146
• The sensor’s point spatial function (PSF), which determines if the central parts
of the pixel are going to have more relevance than the outer parts, and also the
non- negligible part outside of the GIFOV (Schowengerdt 2007);
• Radiance incorporated by the atmosphere, with photons coming outside of the
GIFOV by the adjacency effect from surfaces surrounding the pixel (Richter
et al. 2006).
Spectral unmixing is the decomposition of a mixed pixel into a collection of
distinct spectra (endmembers), and a set of fractional abundances that indicate the
proportion of each endmember (Keshava and Mustard 2002). It is a physically based
model that transforms radiance or reflectance to physical variables, which are linked
to the sub-pixel abundances of endmembers within each pixel. The Linear Spectral
Unmixing (LSU) is the most frequently used model because of its simplicity and
more direct interpretation, and assumes the pixel spectrum to be a linear combination of a finite number of spectrally distinct endmembers (Keshava and Mustard
2002). The three consecutive procedures for LSU are: (1) reduction of the dimension of the data using Principal Components Analysis (PCA) or Minimum Noise
Fraction (MNF), which seeks a minimal representation that sufficiently retains the
requisite information for successful unmixing; (2) endmember determination representative of the physical components on the surface. Endmembers can be obtained
directly from the image employing statistics to capture variability, such as the Pixel
Purity Index (PPI). Similarly, the endmembers could be extracted from spectral
libraries derived from laboratory or field spectroscopy; (3) imagery pixel reflectance
values are inverted using least square methods to minimise the squared-error and
achieve fractional abundances of the components.
Depending on the number of endmembers introduced and constraints applied in
the algorithm, different varieties of LSU have been developed. For example, if only
a few key endmembers are determined without requiring knowledge of the remaining scene endmembers, Mixture-Tuned Matched Filter (MTMF) (Boardman et al.
1995) is an algorithm that allows false positives to be identified and eliminated from
abundance results. Additionally, Multiple Endmember Spectral Mixture Analysis
(MESMA) extends LSU by allowing the number and types of endmembers to vary
on a per-pixel basis (Roberts et al. 1998).
The need to provide sub-pixel proportions of vegetation components is well
reflected in the literature (McGwire et al. 2000). When the endmembers include vegetation, the endmember fraction is considered proportional to the areal abundance of
the projected canopy cover. Although the differences in canopy structure and size
between species can be very noticeable, which entails non-linear mixture model application, the use of LSU provides statistically significant results (McGwire et al. 2000).
Plant Species Mapping
The protocol for mapping plant species proposed in this work is based on collaboration
between an airborne imaging spectroscopy operator, which can be used to acquire
and pre-process the hyperspectral imagery, and a user organization (i.e., Natural
M. Jiménez and R. Díaz-Delgado
• The sensor’s point spatial function (PSF), which determines if the central parts
of the pixel are going to have more relevance than the outer parts, and also the
non- negligible part outside of the GIFOV (Schowengerdt 2007);
• Radiance incorporated by the atmosphere, with photons coming outside of the
GIFOV by the adjacency effect from surfaces surrounding the pixel (Richter
et al. 2006).
Spectral unmixing is the decomposition of a mixed pixel into a collection of
distinct spectra (endmembers), and a set of fractional abundances that indicate the
proportion of each endmember (Keshava and Mustard 2002). It is a physically based
model that transforms radiance or reflectance to physical variables, which are linked
to the sub-pixel abundances of endmembers within each pixel. The Linear Spectral
Unmixing (LSU) is the most frequently used model because of its simplicity and
more direct interpretation, and assumes the pixel spectrum to be a linear combination of a finite number of spectrally distinct endmembers (Keshava and Mustard
2002). The three consecutive procedures for LSU are: (1) reduction of the dimension of the data using Principal Components Analysis (PCA) or Minimum Noise
Fraction (MNF), which seeks a minimal representation that sufficiently retains the
requisite information for successful unmixing; (2) endmember determination representative of the physical components on the surface. Endmembers can be obtained
directly from the image employing statistics to capture variability, such as the Pixel
Purity Index (PPI). Similarly, the endmembers could be extracted from spectral
libraries derived from laboratory or field spectroscopy; (3) imagery pixel reflectance
values are inverted using least square methods to minimise the squared-error and
achieve fractional abundances of the components.
Depending on the number of endmembers introduced and constraints applied in
the algorithm, different varieties of LSU have been developed. For example, if only
a few key endmembers are determined without requiring knowledge of the remaining scene endmembers, Mixture-Tuned Matched Filter (MTMF) (Boardman et al.
1995) is an algorithm that allows false positives to be identified and eliminated from
abundance results. Additionally, Multiple Endmember Spectral Mixture Analysis
(MESMA) extends LSU by allowing the number and types of endmembers to vary
on a per-pixel basis (Roberts et al. 1998).
The need to provide sub-pixel proportions of vegetation components is well
reflected in the literature (McGwire et al. 2000). When the endmembers include vegetation, the endmember fraction is considered proportional to the areal abundance of
the projected canopy cover. Although the differences in canopy structure and size
between species can be very noticeable, which entails non-linear mixture model application, the use of LSU provides statistically significant results (McGwire et al. 2000).
Plant Species Mapping
The protocol for mapping plant species proposed in this work is based on collaboration
between an airborne imaging spectroscopy operator, which can be used to acquire
and pre-process the hyperspectral imagery, and a user organization (i.e., Natural
M. Jiménez and R. Díaz-Delgado