pan‐sharpening of very high resolution multispectral images using genetic algorithms

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PAN‐sharpening of very high resolutionmultispectral images using geneticalgorithmsA. Garzelli a & F. Nencini aa Department of Information Engineering, University of Siena, ViaRoma 56, 53100 Siena, ItalyPublished online: 22 Feb 2007.

To cite this article: A. Garzelli & F. Nencini (2006) PAN‐sharpening of very high resolutionmultispectral images using genetic algorithms, International Journal of Remote Sensing, 27:15,3273-3292, DOI: 10.1080/01431160600554991

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PAN-sharpening of very high resolution multispectral images usinggenetic algorithms

A. GARZELLI* and F. NENCINI

Department of Information Engineering, University of Siena, Via Roma 56, 53100 Siena,

Italy

(Received 28 July 2005; in final form 22 December 2005 )

A novel image fusion method is presented, suitable for sharpening of

multispectral (MS) images by means of a panchromatic (PAN) observation.

The method is based on redundant multiresolution analysis (MRA); the MS

bands expanded to the finer scale of the PAN band are sharpened by adding the

spatial details from the MRA representation of the PAN data. As a direct,

unconditioned injection of PAN details gives unsatisfactory results, a new

injection model is proposed that provides the optimum injection by maximizing a

global quality index of the fused product. To this aim, a real-valued genetic

algorithm (GA) has been defined and tested on Quickbird data. The optimum

GA injection is driven by an index function capable of measuring different types

of possible distortions in the fused images. Fusion tests are carried out on

spatially degraded data to objectively compare the proposed scheme to the most

promising state-of-the-art image fusion methods, and on full-resolution image

data to visually assess the performance of the proposed genetic image fusion

method.

1. Introduction

Spaceborne imaging sensors allow a global coverage of the Earth surface to be

achieved on a routine basis. Multispectral (MS) observations, however, exhibit

ground resolutions that may be inadequate to specific identification tasks, especially

where urban areas are concerned. Following the successful launch of the new

generation of satellite imagers, Ikonos, QuickBird and SPOT-5, very high-resolutionMS and panchromatic (PAN) images are now available.

Data fusion techniques, originally devised to allow integration of different

information sources, may take advantage of the complementary spatial/spectral

resolution characteristics for producing spatially enhanced MS observations. This

specific aspect of data fusion is often referred to as data merge (Scheunders and

Backer 2001) or band-sharpening (Kumar et al. 2000). More specifically, PAN-

sharpened MS is a fusion product in which the MS bands are sharpened through the

higher-resolution PAN image. The latter is acquired with the maximum resolution

allowed by the imaging sensor, as well as by the datalink throughput, while theformer are acquired with coarser resolutions, typically two to four times lower,

because of signal-to-noise ratio (SNR) constraints and transmission bottlenecks.

After being received at ground stations, the PAN images may be merged with the

MS data to enhance their spatial resolution.

*Corresponding author. Email: [email protected]

International Journal of Remote Sensing

Vol. 27, No. 15, 10 August 2006, 3273–3292

International Journal of Remote SensingISSN 0143-1161 print/ISSN 1366-5901 online # 2006 Taylor & Francis

http://www.tandf.co.uk/journalsDOI: 10.1080/01431160600554991

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Data merge methods, based on injecting high-frequency components taken from

the PAN image into resampled versions of the MS data, have demonstrated superior

performances (Wald et al. 1997, Schowengerdt 1980). The pioneering method of

high-pass filtering (HPF; Schowengerdt 1980) consists of an addition of spatial

details, taken from a high-resolution PAN observation, into a bicubically resampled

version of the low-resolution MS image. Such details are obtained by taking the

difference between the PAN image and its lowpass version achieved through a

simple local pixel averaging, that is a box filtering. Later efforts benefit from

multiresolution analysis (MRA), which provides effective tools, such as wavelets

and Laplacian pyramids, to help carry out data fusion/merge tasks (Ranchin and

Wald 2000, Aiazzi et al. 2002, Garzelli and Nencini 2005).

Redundant multiresolution structures, such as the generalized Laplacian pyramid

(GLP; Aiazzi et al. 2002) matching even fractional scale ratios between the images to

be merged, the undecimated discrete wavelet transform (UDWT), and the ‘a-trous’

wavelet transform (ATWT), have been found to be particularly suitable for image

fusion because of their translation-invariance property (not strictly possessed by the

GLP). As all these decompositions are not crucially subsampled, injection artefacts

and canvas-like patterns originated by aliasing are avoided.

