Quoted from:http://www.saga-gis.org/en/index.html

Common binary Opening does not guarantee, that foreground regions which outlast the erosion step are reconstructed to their original shape in the dilation step. Depending on the application, that might be considered as a deficiency. Therefore this tool provides a combination of erosion with the binary Geodesic Morphological Reconstruction, see L. Vincent (1993): Morphological Grayscale Reconstruction in Image Analysis: Applications and Efficient Algorithms. IEEE Transactions on Image Processing, Vol. 2, No 2Here we use the algorithm on p. 194: Breadth-first Scanning.The marker is defined as the eroded INPUT_GRID, whereas the mask is just the INPUT_GRID itself. OUTPUT_GRID is the reconstruction of the marker under the mask.