Image Processing Reference
In-Depth Information
Chapter 5
Bayesian Estimation
5.1 Introduction
In Chap. 3 , we addressed the problem of visualization of hyperspectral data through a
pixel-level fusion of the constituent bands. The fused image has been generated as the
composite of the input spectral bands where the locally dominant features in the data
were used to determine how the pixels should be combined. For pixel-level methods,
the fusion weights are typically calculated from some measure that describes the
relative importance of the pixel (or the band) in the data with reference to its spatial
neighborhood. This importance measure, also known as saliency quantifies how
important the pixel is for fusion purpose. The fusion technique discussed in Chap. 3 ,
makes use of the bilateral filter for the extraction of details from each and every pixel
in the hyperspectral data.
In this chapter, we shall explore a different aspect of fusion process. Let us take a
look at the process of image formation. We assume that the fused image represents
the true scene. The elements of the hyperspectral sensor see the same scene, however,
capture it partially across the set of bands due to the specific spectral responses of the
sensor elements. Thus, each of the hyperspectral bands captures some fraction of the
true scene. The objective of the fusion process is then to obtain the resultant image as
close to the true scene through combining all available input bands representing the
scene partially. The first step towards the solution is to formulate the relation between
the true scene (to be obtained through fusion), and each of the constituent bands using
a certain model. One may consider the statistical model of image formation which
relates the true scene and input images using a first order approximation. According to
this model, every sensor element captures only a fraction of the underlying true scene.
This fraction is regarded as the sensor selectivity factor in this model, which primarily
reflects how well the particular pixel has been captured by the corresponding sensor
element of the particular band of the hyperspectral image. When the sensor selectivity
factor is 1, the corresponding pixel in the true scene has been seen exactly by the
corresponding sensor. On the other hand, if the sensor selectivity factor is zero, the

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