Fusion schemes based on the ATWT have been proposed recently (Nunez et al.

1999, Garzelli et al. 2000, Chibani and Houacine 2002, Garzelli and Nencini 2005)

and have been successfully used within the ARSIS (Amelioration de la Resolution

Spatiale par Injection de Structures) concept (Ranchin et al. 2003). Data merge

based on multiresolution analysis, however, requires the definition of a model

establishing how the missing highpass information to be injected into the resampled

MS bands is extracted from the PAN image. Wavelet-based techniques that do not

consider any injection model (Li et al. 2002) may produce unsatisfactory results in

terms of spectral preservation of the fused product. This means that the spatial

information of the PAN data has to be opportunely weighted and equalized before

being injected onto each band of the MS data. This is the case with Spectral

Distortion Minimizing (SDM; Alparone et al. 2003), Context Based Decision (CBD;

Aiazzi et al. 2002) and Ranchin, Wald, Mangolini (RWM; Ranchin et al. 2003)

techniques, which use space-varying models. These fusion algorithms produce good

results but are typically effected by numerical instabilities. In particular, the SDM

algorithm implements an easy and efficient model of injection but suffers the

drawbacks of instability and data-dependent results.

To overcome these problems, in this paper we propose an injection model PAN-

sharpening by genetic algorithm (GA), in which the coefficients that equalize the

PAN image before details are injected into the MS image are derived globally – one

for each band – from coarser scales, similar to previous schemes such as SDM, CBD

and RWM, but not a priori defined on image local statistics (e.g. variance, mean,

correlation coefficient). A GA is applied to determine the gains that maximize an

image quality score index, namely the Q4 quality index (Alparone et al. 2004), which

has proved to be particularly efficient for measuring radiometric and spectral

distortions on four-band multispectral images. The ability to find quickly and

efficiently an optimum solution is verified by testing the GA on Quickbird images,

and both visual and objective experimental comparisons with advanced fusion

methods are also reported.

The remainder of the paper is organized as follows. Section 2 deals with the image

analysis tools used in the proposed PAN-sharpening algorithm with emphasis on the

3274 A. Garzelli and F. Nencini

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ATWT. In section 3 a general GA scheme is described, based on the floating point

representation of chromosomes and on genetic operators borrowed from the most

promising studies on GAs. How the GA is used to regulate the PAN injection is

explained in section 4. Experimental results and comparisons are presented and

discussed in section 5 on Quickbird data. Conclusions are drawn in section 6.

2. Image analysis

2.1 Wavelet ‘a-trous’ transform

The octave multiresolution analysis introduced by Mallat (1999) for digital images

does not preserve the translation invariance property. In other words, a translation

of the original signal does not necessarily imply a translation of the corresponding

wavelet coefficient. This property is essential in image processing. On the contrary,

wavelet coefficients generated by an image discontinuity could disappear arbitrarily.

This non-stationarity in the representation is a direct consequence of the down-

sampling operation following each filtering stage.

To preserve the translation invariance property, the down-sampling operation is

suppressed, but filters are up-sampled by 2j, that is dilated by inserting 2j21 zeros

between any couple of consecutive coefficients. An interesting property of the

undecimated domain (Aiazzi et al. 2002) is that at the jth decomposition level, the

sequences of approximation, cj(k, m), and detail, dj(k, m), coefficients are

straightforwardly obtained by filtering the original signal through a bank of

equivalent filters, given by the convolution of recursively up-sampled versions of the

lowpass filter h and the highpass filter g of the analysis bank:

h�j ~ 6

j{1

m~0h : 2mð Þ ð1Þ

g�j ~ 6

j{2

m~0h : 2mð Þ

� �6 g : 2j{1� �

~h�j{16 g : 2j{1� �

ð2Þ

The ATWT (Dutilleux 1989) is an undecimated non-orthogonal multiresolution

decomposition defined by a filter bank {hi} and {gi5di2hi}, with the Kronecker

operator di denoting an allpass filter. In the absence of decimation, the lowpass filter

is up-sampled by 2j, before processing the jth level; hence the name ‘a-trous’, which

means ‘with holes’. In two dimensions, the filter bank becomes {hihj} and

{didj2hihj}, which means that the 2-dimensional (2D) detail signal is given by the

pixel difference between two successive approximations, which have all the same

scale 20, i.e. 1. The jth level of the ATWT, j50, …, J21, is obtained by filtering the

original image with a separable 2D version of the jth equivalent filter, as in

equation (1).

