Fig. 3

Flowchart of the detail component extraction procedure. An estimate of spectral background (topmost right) is first obtained by applying a smoothing operation on the PSD (topmost middle) of the input image (topmost left). The PSD is then converted to probabilistic form (center) based on the values of the PSD relative to spectral background. An initial 2D Gaussian ‘selector function’ (iteration 1, top row) is formed based on parameters estimated from the PSD. The 2D Gaussian is multiplied with the probabilistic PSD to obtain ‘posterior probabilities’ of belonging to the detail component region (iteration 1, middle row). A threshold of 0.5 is then applied to the ‘posterior’ to obtain the initial detail component region (iteration 1, bottom row; region outlined in red). The process then proceeds in iterative manner. Parameters for the ‘selector function’ used during the second iteration (iteration 2, top row) are estimated based on the detail component spectral region obtained during the first iteration. The same steps are then repeated during each iteration until the parameters of the ‘selector function’ reach convergence at a certain threshold (in this case after four iterations) or the maximum number of allowed iterations is reached. The final estimate of the detail component spectral region is retained for further analysis steps. The x-axis in all of the spectral plots indicates spatial frequency in μm⁻¹ while the y-axis indicates orientation in degrees. The values of the PSD, spectral background and the detail component region plots are given in arbitrary units. The values of the probabilistic PSD, the Gaussian ‘selector function’ and the ‘posterior’ plots are given as probabilities, as indicated by the color bar on the right-hand side of the probabilistic PSD