A Scale-space Approach to the Morphological Simplification of Scalar Fields

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dc.contributor.authorRocca, Luigien_US
dc.contributor.authorPuppo, Enricoen_US
dc.contributor.editorBanterle, Francescoen_US
dc.contributor.editorCaggianese, Giuseppeen_US
dc.contributor.editorCapece, Nicolaen_US
dc.contributor.editorErra, Ugoen_US
dc.contributor.editorLupinetti, Katiaen_US
dc.contributor.editorManfredi, Gildaen_US
dc.date.accessioned2023-11-12T15:37:40Z
dc.date.available2023-11-12T15:37:40Z
dc.date.issued2023
dc.description.abstractWe present a multi-scale morphological model of scalar fields based on the analysis of the spatial frequencies of the underlying function. Morphological models partition the domain of a function into homogeneous regions. The most popular tool in this field is the Morse-Smale complex, where each region is spanned by all integral lines that join a minimum to a maximum, with the integral lines departing from saddles as region boundaries. Morphological features usually occur at very different scales, from noise and high frequency details up to large trends at the lowest frequencies. Without some form of multi-scale analysis, only the morphology at the finest scale is visible and explicit in such a model. The most popular approach in the literature is the filtration provided by persistent homology, a method that combines the amplitude values of critical points with the topology of the sublevel sets of the function. We propose the adoption of an alternative filtration method, based on the analysis of the deep structure of the linear scale-space of the function. To retrieve an adequately fine-grained ranked sequence of pairs of critical points that vanish through the scales, we adopt a continuous representation of the scale-space that overcomes the limits of discrete scale-space approaches. This sequence provides a progressive simplification of the Morse-Smale complex, resulting in a progressive multi-scale model of the morphology that always refers to the geometry of the original function, which is not changed by our model. We apply our method to digital elevation models, with results providing a multi-scale representation of the network of ridges and valley lines that joins peaks, pits and passes and divide the land into mountains and basins.en_US
dc.description.sectionheadersRepresentation of 3D shapes
dc.description.seriesinformationSmart Tools and Applications in Graphics - Eurographics Italian Chapter Conference
dc.identifier.doi10.2312/stag.20231300
dc.identifier.isbn978-3-03868-235-6
dc.identifier.issn2617-4855
dc.identifier.pages113-123
dc.identifier.pages11 pages
dc.identifier.urihttps://doi.org/10.2312/stag.20231300
dc.identifier.urihttps://diglib.eg.org:443/handle/10.2312/stag20231300
dc.publisherThe Eurographics Associationen_US
dc.rightsAttribution 4.0 International License
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.titleA Scale-space Approach to the Morphological Simplification of Scalar Fieldsen_US
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