For a J-level decomposition, the ‘a-trous’ wavelet accommodates a number of

coefficients J + 1 times greater than the number of pixels. Because of the absence of

decimation, as well as the zerophase and 26 dB amplitude cutoff of the filter, the

synthesis is simply obtained by summing all detail levels to the approximation:

exx k, mð Þ~XJ{1

j~0

dj k, mð ÞzcJ k, mð Þ ð3Þ

in which cJ(k, m) and dj(k, m), j50, …, J21, are obtained through 2D separable

PAN-sharpening by genetic algorithm 3275

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linear convolution with h�J and g�j , j50, …, J21, equations (1) and (2), respectively.

Equivalently, they can be calculated by means of a tree-split algorithm, that is by

taking pixel differences between convolutions of the original signal with

progressively up-sampled versions of the lowpass filter.

The number of decomposition levels J, which directly defines the equivalent

lowpass filter hJ, given a half-band prototype filter {hi}, rules the smoothness of the

lowpass approximation.

2.2 Structure of the PAN-sharpening model

The definition of a suitable model for the injection of PAN details is important for

the good quality of the data fusion product. The most promising methods have

developed different models, generally related to a common approach that consists of

calculating the parameters that regulate the injection (typically gain and offset) at a

coarser resolution and then adopting those parameters to the finer resolution. This

means that the scale persistence is exploited, assuming that the characteristics of

edges and texture at coarser scales are not too different from those at finer scales.

This hypothesis is verified if the ratio between the spatial resolutions of MS and

PAN data is not too high and if the model is opportunely defined. Some successful

techniques, namely SDM, CBD and RWM, have developed interesting models in

which the PAN injection is regulated by the ratio between the standard deviations of

the MS and PAN data, or by the first moment of inertia (Wald 2002). Furthermore,

the injection model can be local, that is contextualized to neighbourhood pixels, or

global, derived from analysis of the whole acquired area.

The problem that generally occurs when applying those fusion techniques is that

the definition of the model parameters does not correspond to an optimum choice in

terms of geometric, radiometric and spectral distortions of the fused product. In

addition, the definition of a local model often gives rise to numerical instability and

unsatisfactory visual quality throughout the image.

The proposed model is a simple linear model in which the unknown global gain

parameters gl, l51, 2, …, N, with N denoting the number of MS bands, are not a

priori defined or computed from local statistics, but are calculated by maximizing an

appropriate function at coarser scales (i.e. the Q4 index), which will be recalled in

the following section. In synthesis, the proposed model defines how the spatial

details of the fused MS image edd MSl jð Þ (at scales j50, 1 in the case of the 1 : 4 scale ratio

between PAN and MS images) are obtained from the PAN spatial details

d PANl jð Þ m, nð Þ at the same scales:

eddMSl jð Þ m, nð Þ~gl dPAN

l jð Þ m, nð Þ{dPAN

l jð Þ

� �zdMS

l jð Þ m, nð Þ j~0, 1 ð4Þ

where the index l is related to the band being analysed, :ð Þ is the mean operator, and

the dMSl jð Þ m, nð Þ coefficients of the expanded MS image (which are near to zero) are

also added to avoid possible impairments due to the ATW filtering operations and

to preserve accurately the mean value of the original MS image.

The task of the GA is to find the best combination of the real-valued coefficients

gl, l51, 2, …, N, according to an objective criterion that describes the enhancement

of the MS images. The representation of the chromosomes, g, is therefore a string of


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real numbers as reported in equation (5).

Chromosome g : g1, g2, g3, :, :, :, gNf g ð5Þ

2.3 Quality evaluation criterion

The image quality index Q4 for multispectral images having four spectral bands can

be calculated on PAN-sharpened MS images as described in Alparone et al. (2004).

