering neuriteness filter.  
skimage.filters.prewitt(image[, mask, axis, …]) Find the edge magnitude using the Prewitt transform.  
skimage.filters.prewitt_h(image[, mask]) Find the horizontal edges of an image using the Prewitt transform.  
skimage.filters.prewitt_v(image[, mask]) Find the vertical edges of an image using the Prewitt transform.  
skimage.filters.rank_order(image) Return an image of the same shape where each pixel is the index of the pixel value in the ascending order of the unique values of image, aka the rank-order value.  
skimage.filters.roberts(image[, mask]) Find the edge magnitude using Roberts’ cross operator.  
skimage.filters.roberts_neg_diag(image[, mask]) Find the cross edges of an image using the Roberts’ Cross operator.  
skimage.filters.roberts_pos_diag(image[, mask]) Find the cross edges of an image using Roberts’ cross operator.  
skimage.filters.sato(image[, sigmas, …]) Filter an image with the Sato tubeness filter.  
skimage.filters.scharr(image[, mask, axis, …]) Find the edge magnitude using the Scharr transform.  
skimage.filters.scharr_h(image[, mask]) Find the horizontal edges of an image using the Scharr transform.  
skimage.filters.scharr_v(image[, mask]) Find the vertical edges of an image using the Scharr transform.  
skimage.filters.sobel(image[, mask, axis, …]) Find edges in an image using the Sobel filter.  
skimage.filters.sobel_h(image[, mask]) Find the horizontal edges of an image using the Sobel transform.  
skimage.filters.sobel_v(image[, mask]) Find the vertical edges of an image using the Sobel transform.  
skimage.filters.threshold_isodata([image, …]) Return threshold value(s) based on ISODATA method.  
skimage.filters.threshold_li(image, *[, …]) Compute threshold value by Li’s iterative Minimum Cross Entropy method.  
skimage.filters.threshold_local(image, …) Compute a threshold mask image based on local pixel neighborhood.  
skimage.filters.threshold_mean(image) Return threshold value based on the mean of grayscale values.  
skimage.filters.threshold_minimum([image, …]) Return threshold value based on minimum method.  
skimage.filters.threshold_multiotsu(image[, …]) Generate classes-1 threshold values to divide gray levels in image.  
skimage.filters.threshold_niblack(image[, …]) Applies Niblack local threshold to an array.  
skimage.filters.threshold_otsu([image, …]) Return threshold value based on Otsu’s method.  
skimage.filters.threshold_sauvola(image[, …]) Applies Sauvola local threshold to an array.  
skimage.filters.threshold_triangle(image[, …]) Return threshold value based on the triangle algorithm.  
skimage.filters.threshold_yen([image, …]) Return threshold value based on Yen’s method.  
skimage.filters.try_all_threshold(image[, …]) Returns a figure comparing the outputs of different thresholding methods.  
skimage.filters.unsharp_mask(image[, …]) Unsharp masking filter.  
skimage.filters.wiener(data[, …]) Minimum Mean Square Error (Wiener) inverse filter.  
skimage.filters.window(window_type, shape[, …]) Return an n-dimensional window of a given size and dimensionality.  
skimage.filters.LPIFilter2D(…) Linear Position-Invariant Filter (2-dimensional)  
skimage.filters.rank    apply_hysteresis_threshold  
skimage.filters.apply_hysteresis_threshold(image, low, high) [source]
 
Apply hysteresis thresholding to image. This algorithm finds regions where image is greater than high OR image is greater than low and that region is connected to a region greater than high.  Parameters 
 
imagearray, shape (M,[ N, …, P]) 

Grayscale input image.  
lowfloat, or array of same shape as image 

Lower threshold.  
highfloat, or array of same shape as image 

Higher threshold.    Returns 
 
thresholdedarray of bool, same shape as image 

Array in which True indicates the locations where image was above the hysteresis threshold.     References  
1  
J. Canny. A computational approach to edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence. 1986; vol. 8, pp.679-698. DOI:10.1109/TPAMI.1986.4767851   Examples >>> image = np.array([1, 2, 3, 2, 1, 2, 1, 3, 2])
>>> apply_hysteresis_threshold(image, 1.5, 2.5).astype(int)
array([0, 1, 1, 1, 0, 0, 0, 1, 1])
 
 correlate_sparse  
skimage.filters.correlate_sparse(image, kernel, mode='reflect') [source]
 
Compute valid cross-correlation of padded_array and kernel. This function is fast when kernel is large with many zeros. See scipy.ndimage.correlate for a description of cross-correlation.  Parameters 
 
imagendarray, dtype float, shape (M, N,[ …,] P) 

The input array. If mode is ‘valid’, this array should already be padded, as a margin of the same shape as kernel will be stripped off.  
kernelndarray, dtype float shape (Q, R,[ …,] S) 

The kernel to be correlated. Must have the same number of dimensions as padded_array. For high performance, it should be sparse (few nonzero entries).  
modestring, optional 

See scipy.ndimage.correlate for valid modes. Additionally, mode ‘valid’ is accepted, in which case no padding is applied and the result is the result for the smaller image for which the kernel is entirely inside the original data.    Returns 
 
resultarray of float, shape (M, N,[ …,] P) 

The result of cross-correlating image with kernel. If mode ‘valid’ is used, the resulting shape is (M-Q+1, N-R+1,[ …,] P-S+1).     
 difference_of_gaussians  
skimage.filters.difference_of_gaussians(image, low_sigma, high_sigma=None, *, mode='nearest', cval=0, multichannel=False, truncate=4.0) [source]
 
Find features between low_sigma and high_sigma in size. This function uses the Difference of Gaussians method for applying band-pass filters to multi-dimensional arrays. The input array is blurred with two Gaussian kernels of differing sigmas to produce two intermediate, filtered images. The more-blurred image is then subtracted from the less-blurred image. The final output image will therefore have had high-frequency components attenuated by the smaller-sigma Gaussian, and low frequency components will have been removed due to their presence in the more-blurred intermediate.  Parameters 
 
imagendarray 

Input array to filter.  
low_sigmascalar or sequence of scalars 

Standard deviation(s) for the Gaussian kernel with the smaller sigmas across all axes. The standard deviations are given for each axis as a sequence, or as a single number, in which case the single number is used as the standard deviation value for all axes.  
high_sigmascalar or sequence of scalars, optional (default is None) 

Standard deviation(s) for the Gaussian kernel with the larger sigmas across all axes. The standard deviations are given for each axis as a sequence, or as a single number, in which case the single number is used as the standard deviation value for all axes. If None is given (default), sigmas for all axes are calculated as 1.6 * low_sigma.  
mode{‘reflect’, ‘constant’, ‘nearest’, ‘mirror’, ‘wrap’}, optional 

The mode parameter determines how the array borders are handled, where cval is the value when mode is equal to ‘constant’. Default is ‘nearest’.  
cvalscalar, optional 

Value to fill past edges of input if mode is ‘constant’. Default is 0.0  
multichannelbool, optional (default: False) 

Whether the last axis of the image is to be interpreted as multiple channels. If True, each channel is filtered separately (channels are not mixed together).  
truncatefloat, optional (default is 4.0) 

Truncate the filter at this many standard deviations.    Returns 
 
filtered_imagendarray 

the filtered array.      See also  
skimage.feature.blog_dog 
  Notes This function will subtract an array filtered with a Gaussian kernel with sigmas given by high_sigma from an array filtered with a Gaussian kernel with sigmas provided by low_sigma. The values for high_sigma must always be greater than or equal to the corresponding values in low_sigma, or a ValueError will be raised. When high_sigma is none, the values for high_sigma will be calculated as 1.6x the corresponding values in low_sigma. This ratio was originally proposed by Marr and Hildreth (1980) [1] and is commonly used when approximating the inverted Laplacian of Gaussian, which is used in edge and blob detection. Input image is converted according to the conventions of img_as_float. Except for sigma values, all parameters are used for both filters. References  
1  
Marr, D. and Hildreth, E. Theory of Edge Detection. Proc. R. Soc. Lond. Series B 207, 187-217 (1980). https://doi.org/10.1098/rspb.1980.0020   Examples Apply a simple Difference of Gaussians filter to a color image: >>> from skimage.data import astronaut
>>> from skimage.filters import difference_of_gaussians
>>> filtered_image = difference_of_gaussians(astronaut(), 2, 10,
...                                          multichannel=True)
 Apply a Laplacian of Gaussian filter as approximated by the Difference of Gaussians filter: >>> filtered_image = difference_of_gaussians(astronaut(), 2,
...                                          multichannel=True)
 Apply a Difference of Gaussians filter to a grayscale image using different sigma values for each axis: >>> from skimage.data import camera
>>> filtered_image = difference_of_gaussians(camera(), (2,5), (3,20))
 
 farid  
skimage.filters.farid(image, *, mask=None) [source]
 
