Multiresolution analysis: Difference between revisions

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== Applications ==

=== Image Fusion in Remote Sensing ===

MRA is instrumental in merging images from sensors with varying resolutions and spectral bands .<ref>{{Cite book | author=Bruno Aiazzi, Stefano Baronti, Massimo Selva | title=2 - Image fusion through multiresolution oversampled decompositions | editor=Tania Stathaki | publisher=Academic Press | year=2008 | pages=27–66 | isbn=978-0-12-372529-5 | url=https://www.sciencedirect.com/science/article/pii/B9780123725295000020 | ___location=Oxford }}</ref> For instance, a high-resolution [[panchromatic image]] can be fused with a low-resolution [[multispectral image]], producing a single output with enhanced spatial and spectral resolution. Techniques like the "[[À trous algorithm|à trous]]" wavelet algorithm and [[Laplacian pyramid|Laplacian pyramids]] preserve spatial connectivity and minimize artifacts.

. For instance, a high-resolution [[panchromatic image]] can be fused with a low-resolution [[multispectral image]], producing a single output with enhanced spatial and spectral resolution. Techniques like the "[[À trous algorithm|à trous]]" wavelet algorithm and [[Laplacian pyramid|Laplacian pyramids]] preserve spatial connectivity and minimize artifacts.

=== Multiresolution Editing in Geometric Modeling ===

MRA enhances geometric modeling by enabling efficient representation and manipulation of complex shapes:<ref name="Georges2008">{{Cite book | author=Georges-Pierre Bonneau, Gershon Elber, Stefanie Hahmann, Basile Sauvage | editor=Leila De Floriani, Michela Spagnuolo | title=Multiresolution Analysis | publisher=Springer Berlin Heidelberg | year=2008 | pages=83–114 | isbn=978-3-540-33265-7 | url=https://doi.org/10.1007/978-3-540-33265-7_3 | ___location=Berlin, Heidelberg }}</ref>:

* '''Hierarchical B-splines''': Allow local and global modifications, simplifying both coarse adjustments and detailed refinements.

* '''Flexible design''': Provides a multiresolution framework for iterative editing, streamlining the creative process in [[computer-aided design]] (CAD).

=== Shape Compression Using Semi-Regular Remeshing ===

MRA contributes to efficient 3D model compression through '''semi-regular remeshing''':<ref name="Georges2008" />:

* '''Simplification''': Reduces unnecessary connectivity and parameterization data.

* '''Parameterization''': Maps the input mesh onto base triangular domains, resulting in a compact representation.