The index Q4 is derived from the theory of hypercomplex numbers, in particular of

‘quaternions’, which can be represented in the form a5a1 + a2i + a3j + a4k, where a1,

a2, a3, a4 are real numbers, and i25j25k25i j k521. For MS images with four

spectral bands, typical for new generation satellite images, a1, a2, a3, a4 represent the

values assumed by a given image pixel in the four bands, acquired in the blue, green,

red and near-infrared (NIR) wavelengths. The quality index is a generalization of

the Q index defined in Wang and Bovik (2002) for an original image signal x and a

test image signal y, which can be stated as

Q~4 cov x, yð Þxy

var xð Þzvar yð Þð Þ xð Þ2z yð Þ2h i : ð6Þ

and may be equivalently rewritten as

QN|N~cov x, yð Þ

sxsy

2xy

xð Þ2z yð Þ22sxsy

s2xzs2

y

ð7Þ

where sf denotes the standard deviation of f, and cov(x, y) is the cross-covariance of

x and y, all computed over a given N6N block. In practice, the first factor is the

correlation coefficient (CC), the second factor (always,1 and51 iff x5y) accounts

for the mean bias; analogously, the third factor measures the change in contrast.

Eventually, the quality index Q of y is obtained by averaging the values obtained

starting from all the N6N blocks of the images x and y. This quality factor can be

applied only to monochrome images.

The unique score index Q4 for four-band MS images, which assumes a real value

in the interval [0, 1], is 1 iff the MS image is identical to the reference image. Again,

Q4 is made up of different components (factors) to take into account the correlation,

the mean of each spectral band, the intraband local variance, and the spectral angle.

The first three factors are also taken into account by Q for each band while the

spectral angle is introduced by Q4 by properly defining a CC of multivariate data. In

this way, both radiometric and spectral distortions are considered by a single

parameter. Q4 can be computed from

Q4N|N~4 E x:y�½ �{x:y�½ �

E xk k2h i

{ xk k2zE yk k2

h i{ yk k2

: xk k: yk kxk k2

z yk k2ð8Þ

where quaternions are indicated in bold case (e.g. x5{xr + i x1 + j x2 + k x3}), the

product of x by the (hyper)complex conjugate of y, namely y*, has to be intended as

a product of quaternions, E[?] denotes the quaternion obtained by averaging the

pixel quaternions within an N6N block and ||x||5!(x2r + x2

1 + x22 + x2

3) is the

magnitude of quaternion x. Finally Q4 is obtained by averaging the magnitudes of


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all Q4N6N over the whole image, i.e.

Q4~E Q4N|Nk k½ � ð9Þ

The more Q4 approaches unity, the higher is the radiometric and spectral quality of

the fused image. This suggests that this index can be used not only to evaluate the

performances of fusion algorithms but also as a target function to be maximized to

compute optimal fusion parameters.

Determining the best solution analytically is a difficult task, particularly if we are

looking for a global solution. A genetic approach designed for optimal parameter

computation can solve this problem in a powerful and efficient way.

3. Genetic components

GAs (Davis 1991, Michalewicz 1994) are inspired by the evolution of populations.

In a particular environment, individuals who fit the environment better will be able

to survive and hand down chromosomes to their descendants, while less fit

individuals will become extinct. The aim of GAs is to use simple representations to

encode complex structures and simple operations to improve these structures.

Therefore, GAs are characterized by their representations and operators. A fitness

function is defined that measures the fitness of each individual. The populations are

evolved to find good individuals as measured by the fitness function. GAs have been

used to solve linear and nonlinear problems (Michalewicz 1994, Ghoshray and Yen

1995, Chaiyaratana and Zalzala 1997, Vasconcelos et al. 2001) and in several remote

sensing applications, such as classification (Tso and Mather 1999, Pal and

Bandyopadhyay 2001, Pal et al. 2001, Maulik and Bandyopadhyay 2003, Mertens

et al. 2003), image processing (Liu and Tang 1998, Caorsi et al. 2000, Munteanu

and Rosa 2000, Ho and Lee 2001), feature selection (Lin and Sarabandi 1999, Jin

and Wang 2001, Jeon et al. 2002, Chen 2003, Yao and Tian 2003, Zhan et al. 2003)

and electromagnetic modelling (Anyong et al. 2001). The ability to explore all

regions of the state space of chromosomes, which constitute the population, using

genetic operators (mutation, crossover) and reproduction have led to increased

attention in recent studies. A GA flow diagram is shown in figure 1, and each of the

major components is discussed in the following sections. A GA requires the

definition of these fundamental steps: chromosome representation, selection of a

function, also called the fitness function, creation of the initial population,

reproduction function, mutation and crossover operators, termination criteria,

and evaluation of the fitness function. The following subsections describe these

issues.

