Binary partition tree-based local spectral unmixing

Abstract

The linear mixing model (LMM) is a widely used methodology for the spectral unmixing (SU) of hyperspectral data. In this model, hyperspectral data is formed as a linear combination of spectral signatures corresponding to macroscopically pure materials (endmembers), weighted by their fractional abundances. Some of the drawbacks of the LMM are the presence of multiple mixtures and the spectral variability of the endmembers due to illumination and atmospheric effects. These issues appear as variations of the spectral conditions of the image along its spatial domain. However, these effects are not so severe locally and could be at least mitigated by working in smaller regions of the image. The proposed local SU works over a partition of the image, performing the spectral unmixing locally in each region of the partition. In this work, we first introduce the general local SU methodology, then we propose an implementation of the local SU based on a binary partition tree representation of the hyperspectral image and finally we give an experimental validation of the approach using real data.

Hyperspectral Local Intrinsic Dimensionality

“…Recently, some local approaches have been proposed for spectral unmixing [12], [20], [23], [31], [42], in order to overcome some of the issues of global approaches, i.e. spectral variability [41], [45].…”

On the use of binary partition trees for the tree crown segmentation of tropical rainforest hyperspectral images

“…Among all tree representations, the binary partition tree (BPT) has received much attention lately. Initially proposed by Garrido (2002); Salembier & Garrido (2000) for grayscale and RGB images, BPTs have then been further extended to hyperspectral imagery by Valero et al (2013a) and are now used for classical hyperspectral remote sensing tasks such as segmentation (Valero et al, 2011a;Veganzones et al, 2014), classification (Alonso-Gonzalez et al, 2013), unmixing (Drumetz et al, 2014) and object detection (Valero et al, 2013b(Valero et al, , 2011b notably. The efficiency of the BPT to achieve a given task is greatly impacted by both the pre-processing applied to the image prior to the construction of the BPT and the postprocessing of the BPT representation itself, called pruning.…”

From local to global unmixing of hyperspectral images to reveal spectral variability

“…where the dR endmembers e R i and their associated fractional abundances φ R x,i have been induced using only the spectral information contained in region R. The major challenge of LSU approaches concerns the definition of a suited set of regions {R}. In this paper, we follow the work presented in [9] that makes use of a partition of the spatial support sp(X), π = {Ri ⊆ sp(X)} such that sp(X) = i Ri and Ri ∩ R j =i = ∅ extracted from a hierarchical representation of this HSI. More specifically, the HSI is first decomposed in a set of regions organized hierarchically (such that any two regions of this set are either disjoint or nested).…”

“…In [8] for instance, the original image is first divided into several overlapping tiles, within which the spectral unmixing is locally conducted. To avoid blocking effects, another strategy was proposed in [9], where the LSU is performed on regions of a particular partition of the HSI. However, the main limitation of LSU techniques is that the induced endmembers and abundances are only defined locally in the image, and must somehow be post-processed to be interpretable at the whole image scale.…”

“…In this work, we propose to combine the LSU approach with the ELMM framework and show that it allows to derive global endmembers and abundances from their local counterparts, while providing additional information related to the spectral variability. The rest of this paper is organized as follow: section 2 presents more in details the ELMM framework [7] and a LSU approach relying on a hierarchical representation of the HSI [9]. Section 3 describes the proposed methodology to connect the previous two strategies in order to have access to global endmembers, abundances, as well as spectral variability.…”