Abstract
A new adaptive region-based image fusion approach is proposed. To implement image segmentation, the piecewise smooth Mumford-Shah segmentation algorithm is studied and a fast and simple method is proposed to solve the energy function. Two complementary functions u + and u − of the algorithm, which are respectively looked as objects and background of the image, are extended into the whole image domain, and they are computed by linear or nonlinear diffusion. The key to the algorithm is to make optimal fusion decisions for every segmented region. For this purpose, an evaluation approach has to be given to measure the performances of the available fusion rules. Therefore an energy-based evaluation model, derived from the Total Variation principle, is proposed. By numerical experiment it has been demonstrated that despite an increase in complexity, the new approach has shown a number of advantages over previous ones, for example the ability to preserve all relevant information and remove some of side effects such as reducing contrast and sensitive to error of registration.
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Abbreviations
- u :
-
the observed image
- u + :
-
the object regions of an image
- u − :
-
the background regions of an image
- u 0 :
-
an input image
- R 2 :
-
2D real domains
- \({\left| {\nabla u} \right|}\) :
-
gradient of the image u
- \({\left| {\nabla u^{+}} \right|}\) :
-
gradient of the image u +
- \({\left| {\nabla u^{-}} \right|}\) :
-
gradient of the image u −
- \({\wp}\) :
-
a bounded open subset in 2-dimensional real domains
- ω:
-
an open curve set
- Γ:
-
boundary curves
- \(\phi\) :
-
level set curves
- ∂ω:
-
zero level set curves in 2D space
- \(\phi _{0}\) :
-
zero level set curves in 3D space
- d :
-
distance between point and zero level set
- E TV :
-
energy of the region of an image from TV model
- E MTV :
-
energy of the fused region of an image from the fusion evaluation model
- F :
-
speed of evolution of curves
- \(\delta (\phi)\) :
-
delta function in Chan–Vese–Mumford–Shah model
- u s :
-
a smooth component of the observed image u 0
- s :
-
scale level
- \( \tilde{u}_{{\rm s}}\) :
-
resulting image obtained from u s by the four-point averaging method
- Ω:
-
segmented regions of an image
- u R :
-
a reference image with the least value for each pixel point
- λ:
-
a positive parameter to control the fidelity in the energy formulation
- μ:
-
a positive parameter to control the fidelity in the energy formulation
- k :
-
iteration numbers
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Zhang, Y. Adaptive region-based image fusion using energy evaluation model for fusion decision. SIViP 1, 215–223 (2007). https://doi.org/10.1007/s11760-007-0015-6
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DOI: https://doi.org/10.1007/s11760-007-0015-6