TY - GEN A1 - Sridhar, Vivek A1 - Breuß, Michael T1 - An Exact Fast Fourier Method for Morphological Dilation and Erosion Using the Umbra Technique T2 - 19th Conference on Robots and Vision (CRV), 2022 N2 - In this paper we consider the fundamental operations dilation and erosion of mathematical morphology. It is well known that many powerful image filtering operations can be constructed by their combinations. We propose a fast and novel algorithm based on the Fast Fourier Transform to compute grey-value morphological operations on an image. The novel method may deal with non-flat filters and incorporates no restrictions on shape and size of the filtering window, in contrast to many other fast methods in the field. Unlike fast Fourier techniques from previous works, the novel method gives exact results and is not an approximation. The key aspect which allows to achieve this is to explore here for the first time in this context the umbra formulation of images and filters. We show that the new method is in practice particularly suitable for filtering images with small tonal range or when employing large filter sizes. KW - morphological dilation, morphological erosion, fast Fourier transform Y1 - 2022 SN - 978-1-6654-9774-9 SN - 978-1-6654-9775-6 U6 - https://doi.org/10.1109/CRV55824.2022.00032 SP - 190 EP - 196 PB - IEEE ER -