Optimization-Based Fusion - Hyperspectral Image Fusion - page 102

4. Contrast : It is another attribute which makes an object distinguishable from
the rest of the image contents. Contrast is largely related to the image sharpness.
Often, the perceived sharpness refers to themixture of spatial resolution, acutance,
and contrast [98]. As the contrast is ultimately perceived by the human observers,
it is often defined based on the human visual system (HVS). Several definitions
of contrast based on HVS co-exist in the literature. The Weber contrast is defined
as the ratio of the difference between luminance of the object and that of the
background to the background luminance [80]. The Michelson contrast is defined
as the ratio of half value of the available luminance range to the sum of this half
value and the object luminance [128]. The dynamic range of this measure is [0, 1],
as opposed to the former case of Weber contrast where it is [ ]. Peli [128]

discussed the RMS contrast which does not involve the HVS factors. The RMS
contrast is defined as the standard deviation of the image intensity. Variance of an
image is also used as one of the contrast indicators due to ease of computation, and
non dependency on any other factors. Lee has proposed contrast enhancement of
images based on their local mean and variance [99]. The variance has been used
as the performance measure for several image enhancement techniques including
image fusion.
5. Exposedness : It refers to the clipping of intensity levels due to finite length
storage space per pixel. The real world scene has a large dynamic range. In order
to compress it within the limits dictated by the storage and/or display system, the
intensity (gray) values above the pre-decided maximum, and the values below
the pre-decided minimum have to be clipped to the respective gray levels. This
operation gives rise to a large number of pixels with improper intensity values, and
reduces the information content in the image. An incorrect exposure time of the
imaging device gives rise to over- or under-saturated regions. This phenomenon is
also referred to as over- or under-exposure in photography. Too bright or too dull
images are not visually appealing. It can also be easily understood that saturated
regions lack contrast, and hence it reduces image clarity.
The maximum of Laplacian has been considered as the measure of saturation
in [16] for fusion of monochrome and color images. In [113], well-exposedness
of the scene has been regarded as one of requirements while obtaining visually
appealing images, which is measured as the closeness of the pixel to the mean
gray value.

− 1 , ∞

We shall be using some of these image quality measures while designing the
fusion strategy. Section 7.3 explains the formulation of a multi-objective function
based on some of the characteristics discussed in this section. The solution of this
optimization problem has been provided using the Euler-Lagrange equation which
are among most popular tools for solving problems in variational framework. We
have already provided a brief overview of the calculus of variations and the Euler-
Lagrange equation in Sect. 6.2 . We have also demonstrated their use in developing
a fusion solution that does not require explicit computation of fusion weights. In
this chapter, we employ the variational framework to develop a multi-objective cost
function based on the properties of the fused image.