Profile

Set of functions for calculating roughness parameters along profiles

To demonstrate, we’re going to build on the data we processed in data

image = np.loadtxt('example.txt')
profiles = np.loadtxt('example_profiles.txt')
plt.imshow(image)
plt.show()

Statistical Parameters

The following methods are statistical in nature, providing a single number as a broad description of the distribution of the height values.

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Ra

 Ra (im, axis=1, norm=True)

Calculates Mean Absolute Roughness (Ra) along given axis. Defined as the average deviation of absolute height values from the mean line.

Type Default Details
im Numpy array or arraylike
axis int 1 Default to Ra of rows
norm bool True Normalize the profile by subtracting the mean 
#test_close(0.14539179526852036,Ra(cor2pgau,norm=False,axis=None),eps=1e-4)
Ra(image)[:5]
array([0.00042559, 0.00041652, 0.00040715, 0.00039409, 0.00037837])

Remember, if you just want the parameters of a certain profile, you just index into your image and be mindful of the axis.

first_row_profile    = image[0,:]
first_column_profile = image[:,0]
Ra(first_column_profile, axis = 0)
0.0004406996100199229

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Rms

 Rms (im, axis=1, norm=True)

*Calculates Root Mean Square Roughness (Rms) along given axis. Defined as the root mean square of deviations of height from the mean line of a given profile.

Also known as Rq*

Type Default Details
im Numpy array or array like
axis int 1 Default to Rms of rows
norm bool True Normalize the profile by subtracting the mean 
#test_close(0.195597300779425,Rms(cor2pgau,axis=None),1e-3)
Rms(image)[:5]
array([0.00053041, 0.0005153 , 0.0004984 , 0.00048217, 0.00046463])

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Rsk

 Rsk (im, axis=1, norm=True, **kwargs)

Calcultes the Skew (Rsk) along given axis. Thin wrapper around scipy.stats.skew with bias set to False

Type Default Details
im Numpy array or array like
axis int 1 Default to Skew of rows
norm bool True Normalize the profile by subtracting the mean
kwargs 
#test_close(1.094210880233907,Rsk(cor2pgau[50:-50],axis=None),1e-4)
Rsk(image)[:5]
array([-0.33567068, -0.33327936, -0.33261958, -0.32251   , -0.28183241])

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Rku

 Rku (im, axis=1, norm=True, **kwargs)

Calculates the Kurtosis (Rku) along given axis. This wrapper around scipy.stats.kurtosis

Type Default Details
im Numpy array or array like
axis int 1 Default to Kurtosis of rows
norm bool True Normalize the profile by subtracting the mean
kwargs 
#test_close(6.8550747244379355,Rku(cor2pgau,axis=None),1e-4)
Rku(image)[:5]
array([-0.65026388, -0.70209278, -0.75579608, -0.75657439, -0.73669875])

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Rp

 Rp (im, axis=1, norm=True, **kwargs)

Calculates the peak height of the profile.

Type Default Details
im Numpy array or array like
axis int 1 Default to peaks of rows
norm bool True Normalize the profile by subtracting the mean
kwargs 
#test_close(1.1930965342677724,Rp(cor2pgau,axis=None),1e-4)

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Rv

 Rv (im, axis=1, norm=True, **kwargs)

Calculates the absolute max valley depth of the profile.

Type Default Details
im Numpy array or array like
axis int 1 Default to peaks of rows
norm bool True Normalize the profile by subtracting the mean
kwargs 
#test_close(0.5760229498158181,Rv(cor2pgau,axis=None),1e-4)

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Rz

 Rz (im, axis=1, norm=True, **kwargs)

Calculates the maximum height (max height + absolute max depth) of the profile. Synonymous with range. Also called Rt

Type Default Details
im Numpy array or array like
axis int 1 Default to peaks of rows
norm bool True Normalize the profile by subtracting the mean
kwargs 
#test_close(1.7691194840835909,Rz(cor2pgau,axis=None),1e-4)
## Texture Parameters
def local_max_min(im,
                  axis = 1,
                  norm = True,
                  **kwargs
                 ):
    ''' 
    Returns the number of local maxima and minima per unit length, also known as the density of extremes from Nayak (1971).
    Assumes the surface is random, with a gaussian distribution of heights (usually pretty safe). 
    '''
    if norm:
        im = im - np.mean(im, axis = axis, keepdims = True)
    
    m2 = moment(im, moment=2, axis = axis)
    m4 = moment(im, moment=4, axis = axis)
    return (1/math.pi) * ((m4/m2)**(1/2))
def Sds(im,
        axis = 1,
        norm = True,
        **kwargs
       ):
    '''
    Density of summits, as described by Nayak (1971).
    Assumes gaussian, isotropic surface. 
    '''
    m2 = moment(im, moment=2, axis = axis)
    m4 = moment(im, moment=4, axis = axis)
    
    return (1 / (6 * math.pi * (3**(1/2)))) * (m4/m2)