International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004 Int 
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in the equation for A, represents the up-sampled and Down-sampling by a factor of two in horizontal and vertical sali 
ct e directions recursive processing over successive levels "es is 
interpolated version of G; 4; - À hyperpixel in this interpolated eum c Ve processing GVCF. SUCCOssTve levels produces fus 
: : à a Gaussian pyramid. (or 
image corresponds to a wel ghted local average in the 
. x ^ LS A y * . ~ hy 
neighbourhood of the hyperpixel at the same location in G, . The next step in image decomposition is extracting the Sch 
Hence, the denominator in. A, is proportional to Lj, whereas the orientation gradient details on each level (except the top) of the ob 
  
Gaussian pyramid. Burt calls this step creating the orientation 
numerator is proportional to L . Therefore the pyramid whose : : ; : 
gradient pyramid (Burt and Kolczynski, 1993). It is called the 
avais Are her ie th ‘el Of the ; : ; ; 
levels are Ry —I, (where [is the k™ level of the unit Orientation gradient because the kernels are the gradient filters 
pyramid with all hyperpixels having value 1) represents a d, through d, : 
contrast pyramid. The original image can be perfectly All 
reconstructed by reversing the pyramid generation operations D,, 2 dj * [5 Lu 5d (23) Bel 
described above. im] 
[o —1] -] -1 0 i 
; : He : d, «li <1): dy =] , dy = , dy = (24) eas 
The fused contrast pyramid Apis formed from the contrast | +0 l 0 | Dre 
py [ [ 
pyramids R, and Rp of the images A and B by using the vai 
selection rule: D,, are the details for level k and orientation /, Gy is the level k Ser 
: : ; yq m pu me 
input from the reduced image pyramid. The process for fusion m: 
bu» i Ww NT ri follows the concept outlined in Section 2.4. 
t, R^ (i, j) if ea.) > [Rb Gi.) : | Le 
R} (i, j) = (19) ; ; : ext 
2.8. Fusion method based on Morphological pyramids es 
R5 G, J) Otherwise 
Mathematical morphology offers another conceptual approach 
where kis the level of the pyramid and (i,j) denote the to image fusion. The morphological filters, in particular opening 
and closing are employed for creating a morphological pyramid 
(Morales et al., 1995). The filters are designed to preserve edges 
or shapes of objects, while eliminating noise and details in an 
image. The morphological opening followed by-closing and 
closing followed by opening are chosen because they are 
hyperpixels at that level. The fusion rule selects the hyperpixels 
corresponding to the largest local luminance contrast. As a 
result, image features with high contrast are preserved in the 
fused image. 
2.6. Fusion method based on FSD Laplacian pyramids biased-reduced operators. The morphological pyramid is 
constructed by successively morphological filtering and down 
The  filter-subtract-decimate (FSD) hierarchical pyramid sampling: 
proposed by Anderson (1987) is conceptually identical with the 
the Laplacian concept explained in section 2.4. I. Alan  K)* Kl, L 2 0L... n (25) 
In the following we refer to the input image as Gy the low-pass 
where L is the pyramid level. Ip is the original image, 
  
  
filtered versions are G, to Gy with decreasing resolutions and | 
the corresponding difference images are pu CL kids, represents down sampling by a factor of d in both spatial D 
SI g ages e p. XK N > 
respectively. A recursive procedure for the creationsofithe ESD dimension. (/ » K) represents the morphological opening of the Fi 
pyramid reads as follows: image / with structuring element K. and. (/ * K) represents tlt 
morphological closing. The finest level L=0 of the Fig 
6h -W*G, morphological pyramid contains the input image. The image a int 
; any level L is created by applying morphological filtering witha M, 
L, =G, Gh (20) 3x3 structuring element to the image level (L-/) followed by 
down-sampling the filtered image with d-2. The process for 
: 40 
G,, = Subsampled G 
+ + 2 em : : . . 
"t a fusion follows the concept outlined in Section 2.4. 
With the Gaussian filter W the process for fusion coincides with 2.9. Fusion method based on Averaging Th 
the Laplacian concept outlined above (Section 2.4). AS 
A simple approach for fusion, based on the assumption oi the 
2.7. Fusion method based on Gradient pyramids additive Gaussian noise, consists of synthesizing the fused bar 
; : Sr image by averaging corresponding pixels of the sensor images she 
Fusion based on gradient pyramids Is another alternative to the Averaging should work well (Sharma, 1999) when the imag in i 
Laplacian concept. As above a first step consist of construcüng to be fused are from the same type of sensor and contain 
a Gaussian pyramid. Burt and Kolczynski (1993) used the 3 x 9 additive noise only. If the variance of noise in q sensor images Th 
Gaussian kernel is equal then averaging them reduces the variance of noise in ide 
. j the fused image according to the error propagation law. I5 
w= Wikw (21) E Th 
to lowpass filter the image with 2.10. Fusion method based on Selection and 
res 
| 3 4 Fusion based on some selection process is an alternative p IR: 
d d 4 2 (22) simple averaging. Selection may use the Laplacian pyramid > cor 
16 uut basis. This technique has then three distinct stages - pyram 
k 2 1d construction, selection of pyramid coefficients based on 
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