Feature maps

This section details methods for extracting information from pattern intensities, called feature maps (for lack of a better description).

Image quality

The image quality metric \(Q\) presented by Krieger Lassen [Lassen1994] can be calculated for an EBSD object with get_image_quality(), or, for a single pattern (numpy.ndarray), with get_image_quality(). Following the notation in [Marquardt2017], it is given by

\[\begin{split}\begin{align} Q &= 1 - \frac{J}{J_{\mathrm{res}}w_{\mathrm{tot}}},\\ J &= \sum_{h = -N/2}^{N/2} \sum_{k = -N/2}^{N/2} w(h, k) \left|\mathbf{q}\right|^2,\\ J_{\mathrm{res}} &= \frac{1}{N^2} \sum_{h = -N/2}^{N/2} \sum_{k = -N/2}^{N/2} \left|\mathbf{q}\right|^2,\\ w_{\mathrm{tot}} &= \sum_{h = -N/2}^{N/2} \sum_{k = -N/2}^{N/2} w(h, k). \end{align}\end{split}\]

The function \(w(h, k)\) is the Fast Fourier Transform (FFT) power spectrum of the EBSD pattern, and the vectors \(\mathbf{q}\) are the frequency vectors with components \((h, k)\). The sharper the Kikuchi bands, the greater the high frequency content of the power spectrum, and thus the closer \(Q\) will be to unity. To visualize parts of the computation, we compute the power spectrum of a pattern in an EBSD object s and the frequency vectors, shift the zero-frequency components to the centre, and plot them:

>>> import kikuchipy as kp
>>> import matplotlib.pyplot as plt
>>> import numpy as np

>>> p = s.inav[0, 0].data
>>> plt.figure()
>>> plt.imshow(p)
>>> plt.colorbar()

>>> p_fft = kp.pattern.fft(p, shift=True)
>>> plt.figure()
>>> plt.imshow(np.log(kp.pattern.fft_spectrum(p_fft)))
>>> plt.colorbar()

>>> q = kp.pattern.fft_frequency_vectors(shape=p.shape)
>>> plt.figure()
>>> plt.imshow(np.fft.fftshift(q))
>>> plt.colorbar()

A background corrected EBSD pattern (left), the logarithm of the shifted power spectrum \(w(h, k)\) of its FFT (middle), and the shifted frequency vectors \(\mathbf{q}\) (right).

If we don’t want the EBSD patterns to be zero-mean normalized before computing \(Q\), we must pass normalized=False. Let’s compute the image quality \(Q\) and plot it for a Nickel data set from [Anes2019]:

>>> iq = s.get_image_quality(normalize=True)  # Default
>>> plt.figure()
>>> plt.imshow(iq)
>>> plt.colorbar()

The image quality map of a Nickel data set from [Anes2019].

If we want to use this map to navigate around in when plotting patterns, we can easily do that as explained in the visualizing patterns guide.