Find the edge magnitude using the Farid transform.  Parameters 
 
image2-D array 

Image to process.  
mask2-D array, optional 

An optional mask to limit the application to a certain area. Note that pixels surrounding masked regions are also masked to prevent masked regions from affecting the result.    Returns 
 
output2-D array 

The Farid edge map.      See also  
sobel, prewitt, canny 
  Notes Take the square root of the sum of the squares of the horizontal and vertical derivatives to get a magnitude that is somewhat insensitive to direction. Similar to the Scharr operator, this operator is designed with a rotation invariance constraint. References  
1  
Farid, H. and Simoncelli, E. P., “Differentiation of discrete multidimensional signals”, IEEE Transactions on Image Processing 13(4): 496-508, 2004. DOI:10.1109/TIP.2004.823819  
2  
Wikipedia, “Farid and Simoncelli Derivatives.” Available at: <https://en.wikipedia.org/wiki/Image_derivatives#Farid_and_Simoncelli_Derivatives>   Examples >>> from skimage import data
>>> camera = data.camera()
>>> from skimage import filters
>>> edges = filters.farid(camera)
 
 farid_h  
skimage.filters.farid_h(image, *, mask=None) [source]
 
Find the horizontal edges of an image using the Farid transform.  Parameters 
 
image2-D array 

Image to process.  
mask2-D array, optional 

An optional mask to limit the application to a certain area. Note that pixels surrounding masked regions are also masked to prevent masked regions from affecting the result.    Returns 
 
output2-D array 

The Farid edge map.     Notes The kernel was constructed using the 5-tap weights from [1]. References  
1  
Farid, H. and Simoncelli, E. P., “Differentiation of discrete multidimensional signals”, IEEE Transactions on Image Processing 13(4): 496-508, 2004. DOI:10.1109/TIP.2004.823819  
2  
Farid, H. and Simoncelli, E. P. “Optimally rotation-equivariant directional derivative kernels”, In: 7th International Conference on Computer Analysis of Images and Patterns, Kiel, Germany. Sep, 1997.   
 farid_v  
skimage.filters.farid_v(image, *, mask=None) [source]
 
Find the vertical edges of an image using the Farid transform.  Parameters 
 
image2-D array 

Image to process.  
mask2-D array, optional 

An optional mask to limit the application to a certain area. Note that pixels surrounding masked regions are also masked to prevent masked regions from affecting the result.    Returns 
 
output2-D array 

The Farid edge map.     Notes The kernel was constructed using the 5-tap weights from [1]. References  
1  
Farid, H. and Simoncelli, E. P., “Differentiation of discrete multidimensional signals”, IEEE Transactions on Image Processing 13(4): 496-508, 2004. DOI:10.1109/TIP.2004.823819   
 frangi  
skimage.filters.frangi(image, sigmas=range(1, 10, 2), scale_range=None, scale_step=None, alpha=0.5, beta=0.5, gamma=15, black_ridges=True, mode='reflect', cval=0) [source]
 
Filter an image with the Frangi vesselness filter. This filter can be used to detect continuous ridges, e.g. vessels, wrinkles, rivers. It can be used to calculate the fraction of the whole image containing such objects. Defined only for 2-D and 3-D images. Calculates the eigenvectors of the Hessian to compute the similarity of an image region to vessels, according to the method described in [1].  Parameters 
 
image(N, M[, P]) ndarray 

Array with input image data.  
sigmasiterable of floats, optional 

Sigmas used as scales of filter, i.e., np.arange(scale_range[0], scale_range[1], scale_step)  
scale_range2-tuple of floats, optional 

The range of sigmas used.  
scale_stepfloat, optional 

Step size between sigmas.  
alphafloat, optional 

Frangi correction constant that adjusts the filter’s sensitivity to deviation from a plate-like structure.  
betafloat, optional 

Frangi correction constant that adjusts the filter’s sensitivity to deviation from a blob-like structure.  
gammafloat, optional 

Frangi correction constant that adjusts the filter’s sensitivity to areas of high variance/texture/structure.  
black_ridgesboolean, optional 

When True (the default), the filter detects black ridges; when False, it detects white ridges.  
mode{‘constant’, ‘reflect’, ‘wrap’, ‘nearest’, ‘mirror’}, optional 

How to handle values outside the image borders.  
cvalfloat, optional 

Used in conjunction with mode ‘constant’, the value outside the image boundaries.    Returns 
 
out(N, M[, P]) ndarray 

Filtered image (maximum of pixels across all scales).      See also  
meijering


sato


hessian

  Notes Written by Marc Schrijver, November 2001 Re-Written by D. J. Kroon, University of Twente, May 2009, [2] Adoption of 3D version from D. G. Ellis, Januar 20017, [3] References  
1  
Frangi, A. F., Niessen, W. J., Vincken, K. L., & Viergever, M. A. (1998,). Multiscale vessel enhancement filtering. In International Conference on Medical Image Computing and Computer-Assisted Intervention (pp. 130-137). Springer Berlin Heidelberg. DOI:10.1007/BFb0056195  
2  
Kroon, D. J.: Hessian based Frangi vesselness filter.  
3  
Ellis, D. G.: https://github.com/ellisdg/frangi3d/tree/master/frangi   
 gabor  
skimage.filters.gabor(image, frequency, theta=0, bandwidth=1, sigma_x=None, sigma_y=None, n_stds=3, offset=0, mode='reflect', cval=0) [source]
 
Return real and imaginary responses to Gabor filter. The real and imaginary parts of the Gabor filter kernel are applied to the image and the response is returned as a pair of arrays. Gabor filter is a linear filter with a Gaussian kernel which is modulated by a sinusoidal plane wave. Frequency and orientation representations of the Gabor filter are similar to those of the human visual system. Gabor filter banks are commonly used in computer vision and image processing. They are especially suitable for edge detection and texture classification.  Parameters 
 
image2-D array 

Input image.  
frequencyfloat 

Spatial frequency of the harmonic function. Specified in pixels.  
thetafloat, optional 

Orientation in radians. If 0, the harmonic is in the x-direction.  
bandwidthfloat, optional 

The bandwidth captured by the filter. For fixed bandwidth, sigma_x and sigma_y will decrease with increasing frequency. This value is ignored if sigma_x and sigma_y are set by the user.  
sigma_x, sigma_yfloat, optional 

Standard deviation in x- and y-directions. These directions apply to the kernel before rotation. If theta = pi/2, then the kernel is rotated 90 degrees so that sigma_x controls the vertical direction.  
n_stdsscalar, optional 

The linear size of the kernel is n_stds (3 by default) standard deviations.  
offsetfloat, optional 

Phase offset of harmonic function in radians.  
mode{‘constant’, ‘nearest’, ‘reflect’, ‘mirror’, ‘wrap’}, optional 

Mode used to convolve image with a kernel, passed to ndi.convolve  
cvalscalar, optional 

Value to fill past edges of input if mode of convolution is ‘constant’. The parameter is passed to ndi.convolve.    Returns 
 
real, imagarrays 

Filtered images using the real and imaginary parts of the Gabor filter kernel. Images are of the same dimensions as the input one.     References  
1  
https://en.wikipedia.org/wiki/Gabor_filter  
2  
https://web.archive.org/web/20180127125930/http://mplab.ucsd.edu/tutorials/gabor.pdf   Examples >>> from skimage.filters import gabor
>>> from skimage import data, io
>>> from matplotlib import pyplot as plt  
 >>> image = data.coins()
>>> # detecting edges in a coin image
>>> filt_real, filt_imag = gabor(image, frequency=0.6)
>>> plt.figure()            
>>> io.imshow(filt_real)    
>>> io.show()               
 >>> # less sensitivity to finer details with the lower frequency kernel
>>> filt_real, filt_imag = gabor(image, frequency=0.1)
>>> plt.figure()            
>>> io.imshow(filt_real)    
>>> io.show()               
 
 gabor_kernel  
skimage.filters.gabor_kernel(frequency, theta=0, bandwidth=1, sigma_x=None, sigma_y=None, n_stds=3, offset=0) [source]
 
