A Fourier analysis based algorithm to separate touching kernels in digital images

An algorithm to separate touching grain kernels using an elliptic Fourier series approximation, based on boundary curvature values, is presented. The Fourier approximation smoothes the boundary contours of the images avoiding local pseudo-corners caused by the presence of rough boundaries and image acquisition inefficiencies. Once the curvature values along the boundary of the kernels are calculated, nodal points separate the touching instances. Evaluating the curvature along the boundary of the image and selecting those points at which the curvature falls below a threshold determines nodal points. With multiple nodal points, a nearest-neighbour and a radian critical (cumulative) distance difference [rad] of chain-coded boundary point criteria are used to draw the segmentation lines. The algorithm was tested for different grain types under different touching scenarios and was successful in separating more than 98% of the touching grains. The algorithm appears to be robust enough to separate most of the multiple touching scenarios with few exceptions where the kernels are broken or have rough boundaries.