Automatic band detection in Kikuchi patterns using Hough transform

Abstract

The principles of obtaining Kikuchi band images (Kikuchi pattern) and methods of their analysis in order to determine local deformations for the studied crystals are considered. Digital pre-processing of Kikuchi images is performed, namely, noise is removed by bilateral filtering and their local contrast is increased. The image processing program is developed in Python. Contours on the image are selected using the Canny method. The band boundaries are first approximated by straight lines using the Hough method based on the image contours, and then the band boundaries are more accurately approximated by parabolas and hyperbolas. The Hough method selected only straight line segments that exceed a given length and the size of the gaps for which does not exceed a given one. The resulting bands were also selected by direction, which allows each band corresponding to a specific crystallographic direction to be separately investigated. The image was rotated by the bicubic interpolation method to the angle of inclination of the band, which simplifies further approximation of the band boundaries. For each point of the band boundary, the weight centre of the contours was calculated, and the obtained weight centres were approximated by a parabola using the least squares method. After that, the Kikuchi band boundary was approximated by a hyperbola, the parameters of which were obtained by the coordinate descent method by minimizing the mean square difference between the corresponding points of the parabola and hyperbola. A series of experimental images of Kikuchi bands obtained from synthesized diamond crystals was studied. For the studied images, the shape of the hyperbola describing the band boundary is close to a parabola in the vicinity of the vertex. The obtained hyperbolas provide a much more accurate description of the band boundaries compared to straight lines. Based on the analysis of the averaged profiles of Kikuchi bands, the deformations of the crystals, which are described by the relative change in their interplanar distances, were determined.