Return complex 2D Gabor filter kernel. Gabor kernel is a Gaussian kernel modulated by a complex harmonic function. Harmonic function consists of an imaginary sine function and a real cosine function. Spatial frequency is inversely proportional to the wavelength of the harmonic and to the standard deviation of a Gaussian kernel. The bandwidth is also inversely proportional to the standard deviation.  Parameters 
 
frequencyfloat 

Spatial frequency of the harmonic function. Specified in pixels.  
thetafloat, optional 

Orientation in radians. If 0, the harmonic is in the x-direction.  
bandwidthfloat, optional 

The bandwidth captured by the filter. For fixed bandwidth, sigma_x and sigma_y will decrease with increasing frequency. This value is ignored if sigma_x and sigma_y are set by the user.  
sigma_x, sigma_yfloat, optional 

Standard deviation in x- and y-directions. These directions apply to the kernel before rotation. If theta = pi/2, then the kernel is rotated 90 degrees so that sigma_x controls the vertical direction.  
n_stdsscalar, optional 

The linear size of the kernel is n_stds (3 by default) standard deviations  
offsetfloat, optional 

Phase offset of harmonic function in radians.    Returns 
 
gcomplex array 

Complex filter kernel.     References  
1  
https://en.wikipedia.org/wiki/Gabor_filter  
2  
https://web.archive.org/web/20180127125930/http://mplab.ucsd.edu/tutorials/gabor.pdf   Examples >>> from skimage.filters import gabor_kernel
>>> from skimage import io
>>> from matplotlib import pyplot as plt  
 >>> gk = gabor_kernel(frequency=0.2)
>>> plt.figure()        
>>> io.imshow(gk.real)  
>>> io.show()           
 >>> # more ripples (equivalent to increasing the size of the
>>> # Gaussian spread)
>>> gk = gabor_kernel(frequency=0.2, bandwidth=0.1)
>>> plt.figure()        
>>> io.imshow(gk.real)  
>>> io.show()           
 
 gaussian  
skimage.filters.gaussian(image, sigma=1, output=None, mode='nearest', cval=0, multichannel=None, preserve_range=False, truncate=4.0) [source]
 
Multi-dimensional Gaussian filter.  Parameters 
 
imagearray-like 

Input image (grayscale or color) to filter.  
sigmascalar or sequence of scalars, optional 

Standard deviation for Gaussian kernel. The standard deviations of the Gaussian filter are given for each axis as a sequence, or as a single number, in which case it is equal for all axes.  
outputarray, optional 

The output parameter passes an array in which to store the filter output.  
mode{‘reflect’, ‘constant’, ‘nearest’, ‘mirror’, ‘wrap’}, optional 

The mode parameter determines how the array borders are handled, where cval is the value when mode is equal to ‘constant’. Default is ‘nearest’.  
cvalscalar, optional 

Value to fill past edges of input if mode is ‘constant’. Default is 0.0  
multichannelbool, optional (default: None) 

Whether the last axis of the image is to be interpreted as multiple channels. If True, each channel is filtered separately (channels are not mixed together). Only 3 channels are supported. If None, the function will attempt to guess this, and raise a warning if ambiguous, when the array has shape (M, N, 3).  
preserve_rangebool, optional 

Whether to keep the original range of values. Otherwise, the input image is converted according to the conventions of img_as_float. Also see https://scikit-image.org/docs/dev/user_guide/data_types.html  
truncatefloat, optional 

Truncate the filter at this many standard deviations.    Returns 
 
filtered_imagendarray 

the filtered array     Notes This function is a wrapper around scipy.ndi.gaussian_filter(). Integer arrays are converted to float. The output should be floating point data type since gaussian converts to float provided image. If output is not provided, another array will be allocated and returned as the result. The multi-dimensional filter is implemented as a sequence of one-dimensional convolution filters. The intermediate arrays are stored in the same data type as the output. Therefore, for output types with a limited precision, the results may be imprecise because intermediate results may be stored with insufficient precision. Examples >>> a = np.zeros((3, 3))
>>> a[1, 1] = 1
>>> a
array([[0., 0., 0.],
       [0., 1., 0.],
       [0., 0., 0.]])
>>> gaussian(a, sigma=0.4)  # mild smoothing
array([[0.00163116, 0.03712502, 0.00163116],
       [0.03712502, 0.84496158, 0.03712502],
       [0.00163116, 0.03712502, 0.00163116]])
>>> gaussian(a, sigma=1)  # more smoothing
array([[0.05855018, 0.09653293, 0.05855018],
       [0.09653293, 0.15915589, 0.09653293],
       [0.05855018, 0.09653293, 0.05855018]])
>>> # Several modes are possible for handling boundaries
>>> gaussian(a, sigma=1, mode='reflect')
array([[0.08767308, 0.12075024, 0.08767308],
       [0.12075024, 0.16630671, 0.12075024],
       [0.08767308, 0.12075024, 0.08767308]])
>>> # For RGB images, each is filtered separately
>>> from skimage.data import astronaut
>>> image = astronaut()
>>> filtered_img = gaussian(image, sigma=1, multichannel=True)
 
 hessian  
skimage.filters.hessian(image, sigmas=range(1, 10, 2), scale_range=None, scale_step=None, alpha=0.5, beta=0.5, gamma=15, black_ridges=True, mode=None, cval=0) [source]
 
Filter an image with the Hybrid Hessian filter. This filter can be used to detect continuous edges, e.g. vessels, wrinkles, rivers. It can be used to calculate the fraction of the whole image containing such objects. Defined only for 2-D and 3-D images. Almost equal to Frangi filter, but uses alternative method of smoothing. Refer to [1] to find the differences between Frangi and Hessian filters.  Parameters 
 
image(N, M[, P]) ndarray 

Array with input image data.  
sigmasiterable of floats, optional 

Sigmas used as scales of filter, i.e., np.arange(scale_range[0], scale_range[1], scale_step)  
scale_range2-tuple of floats, optional 

The range of sigmas used.  
scale_stepfloat, optional 

Step size between sigmas.  
betafloat, optional 

Frangi correction constant that adjusts the filter’s sensitivity to deviation from a blob-like structure.  
gammafloat, optional 

Frangi correction constant that adjusts the filter’s sensitivity to areas of high variance/texture/structure.  
black_ridgesboolean, optional 

When True (the default), the filter detects black ridges; when False, it detects white ridges.  
mode{‘constant’, ‘reflect’, ‘wrap’, ‘nearest’, ‘mirror’}, optional 

How to handle values outside the image borders.  
cvalfloat, optional 

Used in conjunction with mode ‘constant’, the value outside the image boundaries.    Returns 
 
out(N, M[, P]) ndarray 

Filtered image (maximum of pixels across all scales).      See also  
meijering


sato


frangi

  Notes Written by Marc Schrijver (November 2001) Re-Written by D. J. Kroon University of Twente (May 2009) [2] References  
1  
Ng, C. C., Yap, M. H., Costen, N., & Li, B. (2014,). Automatic wrinkle detection using hybrid Hessian filter. In Asian Conference on Computer Vision (pp. 609-622). Springer International Publishing. DOI:10.1007/978-3-319-16811-1_40  
2  
Kroon, D. J.: Hessian based Frangi vesselness filter.   
 inverse  
skimage.filters.inverse(data, impulse_response=None, filter_params={}, max_gain=2, predefined_filter=None) [source]
 
Apply the filter in reverse to the given data.  Parameters 
 
data(M,N) ndarray 

Input data.  
impulse_responsecallable f(r, c, **filter_params) 

Impulse response of the filter. See LPIFilter2D.__init__.  
filter_paramsdict 

Additional keyword parameters to the impulse_response function.  
max_gainfloat 

Limit the filter gain. Often, the filter contains zeros, which would cause the inverse filter to have infinite gain. High gain causes amplification of artefacts, so a conservative limit is recommended.    Other Parameters 
 
predefined_filterLPIFilter2D 

If you need to apply the same filter multiple times over different images, construct the LPIFilter2D and specify it here.     
 laplace  
skimage.filters.laplace(image, ksize=3, mask=None) [source]
 
