Image Processing Reference

In-Depth Information

Fig. 2.2

Illustration of wavelet-based image fusion

then recovered via an inverse discrete wavelet transform (IDWT) to generate the final

image. The schematic of the generalized DWT-based fusion techniques is shown in

Fig.
2.2
. The pyramidal representations of the input images are subjected to the fusion

rule specified by the technique. This process generates the pyramid representing the

decomposed fused image. The final image is obtained by an appropriate inverse

transformation.

As stated earlier in this monograph, the key step lies in choosing an appropriate

strategy to combine the coefficients, i.e., fusion rule. In [172, 174], the fusion rule

has been defined to select the maximum of the corresponding coefficients of the

ratio pyramid of input images, while the fusion rule that selects the maximum across

discrete wavelet coefficients of the input images has been proposed in [104]. Math-

ematically, the general wavelet-based image fusion can be represented by Eq. (
2.2
).

=
W
−
1
F
W (

I
2
),...
,

F

I
1
), W (

(2.2)

W , W
−
1
are the forward and inverse wavelet trans-

formoperators, respectively. Wavelets have probably been themost successful family

of fusion techniques. Wavelet-based fusion techniques have been implemented for

various other application areas. Wen and Chen have demonstrated several applica-

tions of DWT-based fusion for forensic science [188]. Another application of wavelet

decomposition for fusion of multi-focus images using the log-Gabor wavelets has

been described by Redondo et al. [151]. The wavelet-based fusion techniques have

also been proved to be useful for fusion of medical images. Performance of vari-

ous multi-resolution techniques for fusion of retinal images has been analyzed in

[96, 97]. In [86], wavelets have been shown to be useful for fusion of CT and MRI

images.

Let us now take a brief look at some of the fusion techniques based on the variants

of wavelets. A region-based fusion technique that generates a feature map through

segmentation of the features of input images using a dual-tree complex wavelet

where

F

is the fusion rule, and