In: Wagner W., Szekely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B 
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where Aj and B- are the compared bands of a multispectral 
image, RMSE is root mean squared error, ¡u A is the mean value 
of A}, K is the number of bands, ^ is high/low resolution 
images ratio; Zero mean normalised cross-correlation, ZNCC: 
ZNCC(A i ,B i ) = 
M N 
Z Z<,Ai(m,n)~fiAiWi.™**)-MB') 
m=1 n=1 (4) 
M N M N 7 
Z I 
/n=1 n-1 m=1 n=1 
where Aj, Bj are the compared images; ji A ,, ju B are the averages 
of the images Aj,Bj, respectively; M, N is the size of the 
compared images. 
2.2 Spatial consistency 
Spatial consistency is another aspect of fused imagery 
assessment. Up to now not many papers deal with spatial 
consistency assessment. Almost all the works use single scale 
edge detector (Gradient, Laplacian, Sobel edge detector) and an 
evaluation metric to calculate the distance between the edge 
maps (usually correlation coefficient) (Shi, 2003; Zhou, 1998; 
Pradhan, 2006). Here the comparison is made between the fused 
bands and the corresponding panchromatic image. Another 
approach calculates the percentage of true and false edges 
introduced into the fused band using Sobel edge detector 
(Pradhan, 2006). Several works on fusion report use of SSIM 
and ERGAS measures for spatial consistency assessment (Lillo- 
Saavedra, 2005) (panchromatic image is used as the reference 
instead of a spectral band). 
In this paper we propose to use an additional measure for spatial 
consistency assessment. This measure uses phase congruency 
(PC) (Kovesi, 1999) for feature extraction on an image. 
Invariance to intensity and contrast change as well as multiscale 
nature of this measure allows to obtain more confident 
assessment comparing to single-scale edge detectors. 
3. PHASE CONGRUENCY FOR SPATIAL 
CONSISTENCY ASSESSMENT 
3.1 Phase congruency 
Phase congruency was proposed as intensity and contrast 
invariant dimensionless measure of feature significance, and 
used for signal matching and feature extraction (Kovesi, 1999). 
Phase congruency at point x may be defined in the following 
way: 
To Ts K MLFA S0 (x)a<d„ (x) - t„ J 
,PA„(x) + e ’ W 
where FA S0 is the amplitude of the component in Fourier series 
expansion, AO so is the phase deviation function, W 0 is the PC 
weighting function, o is the index over orientation, s is the index 
over scale, T 0 is the noise compensation term, e is the term 
added to prevent division by zero, |_ J means that the enclosed 
quantity is permitted to be non-negative (Kovesi, 1999). 
A bank of 2D Log Gabor wavelets is used for feature 
extraction. Different scale and orientation of the wavelets in the 
bank allow extracting more information about the structure 
(detail) of the image under assessment. 
Multiscale image analysis instead of single-scale gradient 
operators allows to extract more information on image 
structure, features and edges. The result of PC extraction is 
phase congruency feature map. This map represents the 
structure of the image and allows to perform feature based 
image comparison. 
3.2 Comparison metric 
Zero mean normalized cross correlation was selected as a 
comparison metric of PC feature maps. Liu et. al. report on 
successful application of the metric for this task (Liu, 2008). 
ZNCC produces a real value in the range [-1,1] where 1 
indicates full similarity of compared maps and -1 indicates 
absolute dissimilarity. 
Pan-sharpened spectral band and corresponding panchromatic 
image are used for extraction of PC feature maps, and the maps 
are compared using ZNCC. The panchromatic image is used as 
the reference image for spatial consistency assessment (Figure 
1). 
3.3 Assessment protocol 
The benefit of PC application for assessment may be illustrated 
by comparison with other assessment methods on pan- 
sharpened dataset, which consists of fused images with known 
quality. PC is expected to show similar trend with other 
assessment measures and provide similar assessment results. 
Well-known fusion methods should be used in order to produce 
the dataset with expected quality. 
Several well-known pan-sharpening methods were selected to 
produce fused images with expected quality (spatial and 
spectral consistency): Intensity-Hue-Saturation (IHS) image 
fusion (Welch, 1987), image fusion using Principal Component 
Analysis (PCA) (Welch, 1987), wavelet image fusion (Aiazzi, 
2002), and General Image Fusion method (GIF) (Wang, 2005). 
Generally, well-known methods IHS and PCA produce fusion 
results with proper spatial consistency; wavelet fusion produces 
proper spectral consistency; GIF method produces a 
compromise of acceptable spectral and spatial consistency. 
Fusion methods can be sorted according to the quality of the 
produced result: in the sense of spectral or in the sense of 
spatial consistency. These methods were chosen as reference 
methods to produce expected results for pan-sharpened dataset 
used for assessment and comparison. 
During the first assessment setup, a set of multispectral images 
was pan-sharpened by the following methods: IHS, PCA, A 
trous wavelet image fusion (ATWT, cubic B-spline), and by 
two modifications of General Image Fusion method (GIF-1 and 
GIF-2). GIF-1 extracts high-resolution image detail (high 
frequency component) from panchromatic image and adds to 
interpolated spectral image. The amount of transferred image 
detail data is established using regression (Starovoitov, 2007). 
GIF-2 employs image detail addition to interpolated spectral 
image (Ehlers, 2004). IHS and PCA image fusion methods were 
run using ENVI software, while all the other fusion methods 
were implemented using IDL system.