Find the edges of an image using the Laplace operator.  Parameters 
 
imagendarray 

Image to process.  
ksizeint, optional 

Define the size of the discrete Laplacian operator such that it will have a size of (ksize,) * image.ndim.  
maskndarray, optional 

An optional mask to limit the application to a certain area. Note that pixels surrounding masked regions are also masked to prevent masked regions from affecting the result.    Returns 
 
outputndarray 

The Laplace edge map.     Notes The Laplacian operator is generated using the function skimage.restoration.uft.laplacian(). 
 median  
skimage.filters.median(image, selem=None, out=None, mode='nearest', cval=0.0, behavior='ndimage') [source]
 
Return local median of an image.  Parameters 
 
imagearray-like 

Input image.  
selemndarray, optional 

If behavior=='rank', selem is a 2-D array of 1’s and 0’s. If behavior=='ndimage', selem is a N-D array of 1’s and 0’s with the same number of dimension than image. If None, selem will be a N-D array with 3 elements for each dimension (e.g., vector, square, cube, etc.)  
outndarray, (same dtype as image), optional 

If None, a new array is allocated.  
mode{‘reflect’, ‘constant’, ‘nearest’, ‘mirror’,’‘wrap’}, optional 

The mode parameter determines how the array borders are handled, where cval is the value when mode is equal to ‘constant’. Default is ‘nearest’.  New in version 0.15: mode is used when behavior='ndimage'.   
cvalscalar, optional 

Value to fill past edges of input if mode is ‘constant’. Default is 0.0  New in version 0.15: cval was added in 0.15 is used when behavior='ndimage'.   
behavior{‘ndimage’, ‘rank’}, optional 

Either to use the old behavior (i.e., < 0.15) or the new behavior. The old behavior will call the skimage.filters.rank.median(). The new behavior will call the scipy.ndimage.median_filter(). Default is ‘ndimage’.  New in version 0.15: behavior is introduced in 0.15   Changed in version 0.16: Default behavior has been changed from ‘rank’ to ‘ndimage’     Returns 
 
out2-D array (same dtype as input image) 

Output image.      See also  
skimage.filters.rank.median


Rank-based implementation of the median filtering offering more flexibility with additional parameters but dedicated for unsigned integer images.    Examples >>> from skimage import data
>>> from skimage.morphology import disk
>>> from skimage.filters import median
>>> img = data.camera()
>>> med = median(img, disk(5))
 
 meijering  
skimage.filters.meijering(image, sigmas=range(1, 10, 2), alpha=None, black_ridges=True, mode='reflect', cval=0) [source]
 
Filter an image with the Meijering neuriteness filter. This filter can be used to detect continuous ridges, e.g. neurites, wrinkles, rivers. It can be used to calculate the fraction of the whole image containing such objects. Calculates the eigenvectors of the Hessian to compute the similarity of an image region to neurites, according to the method described in [1].  Parameters 
 
image(N, M[, …, P]) ndarray 

Array with input image data.  
sigmasiterable of floats, optional 

Sigmas used as scales of filter  
alphafloat, optional 

Frangi correction constant that adjusts the filter’s sensitivity to deviation from a plate-like structure.  
black_ridgesboolean, optional 

When True (the default), the filter detects black ridges; when False, it detects white ridges.  
mode{‘constant’, ‘reflect’, ‘wrap’, ‘nearest’, ‘mirror’}, optional 

How to handle values outside the image borders.  
cvalfloat, optional 

Used in conjunction with mode ‘constant’, the value outside the image boundaries.    Returns 
 
out(N, M[, …, P]) ndarray 

Filtered image (maximum of pixels across all scales).      See also  
sato


frangi


hessian

  References  
1  
Meijering, E., Jacob, M., Sarria, J. C., Steiner, P., Hirling, H., Unser, M. (2004). Design and validation of a tool for neurite tracing and analysis in fluorescence microscopy images. Cytometry Part A, 58(2), 167-176. DOI:10.1002/cyto.a.20022   
 prewitt  
skimage.filters.prewitt(image, mask=None, *, axis=None, mode='reflect', cval=0.0) [source]
 
Find the edge magnitude using the Prewitt transform.  Parameters 
 
imagearray 

The input image.  
maskarray of bool, optional 

Clip the output image to this mask. (Values where mask=0 will be set to 0.)  
axisint or sequence of int, optional 

Compute the edge filter along this axis. If not provided, the edge magnitude is computed. This is defined as: prw_mag = np.sqrt(sum([prewitt(image, axis=i)**2
                       for i in range(image.ndim)]) / image.ndim)
 The magnitude is also computed if axis is a sequence.  
modestr or sequence of str, optional 

The boundary mode for the convolution. See scipy.ndimage.convolve for a description of the modes. This can be either a single boundary mode or one boundary mode per axis.  
cvalfloat, optional 

When mode is 'constant', this is the constant used in values outside the boundary of the image data.    Returns 
 
outputarray of float 

The Prewitt edge map.      See also  
sobel, scharr

  Notes The edge magnitude depends slightly on edge directions, since the approximation of the gradient operator by the Prewitt operator is not completely rotation invariant. For a better rotation invariance, the Scharr operator should be used. The Sobel operator has a better rotation invariance than the Prewitt operator, but a worse rotation invariance than the Scharr operator. Examples >>> from skimage import data
>>> from skimage import filters
>>> camera = data.camera()
>>> edges = filters.prewitt(camera)
 
 prewitt_h  
skimage.filters.prewitt_h(image, mask=None) [source]
 
Find the horizontal edges of an image using the Prewitt transform.  Parameters 
 
image2-D array 

Image to process.  
mask2-D array, optional 

An optional mask to limit the application to a certain area. Note that pixels surrounding masked regions are also masked to prevent masked regions from affecting the result.    Returns 
 
output2-D array 

The Prewitt edge map.     Notes We use the following kernel:  1/3   1/3   1/3
  0     0     0
-1/3  -1/3  -1/3
 
 prewitt_v  
skimage.filters.prewitt_v(image, mask=None) [source]
 
Find the vertical edges of an image using the Prewitt transform.  Parameters 
 
image2-D array 

Image to process.  
mask2-D array, optional 

An optional mask to limit the application to a certain area. Note that pixels surrounding masked regions are also masked to prevent masked regions from affecting the result.    Returns 
 
output2-D array 

The Prewitt edge map.     Notes We use the following kernel: 1/3   0  -1/3
1/3   0  -1/3
1/3   0  -1/3
 
 rank_order  
skimage.filters.rank_order(image) [source]
 
Return an image of the same shape where each pixel is the index of the pixel value in the ascending order of the unique values of image, aka the rank-order value.  Parameters 
 
imagendarray 
  Returns 
 
labelsndarray of type np.uint32, of shape image.shape 

New array where each pixel has the rank-order value of the corresponding pixel in image. Pixel values are between 0 and n - 1, where n is the number of distinct unique values in image.  
original_values1-D ndarray 

Unique original values of image     Examples >>> a = np.array([[1, 4, 5], [4, 4, 1], [5, 1, 1]])
>>> a
array([[1, 4, 5],
       [4, 4, 1],
       [5, 1, 1]])
>>> rank_order(a)
(array([[0, 1, 2],
       [1, 1, 0],
       [2, 0, 0]], dtype=uint32), array([1, 4, 5]))
>>> b = np.array([-1., 2.5, 3.1, 2.5])
>>> rank_order(b)
(array([0, 1, 2, 1], dtype=uint32), array([-1. ,  2.5,  3.1]))
 
 roberts  
skimage.filters.roberts(image, mask=None) [source]
 
Find the edge magnitude using Roberts’ cross operator.  Parameters 
 
image2-D array 

Image to process.  
mask2-D array, optional 

An optional mask to limit the application to a certain area. Note that pixels surrounding masked regions are also masked to prevent masked regions from affecting the result.    Returns 
 
output2-D array 

The Roberts’ Cross edge map.      See also  
sobel, scharr, prewitt, feature.canny 
  Examples >>> from skimage import data
>>> camera = data.camera()
>>> from skimage import filters
>>> edges = filters.roberts(camera)
 
 roberts_neg_diag  
skimage.filters.roberts_neg_diag(image, mask=None) [source]
 
