Image Processing Reference
is calculated by convolving the contrast sensitivity function with the magnitude of
the low frequency Fourier components at each level for every orientation. The fusion
rule is based on the perceptual contrast defined as the ratio of the difference to the
sum of saliencies of input bands. The reconstruction of the fused image involves the
following reverse procedure. The oriented gradient pyramid of the fused image is
converted into an oriented Laplacian pyramid. This structure is then converted into a
Laplacian pyramid through a sequence of filter-subtract-decimate (FSD) operations.
The reduced Laplacian is then converted into a Gaussian pyramid from which the
final fused image is constructed.
The problem of displaying the hyperspectral data onto a standard display device
requires dimensionality reduction. Through fusion, one intends to retain the maxi-
mum features within the reduced data set. The principal component analysis (PCA) is
a classic tool of dimensionality reductionwhich computes the basis vectors by analyz-
ing the direction of maximum data variance, and projects the data onto them .
Tyo et al. have developed a PCA-based technique for hyperspectral image fusion
where the mapping of the principal components (PCs) of the data is closely related
to the human vision . The first three eigenvectors of the covariance matrix of
the input data represent the PC images in this case. To display the fusion result, the
first PC has been mapped to the achromatic channel, while the second and the third
PCs have been mapped to the R-G, and the B-Y color channels, respectively. The
PCA-based method, however, turns out to be computationally very expensive when
it is applied over the entire hyperspectral data cube. In , it has been suggested
that the hyperspectral data should be partitioned before applying the principal com-
ponent transform (PCT) emphasizing on the spectral properties of certain subsets of
bands. Three strategies for partitioning are as following:
1. The basic strategy is to partition the data cube into three groups or subsets of equal
size. This partitioning is based on grouping of successive bands, and referred to as
the equal subgroup scheme by authors in . The final RGB image is formed
from the orthogonal band from each group.
2. The second strategy partitions the data to select the size of each subset using
an iterative procedure such that the eigenvalues corresponding to the first PC
of the subset become maximum . At every iteration, the largest eigenvalue
corresponding to the first principal component of each subgroup is calculated.
3. The aim of the partitioning is to reveal certain spectral characteristics of the
data, so that the materials with significantly different spectral signatures should
be distinguishable in the resultant RGB image. However, this scheme requires
knowledge of the spectral signatures of the each material that is possibly present
in the underlying scene.
Jacobson et al. have proposed the use of color matching functions derived from the
hypothesis of how the synthesized image would be seen by the human eye if its range
of perceived wavelength were to be stretched to the bandwidth of the hyperspectral
image . These functions, which act as the fusion weights specify the fractional
components of the primary colors required to bemixed in order to create the sensation
of the same color as that of viewing the original spectrum. For a K -band hyperspectral