Image Processing Reference

In-Depth Information

assessing the fusion of hyperspectral data. We have explained modifications in sev-

eral existing measures in order to extend their applicability towards an objective

assessment of the fused images, and thereby the performance of the corresponding

techniques. Several improvements in some of the existing measures have also been

suggested which would help in a better analysis and assessment of the fusion process.

The notion of
consistency
of a fusion technique has been illustrated. The consistency

analysis reveals the behavior of a fusion technique as an increasing number of images

are fused. We believe that this analysis would be highly useful in determining the

adaptability and suitability of a generalized fusion technique for fusion of hyper-

spectral data. The performance measures have been categorized into three sets. The

first set of measures evaluates the quality of the fused image without any reference

to ground truth. The measures in the second set analyze the consistency of the fusion

technique. The last set of measures investigates the contribution of each spectral

band towards the final result. Thus, these measures deal with an important but often

neglected aspect of the participation of each band into the fusion process. Although

the main objective here has been a quantitative assessment of fusion of hyperspec-

tral data, these performance measures can effectively be used for the assessment of

generalized image fusion.

Hyperspectral image fusion deals with selectively combining nearly 200

bands

to obtain a single image representation of the scene. The fusion techniques explained

in this monograph, as well as other existing techniques process each of the bands

either as a whole or at a per pixel basis, for efficient fusion. The spectral bands in the

hyperspectral image, however, exhibit a large amount of redundancy as the contents

of the scene vary gradually over the successive hyperspectral bands. Due to a very

high degree of inter-band correlation, the adjacent bands contribute a very little addi-

tional information towards the fusion result. Hence, one may select a subset of a few,

but specific hyperspectral bands which collectively capture most of the information

content from the input hyperspectral data. Fusion of this subset of data, thus, would

be almost equivalent to fusion of the entire set of hyperspectral bands. In this mono-

graph, we discuss two information theoretic schemes for band selection based on

redundancy elimination. The first scheme selects a subset of the hyperspectral bands

that are mutually less correlated from each other. The process of band selection, thus

involves computation of the conditional entropy of the given hyperspectral band with

respect to each of the previously selected bands. As the hyperspectral bands are usu-

ally ordered according to the wavelengths, we can assume a specific model to define

the conditional entropy as a function of the spectral distance between the bands.

Under this assumption, the process of band selection reduces to the computation of

conditional entropy of the given band with respect to the last selected band only.

Along with visual illustrations for the quality of fused image over a reduced subset,

we have also provided the bounds on the savings in computation. This scheme is

independent of the fusion process, and depends only on the properties of the input

hyperspectral data. We have also discussed another band selection scheme based

on the fusion technique to be applied. In this scheme, the subset of selected hyper-

spectral bands is fused to generate an intermediate fused image. A hyperspectral

band is included in this subset only when it is significantly less correlated with this

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