Find the cross edges of an image using the Roberts’ Cross operator. The kernel is applied to the input image to produce separate measurements of the gradient component one orientation.  Parameters 
 
image2-D array 

Image to process.  
mask2-D array, optional 

An optional mask to limit the application to a certain area. Note that pixels surrounding masked regions are also masked to prevent masked regions from affecting the result.    Returns 
 
output2-D array 

The Robert’s edge map.     Notes We use the following kernel:  0   1
-1   0
 
 roberts_pos_diag  
skimage.filters.roberts_pos_diag(image, mask=None) [source]
 
Find the cross edges of an image using Roberts’ cross operator. The kernel is applied to the input image to produce separate measurements of the gradient component one orientation.  Parameters 
 
image2-D array 

Image to process.  
mask2-D array, optional 

An optional mask to limit the application to a certain area. Note that pixels surrounding masked regions are also masked to prevent masked regions from affecting the result.    Returns 
 
output2-D array 

The Robert’s edge map.     Notes We use the following kernel: 1   0
0  -1
 
 sato  
skimage.filters.sato(image, sigmas=range(1, 10, 2), black_ridges=True, mode=None, cval=0) [source]
 
Filter an image with the Sato tubeness filter. This filter can be used to detect continuous ridges, e.g. tubes, wrinkles, rivers. It can be used to calculate the fraction of the whole image containing such objects. Defined only for 2-D and 3-D images. Calculates the eigenvectors of the Hessian to compute the similarity of an image region to tubes, according to the method described in [1].  Parameters 
 
image(N, M[, P]) ndarray 

Array with input image data.  
sigmasiterable of floats, optional 

Sigmas used as scales of filter.  
black_ridgesboolean, optional 

When True (the default), the filter detects black ridges; when False, it detects white ridges.  
mode{‘constant’, ‘reflect’, ‘wrap’, ‘nearest’, ‘mirror’}, optional 

How to handle values outside the image borders.  
cvalfloat, optional 

Used in conjunction with mode ‘constant’, the value outside the image boundaries.    Returns 
 
out(N, M[, P]) ndarray 

Filtered image (maximum of pixels across all scales).      See also  
meijering


frangi


hessian

  References  
1  
Sato, Y., Nakajima, S., Shiraga, N., Atsumi, H., Yoshida, S., Koller, T., …, Kikinis, R. (1998). Three-dimensional multi-scale line filter for segmentation and visualization of curvilinear structures in medical images. Medical image analysis, 2(2), 143-168. DOI:10.1016/S1361-8415(98)80009-1   
 scharr  
skimage.filters.scharr(image, mask=None, *, axis=None, mode='reflect', cval=0.0) [source]
 
Find the edge magnitude using the Scharr transform.  Parameters 
 
imagearray 

The input image.  
maskarray of bool, optional 

Clip the output image to this mask. (Values where mask=0 will be set to 0.)  
axisint or sequence of int, optional 

Compute the edge filter along this axis. If not provided, the edge magnitude is computed. This is defined as: sch_mag = np.sqrt(sum([scharr(image, axis=i)**2
                       for i in range(image.ndim)]) / image.ndim)
 The magnitude is also computed if axis is a sequence.  
modestr or sequence of str, optional 

The boundary mode for the convolution. See scipy.ndimage.convolve for a description of the modes. This can be either a single boundary mode or one boundary mode per axis.  
cvalfloat, optional 

When mode is 'constant', this is the constant used in values outside the boundary of the image data.    Returns 
 
outputarray of float 

The Scharr edge map.      See also  
sobel, prewitt, canny 
  Notes The Scharr operator has a better rotation invariance than other edge filters such as the Sobel or the Prewitt operators. References  
1  
D. Kroon, 2009, Short Paper University Twente, Numerical Optimization of Kernel Based Image Derivatives.  
2  
https://en.wikipedia.org/wiki/Sobel_operator#Alternative_operators   Examples >>> from skimage import data
>>> from skimage import filters
>>> camera = data.camera()
>>> edges = filters.scharr(camera)
 
 scharr_h  
skimage.filters.scharr_h(image, mask=None) [source]
 
Find the horizontal edges of an image using the Scharr transform.  Parameters 
 
image2-D array 

Image to process.  
mask2-D array, optional 

An optional mask to limit the application to a certain area. Note that pixels surrounding masked regions are also masked to prevent masked regions from affecting the result.    Returns 
 
output2-D array 

The Scharr edge map.     Notes We use the following kernel:  3   10   3
 0    0   0
-3  -10  -3
 References  
1  
D. Kroon, 2009, Short Paper University Twente, Numerical Optimization of Kernel Based Image Derivatives.   
 scharr_v  
skimage.filters.scharr_v(image, mask=None) [source]
 
Find the vertical edges of an image using the Scharr transform.  Parameters 
 
image2-D array 

Image to process  
mask2-D array, optional 

An optional mask to limit the application to a certain area. Note that pixels surrounding masked regions are also masked to prevent masked regions from affecting the result.    Returns 
 
output2-D array 

The Scharr edge map.     Notes We use the following kernel:  3   0   -3
10   0  -10
 3   0   -3
 References  
1  
D. Kroon, 2009, Short Paper University Twente, Numerical Optimization of Kernel Based Image Derivatives.   
 sobel  
skimage.filters.sobel(image, mask=None, *, axis=None, mode='reflect', cval=0.0) [source]
 
Find edges in an image using the Sobel filter.  Parameters 
 
imagearray 

The input image.  
maskarray of bool, optional 

Clip the output image to this mask. (Values where mask=0 will be set to 0.)  
axisint or sequence of int, optional 

Compute the edge filter along this axis. If not provided, the edge magnitude is computed. This is defined as: sobel_mag = np.sqrt(sum([sobel(image, axis=i)**2
                         for i in range(image.ndim)]) / image.ndim)
 The magnitude is also computed if axis is a sequence.  
modestr or sequence of str, optional 

The boundary mode for the convolution. See scipy.ndimage.convolve for a description of the modes. This can be either a single boundary mode or one boundary mode per axis.  
cvalfloat, optional 

When mode is 'constant', this is the constant used in values outside the boundary of the image data.    Returns 
 
outputarray of float 

The Sobel edge map.      See also  
scharr, prewitt, canny 
  References  
1  
D. Kroon, 2009, Short Paper University Twente, Numerical Optimization of Kernel Based Image Derivatives.  
2  
https://en.wikipedia.org/wiki/Sobel_operator   Examples >>> from skimage import data
>>> from skimage import filters
>>> camera = data.camera()
>>> edges = filters.sobel(camera)
 
 Examples using skimage.filters.sobel
 
  Flood Fill   sobel_h  
skimage.filters.sobel_h(image, mask=None) [source]
 
Find the horizontal edges of an image using the Sobel transform.  Parameters 
 
image2-D array 

Image to process.  
mask2-D array, optional 

An optional mask to limit the application to a certain area. Note that pixels surrounding masked regions are also masked to prevent masked regions from affecting the result.    Returns 
 
output2-D array 

The Sobel edge map.     Notes We use the following kernel:  1   2   1
 0   0   0
-1  -2  -1
 
 sobel_v  
skimage.filters.sobel_v(image, mask=None) [source]
 
Find the vertical edges of an image using the Sobel transform.  Parameters 
 
image2-D array 

Image to process.  
mask2-D array, optional 

An optional mask to limit the application to a certain area. Note that pixels surrounding masked regions are also masked to prevent masked regions from affecting the result.    Returns 
 
output2-D array 

The Sobel edge map.     Notes We use the following kernel: 1   0  -1
2   0  -2
1   0  -1
 
 threshold_isodata  
skimage.filters.threshold_isodata(image=None, nbins=256, return_all=False, *, hist=None) [source]
 
Return threshold value(s) based on ISODATA method. Histogram-based threshold, known as Ridler-Calvard method or inter-means. Threshold values returned satisfy the following equality: threshold = (image[image <= threshold].mean() +
             image[image > threshold].mean()) / 2.0
 That is, returned thresholds are intensities that separate the image into two groups of pixels, where the threshold intensity is midway between the mean intensities of these groups. For integer images, the above equality holds to within one; for floating- point images, the equality holds to within the histogram bin-width. Either image or hist must be provided. In case hist is given, the actual histogram of the image is ignored.  Parameters 
 
image(N, M) ndarray, optional 

Input image.  
nbinsint, optional 

Number of bins used to calculate histogram. This value is ignored for integer arrays.  
return_allbool, optional 

If False (default), return only the lowest threshold that satisfies the above equality. If True, return all valid thresholds.  
histarray, or 2-tuple of arrays, optional 

