Abstract
The basic filters in mathematical morphology are dilation and erosion. They are defined by a flat or non-flat structuring element that is usually shifted pixel-wise over an image and a comparison process that takes place within the corresponding mask. Existing fast algorithms that realise dilation and erosion for grey value images are often limited with respect to size or shape of the structuring element. Usually their algorithmic complexity depends on these aspects. Many fast methods only address flat morphology.
In this paper we propose a novel way to make use of the fast Fourier transform for the computation of dilation and erosion. Our method is by design highly flexible, as it can be used with flat and non-flat structuring elements of any size and shape. Moreover, its complexity does not depend on size or shape of the structuring element, but only on the number of pixels in the filtered images. We show experimentally that we obtain results of very reasonable quality with the proposed method.
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The work was partly supported by the European Regional Development Fund, EFRE 85037495.
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Kahra, M., Sridhar, V., Breuß, M. (2021). Fast Morphological Dilation and Erosion for Grey Scale Images Using the Fourier Transform. In: Elmoataz, A., Fadili, J., Quéau, Y., Rabin, J., Simon, L. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2021. Lecture Notes in Computer Science(), vol 12679. Springer, Cham. https://doi.org/10.1007/978-3-030-75549-2_6
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