Fig. 1
Schematic illustrating the fundamentals of the singular value decomposition (SVD)-based image denoising technique and the pattern matching-based techniques for identifying atoms in images. a The denoising process starts with sliding a small window across the given image column-by-column and then row-by-row. b A stack of (N − m)2 windows, each with m × m pixels, is built by copying the contents of the window at each location. c This 3D stack of windows is flattened to a 2D matrix by flattening the m × m pixel windows to 1D arrays with m2 elements. SVD is performed on this 2D matrix to decompose the data into the most correlated and least uncorrelated (noise) components. The image is denoised by reconstructing the 2D matrix in c with only the most correlated SVD components and reversing the steps from c to a. d K-means clustering on the SVD results groups pixels exhibiting similar trends together in a cluster label map. Representative examples of repeating patterns or motifs in the label map are selected for pattern matching. e Each motif is compared to every section in the label map to generate a pattern matching scores’ map. Each continuous-valued scores map is thresholded to generate binary maps with segments and the centroids of these segments provide the coordinates of the repeating patterns such as atoms