Histogram to determine the threshold from and a corresponding array of bin center intensities. Alternatively, only the histogram can be passed.    Returns 
 
thresholdfloat or int or array 

Threshold value(s).     References  
1  
Ridler, TW & Calvard, S (1978), “Picture thresholding using an iterative selection method” IEEE Transactions on Systems, Man and Cybernetics 8: 630-632, DOI:10.1109/TSMC.1978.4310039  
2  
Sezgin M. and Sankur B. (2004) “Survey over Image Thresholding Techniques and Quantitative Performance Evaluation” Journal of Electronic Imaging, 13(1): 146-165, http://www.busim.ee.boun.edu.tr/~sankur/SankurFolder/Threshold_survey.pdf DOI:10.1117/1.1631315  
3  
ImageJ AutoThresholder code, http://fiji.sc/wiki/index.php/Auto_Threshold   Examples >>> from skimage.data import coins
>>> image = coins()
>>> thresh = threshold_isodata(image)
>>> binary = image > thresh
 
 threshold_li  
skimage.filters.threshold_li(image, *, tolerance=None, initial_guess=None, iter_callback=None) [source]
 
Compute threshold value by Li’s iterative Minimum Cross Entropy method.  Parameters 
 
imagendarray 

Input image.  
tolerancefloat, optional 

Finish the computation when the change in the threshold in an iteration is less than this value. By default, this is half the smallest difference between intensity values in image.  
initial_guessfloat or Callable[[array[float]], float], optional 

Li’s iterative method uses gradient descent to find the optimal threshold. If the image intensity histogram contains more than two modes (peaks), the gradient descent could get stuck in a local optimum. An initial guess for the iteration can help the algorithm find the globally-optimal threshold. A float value defines a specific start point, while a callable should take in an array of image intensities and return a float value. Example valid callables include numpy.mean (default), lambda arr: numpy.quantile(arr, 0.95), or even skimage.filters.threshold_otsu().  
iter_callbackCallable[[float], Any], optional 

A function that will be called on the threshold at every iteration of the algorithm.    Returns 
 
thresholdfloat 

Upper threshold value. All pixels with an intensity higher than this value are assumed to be foreground.     References  
1  
Li C.H. and Lee C.K. (1993) “Minimum Cross Entropy Thresholding” Pattern Recognition, 26(4): 617-625 DOI:10.1016/0031-3203(93)90115-D  
2  
Li C.H. and Tam P.K.S. (1998) “An Iterative Algorithm for Minimum Cross Entropy Thresholding” Pattern Recognition Letters, 18(8): 771-776 DOI:10.1016/S0167-8655(98)00057-9  
3  
Sezgin M. and Sankur B. (2004) “Survey over Image Thresholding Techniques and Quantitative Performance Evaluation” Journal of Electronic Imaging, 13(1): 146-165 DOI:10.1117/1.1631315  
4  
ImageJ AutoThresholder code, http://fiji.sc/wiki/index.php/Auto_Threshold   Examples >>> from skimage.data import camera
>>> image = camera()
>>> thresh = threshold_li(image)
>>> binary = image > thresh
 
 threshold_local  
skimage.filters.threshold_local(image, block_size, method='gaussian', offset=0, mode='reflect', param=None, cval=0) [source]
 
Compute a threshold mask image based on local pixel neighborhood. Also known as adaptive or dynamic thresholding. The threshold value is the weighted mean for the local neighborhood of a pixel subtracted by a constant. Alternatively the threshold can be determined dynamically by a given function, using the ‘generic’ method.  Parameters 
 
image(N, M) ndarray 

Input image.  
block_sizeint 

Odd size of pixel neighborhood which is used to calculate the threshold value (e.g. 3, 5, 7, …, 21, …).  
method{‘generic’, ‘gaussian’, ‘mean’, ‘median’}, optional 

Method used to determine adaptive threshold for local neighbourhood in weighted mean image.  ‘generic’: use custom function (see param parameter) ‘gaussian’: apply gaussian filter (see param parameter for custom sigma value) ‘mean’: apply arithmetic mean filter ‘median’: apply median rank filter  By default the ‘gaussian’ method is used.  
offsetfloat, optional 

Constant subtracted from weighted mean of neighborhood to calculate the local threshold value. Default offset is 0.  
mode{‘reflect’, ‘constant’, ‘nearest’, ‘mirror’, ‘wrap’}, optional 

The mode parameter determines how the array borders are handled, where cval is the value when mode is equal to ‘constant’. Default is ‘reflect’.  
param{int, function}, optional 

Either specify sigma for ‘gaussian’ method or function object for ‘generic’ method. This functions takes the flat array of local neighbourhood as a single argument and returns the calculated threshold for the centre pixel.  
cvalfloat, optional 

Value to fill past edges of input if mode is ‘constant’.    Returns 
 
threshold(N, M) ndarray 

Threshold image. All pixels in the input image higher than the corresponding pixel in the threshold image are considered foreground.     References  
1  
https://docs.opencv.org/modules/imgproc/doc/miscellaneous_transformations.html?highlight=threshold#adaptivethreshold   Examples >>> from skimage.data import camera
>>> image = camera()[:50, :50]
>>> binary_image1 = image > threshold_local(image, 15, 'mean')
>>> func = lambda arr: arr.mean()
>>> binary_image2 = image > threshold_local(image, 15, 'generic',
...                                         param=func)
 
 threshold_mean  
skimage.filters.threshold_mean(image) [source]
 
Return threshold value based on the mean of grayscale values.  Parameters 
 
image(N, M[, …, P]) ndarray 

Grayscale input image.    Returns 
 
thresholdfloat 

Upper threshold value. All pixels with an intensity higher than this value are assumed to be foreground.     References  
1  
C. A. Glasbey, “An analysis of histogram-based thresholding algorithms,” CVGIP: Graphical Models and Image Processing, vol. 55, pp. 532-537, 1993. DOI:10.1006/cgip.1993.1040   Examples >>> from skimage.data import camera
>>> image = camera()
>>> thresh = threshold_mean(image)
>>> binary = image > thresh
 
 threshold_minimum  
skimage.filters.threshold_minimum(image=None, nbins=256, max_iter=10000, *, hist=None) [source]
 
Return threshold value based on minimum method. The histogram of the input image is computed if not provided and smoothed until there are only two maxima. Then the minimum in between is the threshold value. Either image or hist must be provided. In case hist is given, the actual histogram of the image is ignored.  Parameters 
 
image(M, N) ndarray, optional 

Input image.  
nbinsint, optional 

Number of bins used to calculate histogram. This value is ignored for integer arrays.  
max_iterint, optional 

Maximum number of iterations to smooth the histogram.  
histarray, or 2-tuple of arrays, optional 

Histogram to determine the threshold from and a corresponding array of bin center intensities. Alternatively, only the histogram can be passed.    Returns 
 
thresholdfloat 

Upper threshold value. All pixels with an intensity higher than this value are assumed to be foreground.    Raises 
 RuntimeError

If unable to find two local maxima in the histogram or if the smoothing takes more than 1e4 iterations.     References  
1  
C. A. Glasbey, “An analysis of histogram-based thresholding algorithms,” CVGIP: Graphical Models and Image Processing, vol. 55, pp. 532-537, 1993.  
2  
Prewitt, JMS & Mendelsohn, ML (1966), “The analysis of cell images”, Annals of the New York Academy of Sciences 128: 1035-1053 DOI:10.1111/j.1749-6632.1965.tb11715.x   Examples >>> from skimage.data import camera
>>> image = camera()
>>> thresh = threshold_minimum(image)
>>> binary = image > thresh
 
 threshold_multiotsu  
skimage.filters.threshold_multiotsu(image, classes=3, nbins=256) [source]
 
Generate classes-1 threshold values to divide gray levels in image. The threshold values are chosen to maximize the total sum of pairwise variances between the thresholded graylevel classes. See Notes and [1] for more details.  Parameters 
 
image(N, M) ndarray 

Grayscale input image.  
classesint, optional 

Number of classes to be thresholded, i.e. the number of resulting regions.  
nbinsint, optional 

Number of bins used to calculate the histogram. This value is ignored for integer arrays.    Returns 
 
thresharray 

Array containing the threshold values for the desired classes.    Raises 
 ValueError

