Hyperspectral Local Intrinsic Dimensionality

Lucas Drumetz 1 Miguel Angel Veganzones 1, 2 Rubén Marrero 3 Guillaume Tochon 1 Mauro Dalla Mura 1 Giorgio Licciardi 1 Christian Jutten 4 Jocelyn Chanussot 1
1 GIPSA-SIGMAPHY - SIGMAPHY
GIPSA-DIS - Département Images et Signal
2 GIPSA-CICS - CICS
GIPSA-DIS - Département Images et Signal
3 Planeto
IPAG - Institut de Planétologie et d'Astrophysique de Grenoble
4 GIPSA-VIBS - VIBS
GIPSA-DIS - Département Images et Signal
Abstract : The Intrinsic Dimensionality (ID) of multivariate data is a very important concept in spectral unmixing of hyperspectral images. A good estimation of the ID is crucial for a correct retrieval of the number of endmembers (the spectral signatures of macroscopic materials) in the image, for dimensionality reduction or for subspace learning, among others. Recently, some approaches to perform spectral unmixing and super-resolution locally have been proposed, which require a local estimation of the number of endmembers to use. However, the role of ID in local regions of hyperspectral images has not been properly addressed. Some important issues when dealing with small regions of hyperspectral data can seriously affect the performance of conventional hyperspectral ID estimators. We show that three factors mainly affect local ID estimation: the number of pixels in the local regions, which has to be high enough for the estimations to be relevant, the number of hyperspectral bands which complicates the estimations if the ambient space has a high dimensionality, and the noise, which can be misinterpreted as signal when its power is important. Here, we review the hyperspectral ID estimators on the literature for local ID estimation, we show how they behave in a local setting on synthetic and real datasets, and we provide some guidelines to make proper use of these estimators in local approaches.
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IEEE Transactions on Geoscience and Remote Sensing, Institute of Electrical and Electronics Engineers, 2016, 〈10.1109/TGRS.2016.2536480〉
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Lucas Drumetz, Miguel Angel Veganzones, Rubén Marrero, Guillaume Tochon, Mauro Dalla Mura, et al.. Hyperspectral Local Intrinsic Dimensionality. IEEE Transactions on Geoscience and Remote Sensing, Institute of Electrical and Electronics Engineers, 2016, 〈10.1109/TGRS.2016.2536480〉. 〈hal-01292198〉

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