Image Processing Reference
In-Depth Information
of these measures is used to construct a decision map which in turn forms an actual
weight of the fusion.
In [201], authors have explained the use of non-subsampled contourlet transform
for fusion of multi-focus images. In this technique, low frequency coefficients have
been combined with selection and averaging rules, while the high frequency coef-
ficients have been selected on the basis of standard deviation at the corresponding
level. In [197] the use of contourlet transform has been proposed for medical image
fusion where the fusion rules include weighted average and local energy which are
applied in the transform domain. The CT and MRI images have been fused using
contourlet transform in [26] where the fusion weights are inversely proportional to
the distance of the pixel from the current value of the fused pixel.
Curvelets have been another popular choice to represent edges [23, 52]. Curvelets
are a multi-scale transform that more efficiently represent the edges and other
singularities along curves than the wavelets. The efficiency refers to the ability to
represent the data in a fewer number of coefficients for a given accuracy of recon-
struction [52]. Choi et al. have experimented with curvelet transform for fusion of
satellite images [40]. A finite ridgelet transform is obtained by taking a DWT of the
coefficient vector of the finite Radon transform. Fusion of remote sensing images
using the ridgelet transform has been proposed in [36].
A few researchers have applied the estimation theory to the problem of image
fusion. The problem of fusion has been formulated as the following: The fused
image is considered to be the underlying true scene . The input images obtained from
multiple imaging sensors are assumed to depict the partial scene. The images contain
an incomplete scene contaminated with some noise. The fusion problem thus gets
transformed into the problem of estimation of the underlying true scene—which
is the fused image itself. Once the relationship between the input images and the
fused image is modeled, one can employ suitable techniques from the estimation
theory which has a highly rich literature. Sharma [163], and Sharma et al. [164] have
modeled the input images as noisy, locally affine functions of the true scene to be
estimated. A Bayesian framework has been employed to obtain either the maximum
likelihood (ML), or the maximum a posteriori (MAP) estimates of the true scene,
i.e., the fused image. The parameters of this model have been estimated from the
local covariance of the images. This model also offers flexibility to add a prior about
the scene, if known; however, it assumes the noise component to follow a Gaussian
distribution. Blum [15], and Yang and Blum [196] have improved the probabilistic
fusion by allowing non-Gaussian noise distribution. An expectation maximization
(EM)-based solution to detect concealed weapon through image fusion has been
presented in [196]. For robustness against noise, a total variation (TV)-based prior
has been incorporated into the probabilistic model by Kumar [94], and Kumar and
Dass [95]. Xu et al. have proposed a Markov random field (MRF)-based prior for the
fused image, and a Gaussian assumption of the parameters of the image formation
model for hyperspectral image fusion [192, 193].
When the number of images to be fused is higher than three, the fusion problem
can be viewed as a dimensionality reduction of the input data. Principal component
analysis (PCA) is a powerful tool used for dimensionality reduction of multispectral
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