If image contains less grayscale value then the desired number of classes.     Notes This implementation relies on a Cython function whose complexity is \(O\left(\frac{Ch^{C-1}}{(C-1)!}\right)\), where \(h\) is the number of histogram bins and \(C\) is the number of classes desired. The input image must be grayscale. References  
1  
Liao, P-S., Chen, T-S. and Chung, P-C., “A fast algorithm for multilevel thresholding”, Journal of Information Science and Engineering 17 (5): 713-727, 2001. Available at: <https://ftp.iis.sinica.edu.tw/JISE/2001/200109_01.pdf> DOI:10.6688/JISE.2001.17.5.1  
2  
Tosa, Y., “Multi-Otsu Threshold”, a java plugin for ImageJ. Available at: <http://imagej.net/plugins/download/Multi_OtsuThreshold.java>   Examples >>> from skimage.color import label2rgb
>>> from skimage import data
>>> image = data.camera()
>>> thresholds = threshold_multiotsu(image)
>>> regions = np.digitize(image, bins=thresholds)
>>> regions_colorized = label2rgb(regions)
 
 Examples using skimage.filters.threshold_multiotsu
 
  Multi-Otsu Thresholding  

  Segment human cells (in mitosis)   threshold_niblack  
skimage.filters.threshold_niblack(image, window_size=15, k=0.2) [source]
 
Applies Niblack local threshold to an array. A threshold T is calculated for every pixel in the image using the following formula: T = m(x,y) - k * s(x,y)
 where m(x,y) and s(x,y) are the mean and standard deviation of pixel (x,y) neighborhood defined by a rectangular window with size w times w centered around the pixel. k is a configurable parameter that weights the effect of standard deviation.  Parameters 
 
imagendarray 

Input image.  
window_sizeint, or iterable of int, optional 

Window size specified as a single odd integer (3, 5, 7, …), or an iterable of length image.ndim containing only odd integers (e.g. (1, 5, 5)).  
kfloat, optional 

Value of parameter k in threshold formula.    Returns 
 
threshold(N, M) ndarray 

Threshold mask. All pixels with an intensity higher than this value are assumed to be foreground.     Notes This algorithm is originally designed for text recognition. The Bradley threshold is a particular case of the Niblack one, being equivalent to >>> from skimage import data
>>> image = data.page()
>>> q = 1
>>> threshold_image = threshold_niblack(image, k=0) * q
 for some value q. By default, Bradley and Roth use q=1. References  
1  
W. Niblack, An introduction to Digital Image Processing, Prentice-Hall, 1986.  
2  
D. Bradley and G. Roth, “Adaptive thresholding using Integral Image”, Journal of Graphics Tools 12(2), pp. 13-21, 2007. DOI:10.1080/2151237X.2007.10129236   Examples >>> from skimage import data
>>> image = data.page()
>>> threshold_image = threshold_niblack(image, window_size=7, k=0.1)
 
 threshold_otsu  
skimage.filters.threshold_otsu(image=None, nbins=256, *, hist=None) [source]
 
Return threshold value based on Otsu’s method. Either image or hist must be provided. If hist is provided, the actual histogram of the image is ignored.  Parameters 
 
image(N, M) ndarray, optional 

Grayscale input image.  
nbinsint, optional 

Number of bins used to calculate histogram. This value is ignored for integer arrays.  
histarray, or 2-tuple of arrays, optional 

Histogram from which to determine the threshold, and optionally a corresponding array of bin center intensities. An alternative use of this function is to pass it only hist.    Returns 
 
thresholdfloat 

Upper threshold value. All pixels with an intensity higher than this value are assumed to be foreground.     Notes The input image must be grayscale. References  
1  
Wikipedia, https://en.wikipedia.org/wiki/Otsu’s_Method   Examples >>> from skimage.data import camera
>>> image = camera()
>>> thresh = threshold_otsu(image)
>>> binary = image <= thresh
 
 Examples using skimage.filters.threshold_otsu
 
  Measure region properties  

  Rank filters   threshold_sauvola  
skimage.filters.threshold_sauvola(image, window_size=15, k=0.2, r=None) [source]
 
Applies Sauvola local threshold to an array. Sauvola is a modification of Niblack technique. In the original method a threshold T is calculated for every pixel in the image using the following formula: T = m(x,y) * (1 + k * ((s(x,y) / R) - 1))
 where m(x,y) and s(x,y) are the mean and standard deviation of pixel (x,y) neighborhood defined by a rectangular window with size w times w centered around the pixel. k is a configurable parameter that weights the effect of standard deviation. R is the maximum standard deviation of a greyscale image.  Parameters 
 
imagendarray 

Input image.  
window_sizeint, or iterable of int, optional 

Window size specified as a single odd integer (3, 5, 7, …), or an iterable of length image.ndim containing only odd integers (e.g. (1, 5, 5)).  
kfloat, optional 

Value of the positive parameter k.  
rfloat, optional 

Value of R, the dynamic range of standard deviation. If None, set to the half of the image dtype range.    Returns 
 
threshold(N, M) ndarray 

Threshold mask. All pixels with an intensity higher than this value are assumed to be foreground.     Notes This algorithm is originally designed for text recognition. References  
1  
J. Sauvola and M. Pietikainen, “Adaptive document image binarization,” Pattern Recognition 33(2), pp. 225-236, 2000. DOI:10.1016/S0031-3203(99)00055-2   Examples >>> from skimage import data
>>> image = data.page()
>>> t_sauvola = threshold_sauvola(image, window_size=15, k=0.2)
>>> binary_image = image > t_sauvola
 
 threshold_triangle  
skimage.filters.threshold_triangle(image, nbins=256) [source]
 
Return threshold value based on the triangle algorithm.  Parameters 
 
image(N, M[, …, P]) ndarray 

Grayscale input image.  
nbinsint, optional 

Number of bins used to calculate histogram. This value is ignored for integer arrays.    Returns 
 
thresholdfloat 

Upper threshold value. All pixels with an intensity higher than this value are assumed to be foreground.     References  
1  
Zack, G. W., Rogers, W. E. and Latt, S. A., 1977, Automatic Measurement of Sister Chromatid Exchange Frequency, Journal of Histochemistry and Cytochemistry 25 (7), pp. 741-753 DOI:10.1177/25.7.70454  
2  
ImageJ AutoThresholder code, http://fiji.sc/wiki/index.php/Auto_Threshold   Examples >>> from skimage.data import camera
>>> image = camera()
>>> thresh = threshold_triangle(image)
>>> binary = image > thresh
 
 threshold_yen  
skimage.filters.threshold_yen(image=None, nbins=256, *, hist=None) [source]
 
Return threshold value based on Yen’s method. Either image or hist must be provided. In case hist is given, the actual histogram of the image is ignored.  Parameters 
 
image(N, M) ndarray, optional 

Input image.  
nbinsint, optional 

Number of bins used to calculate histogram. This value is ignored for integer arrays.  
histarray, or 2-tuple of arrays, optional 

Histogram from which to determine the threshold, and optionally a corresponding array of bin center intensities. An alternative use of this function is to pass it only hist.    Returns 
 
thresholdfloat 

Upper threshold value. All pixels with an intensity higher than this value are assumed to be foreground.     References  
1  
Yen J.C., Chang F.J., and Chang S. (1995) “A New Criterion for Automatic Multilevel Thresholding” IEEE Trans. on Image Processing, 4(3): 370-378. DOI:10.1109/83.366472  
2  
Sezgin M. and Sankur B. (2004) “Survey over Image Thresholding Techniques and Quantitative Performance Evaluation” Journal of Electronic Imaging, 13(1): 146-165, DOI:10.1117/1.1631315 http://www.busim.ee.boun.edu.tr/~sankur/SankurFolder/Threshold_survey.pdf  
3  
ImageJ AutoThresholder code, http://fiji.sc/wiki/index.php/Auto_Threshold   Examples >>> from skimage.data import camera
>>> image = camera()
>>> thresh = threshold_yen(image)
>>> binary = image <= thresh
 
 try_all_threshold  
skimage.filters.try_all_threshold(image, figsize=(8, 5), verbose=True) [source]
 
Returns a figure comparing the outputs of different thresholding methods.  Parameters 
 
image(N, M) ndarray 

Input image.  
figsizetuple, optional 

Figure size (in inches).  
verbosebool, optional 

Print function name for each method.    Returns 
 
fig, axtuple 

Matplotlib figure and axes.     Notes The following algorithms are used:  isodata li mean minimum otsu triangle yen  Examples >>> from skimage.data import text
>>> fig, ax = try_all_threshold(text(), figsize=(10, 6), verbose=False)
 
 unsharp_mask  
skimage.filters.unsharp_mask(image, radius=1.0, amount=1.0, multichannel=False, preserve_range=False) [source]
 
Unsharp masking filter. The sharp details are identified as the difference between the original image and its blurred version. These details are then scaled, and added back to the original image.  Parameters 
 
image[P, …, ]M[, N][, C] ndarray 

Input image.  
radiusscalar or sequence of scalars, optional 

If a scalar is given, then its value is used for all dimensions. If sequence is given, then there must be exactly one radius for each dimension except the last dimension for multichannel images. Note that 0 radius means no blurring, and negative values are not allowed.  
amountscalar, optional 

The details will be amplified with this factor. The factor could be 0 or negative. Typically, it is a small positive number, e.g. 1.0.  
multichannelbool, optional 

If True, the last image dimension is considered as a color channel, otherwise as spatial. Color channels are processed individually.  
preserve_rangebool, optional 

Whether to keep the original range of values. Otherwise, the input image is converted according to the conventions of img_as_float. Also see https://scikit-image.org/docs/dev/user_guide/data_types.html    Returns 
 
output[P, …, ]M[, N][, C] ndarray of float 

Image with unsharp mask applied.     Notes Unsharp masking is an image sharpening technique. It is a linear image operation, and numerically stable, unlike deconvolution which is an ill-posed problem. Because of this stability, it is often preferred over deconvolution. The main idea is as follows: sharp details are identified as the difference between the original image and its blurred version. These details are added back to the original image after a scaling step: enhanced image = original + amount * (original - blurred) When applying this filter to several color layers independently, color bleeding may occur. More visually pleasing result can be achieved by processing only the brightness/lightness/intensity channel in a suitable color space such as HSV, HSL, YUV, or YCbCr. Unsharp masking is described in most introductory digital image processing books. This implementation is based on [1]. References  
1  
Maria Petrou, Costas Petrou “Image Processing: The Fundamentals”, (2010), ed ii., page 357, ISBN 13: 9781119994398 DOI:10.1002/9781119994398  
2  
Wikipedia. Unsharp masking https://en.wikipedia.org/wiki/Unsharp_masking   Examples >>> array = np.ones(shape=(5,5), dtype=np.uint8)*100
>>> array[2,2] = 120
>>> array
array([[100, 100, 100, 100, 100],
       [100, 100, 100, 100, 100],
       [100, 100, 120, 100, 100],
       [100, 100, 100, 100, 100],
       [100, 100, 100, 100, 100]], dtype=uint8)
>>> np.around(unsharp_mask(array, radius=0.5, amount=2),2)
array([[0.39, 0.39, 0.39, 0.39, 0.39],
       [0.39, 0.39, 0.38, 0.39, 0.39],
       [0.39, 0.38, 0.53, 0.38, 0.39],
       [0.39, 0.39, 0.38, 0.39, 0.39],
       [0.39, 0.39, 0.39, 0.39, 0.39]])
 >>> array = np.ones(shape=(5,5), dtype=np.int8)*100
>>> array[2,2] = 127
>>> np.around(unsharp_mask(array, radius=0.5, amount=2),2)
array([[0.79, 0.79, 0.79, 0.79, 0.79],
       [0.79, 0.78, 0.75, 0.78, 0.79],
       [0.79, 0.75, 1.  , 0.75, 0.79],
       [0.79, 0.78, 0.75, 0.78, 0.79],
       [0.79, 0.79, 0.79, 0.79, 0.79]])
 >>> np.around(unsharp_mask(array, radius=0.5, amount=2, preserve_range=True), 2)
array([[100.  , 100.  ,  99.99, 100.  , 100.  ],
       [100.  ,  99.39,  95.48,  99.39, 100.  ],
       [ 99.99,  95.48, 147.59,  95.48,  99.99],
       [100.  ,  99.39,  95.48,  99.39, 100.  ],
       [100.  , 100.  ,  99.99, 100.  , 100.  ]])
 
 wiener  
skimage.filters.wiener(data, impulse_response=None, filter_params={}, K=0.25, predefined_filter=None) [source]
 
Minimum Mean Square Error (Wiener) inverse filter.  Parameters 
 
data(M,N) ndarray 

Input data.  
Kfloat or (M,N) ndarray 

Ratio between power spectrum of noise and undegraded image.  
impulse_responsecallable f(r, c, **filter_params) 

Impulse response of the filter. See LPIFilter2D.__init__.  
filter_paramsdict 

Additional keyword parameters to the impulse_response function.    Other Parameters 
 
predefined_filterLPIFilter2D 

If you need to apply the same filter multiple times over different images, construct the LPIFilter2D and specify it here.     
 window  
skimage.filters.window(window_type, shape, warp_kwargs=None) [source]
 
Return an n-dimensional window of a given size and dimensionality.  Parameters 
 
window_typestring, float, or tuple 

The type of window to be created. Any window type supported by scipy.signal.get_window is allowed here. See notes below for a current list, or the SciPy documentation for the version of SciPy on your machine.  
shapetuple of int or int 

The shape of the window along each axis. If an integer is provided, a 1D window is generated.  
warp_kwargsdict 

Keyword arguments passed to skimage.transform.warp (e.g., warp_kwargs={'order':3} to change interpolation method).    Returns 
 
nd_windowndarray 

A window of the specified shape. dtype is np.double.     Notes This function is based on scipy.signal.get_window and thus can access all of the window types available to that function (e.g., "hann", "boxcar"). Note that certain window types require parameters that have to be supplied with the window name as a tuple (e.g., ("tukey", 0.8)). If only a float is supplied, it is interpreted as the beta parameter of the Kaiser window. See https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.windows.get_window.html for more details. Note that this function generates a double precision array of the specified shape and can thus generate very large arrays that consume a large amount of available memory. The approach taken here to create nD windows is to first calculate the Euclidean distance from the center of the intended nD window to each position in the array. That distance is used to sample, with interpolation, from a 1D window returned from scipy.signal.get_window. The method of interpolation can be changed with the order keyword argument passed to skimage.transform.warp. Some coordinates in the output window will be outside of the original signal; these will be filled in with zeros. Window types: - boxcar - triang - blackman - hamming - hann - bartlett - flattop - parzen - bohman - blackmanharris - nuttall - barthann - kaiser (needs beta) - gaussian (needs standard deviation) - general_gaussian (needs power, width) - slepian (needs width) - dpss (needs normalized half-bandwidth) - chebwin (needs attenuation) - exponential (needs decay scale) - tukey (needs taper fraction) References  
1  
Two-dimensional window design, Wikipedia, https://en.wikipedia.org/wiki/Two_dimensional_window_design   Examples Return a Hann window with shape (512, 512): >>> from skimage.filters import window
>>> w = window('hann', (512, 512))
 Return a Kaiser window with beta parameter of 16 and shape (256, 256, 35): >>> w = window(16, (256, 256, 35))
 Return a Tukey window with an alpha parameter of 0.8 and shape (100, 300): >>> w = window(('tukey', 0.8), (100, 300))
 
 LPIFilter2D  
class skimage.filters.LPIFilter2D(impulse_response, **filter_params) [source]
 
Bases: object Linear Position-Invariant Filter (2-dimensional)  
__init__(impulse_response, **filter_params) [source]
 
 Parameters 
 
impulse_responsecallable f(r, c, **filter_params) 

Function that yields the impulse response. r and c are 1-dimensional vectors that represent row and column positions, in other words coordinates are (r[0],c[0]),(r[0],c[1]) etc. **filter_params are passed through. In other words, impulse_response would be called like this: >>> def impulse_response(r, c, **filter_params):
...     pass
>>>
>>> r = [0,0,0,1,1,1,2,2,2]
>>> c = [0,1,2,0,1,2,0,1,2]
>>> filter_params = {'kw1': 1, 'kw2': 2, 'kw3': 3}
>>> impulse_response(r, c, **filter_params)
     Examples Gaussian filter: Use a 1-D gaussian in each direction without normalization coefficients. >>> def filt_func(r, c, sigma = 1):
...     return np.exp(-np.hypot(r, c)/sigma)
>>> filter = LPIFilter2D(filt_func)