3.1 Chromosome representation

A chromosome representation is necessary to describe each individual in the GA

population. The representation scheme determines how the problem is structured in

the GA and also determines the genetic operators that are used. Each chromosome

is made up of a sequence of genes from a predefined alphabet. Binary digits (0 and

1), floating point numbers, integers, symbols (i.e. A, B, C, D), matrices, etc., can be

used as the alphabet in the genes’ representation. In the original design, the alphabet

was limited to binary digits, but it has since been shown that natural representations

are more efficient and more accurate (Michalewicz 1994). One useful representation

of a chromosome for function optimization involves genes from an alphabet of


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floating point numbers with values limited by an upper and a lower bound.

Michalewicz (1994) showed that a real-valued GA is more efficient in terms of CPU

time and more accurate in terms of precisions for replications than binary GA

representations.

3.2 Reproduction

An important role in GAs is the selection of individuals to produce successive

generations, usually called reproduction. A probabilistic selection is performed

based on the individual’s fitness, such that the better individuals have an increased

chance of being selected. An individual in the population can be selected more thanonce, with all individuals in the population having a chance of being selected to

reproduce into the next generation. Several schemes are available for the selection

process: roulette wheel selection, scaling techniques, tournament, elitist models and

ranking methods (Holland 1975, Goldeberg 1989, Michalewicz 1994).

A common selection approach assigns a probability of selection, Pj, to each

individual j based on its fitness value. A series of N random numbers uniformly

Figure 1. Flow diagram of GA.


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distributed between 0 and 1, U(0, 1), is generated and compared against the

cumulative probability, Ci~Pi

j~1 Pj, of the population. If the random number

linked to the appropriate individual i is limited by Ci21 and Ci, the i-individual is

copied into the new population. Various methods exist to assign probabilities to

individuals: roulette wheel, linear ranking and geometric ranking.

Ranking methods, which produce the best performances, require the evaluation

function to map the solutions to a partially ordered set and assign Pi based on the

rank of solution i when all solutions are sorted. Normalized geometric ranking

(Joines and Houck 1994) defines Pi for each individual by:

Pi~q 1{qð Þr{1

1{ 1{qð ÞPopSizeð10Þ

where q is the probability of selecting the best individual, PopSize is the overall

number of chromosomes and r is the rank of the individual, where 1 is the best.

3.3 Genetic operators

Genetic operators provide the basic search mechanism of the GA. The operators are

used to create new solutions based on existing solutions in the population. There are

two basic types of operators: crossover and mutation. Operators for real-valued

representations, that is an alphabet of floats, were developed by Michalewicz (1994).

Crossover takes two individuals and produces two new individuals, while mutation

alters one individual to produce a single new solution. The application of these two

basic types of operators and their derivatives depends on the chromosome

representation used. For real X and Y m-dimensional vectors representing

chromosomes, the following operators are defined: uniform mutation, non-uniform

mutation, multi-non-uniform mutation, boundary mutation, simple crossover,

arithmetic crossover, and heuristic crossover. Let ai and bi be the lower and upper

bounds, respectively, for each variable i.

3.3.1 Mutation. Uniform mutation randomly selects one variable, j, and sets it

equal to a uniform random number bounded by ai and bi terms:

x0i~U ai, bið Þ if i~j

xi otherwise

�ð11Þ

Boundary mutation randomly selects one variable, j, and sets it equal to either its

lower or upper bound, where r5U(0, 1):

x0i~

ai if i~j, rv0:5

bi if i~j, r§0:5

xi otherwise

8><>: ð12Þ

Non-uniform mutation randomly selects one variable, j, and sets it equal to a non-

uniform random number:

x0i~

xiz bi{xið Þ r2 1{ GGmax

� �� b

if r1v0:5

xi{ xizaið Þ r2 1{ GGmax

� �� b

if r1§0:5

xi otherwise

8>>>><>>>>:

ð13Þ


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where r1 and r2 are uniform random numbers between (0, 1), G and Gmax are

respectively the current and the maximum number of generations, and b is a shape

parameter.

The multi-non-uniform mutation operator applies the non-uniform operator to

all of the variables in the parent X.

3.3.2 Crossover. Real-valued simple crossover generates a random number r from

a uniform distribution from 1 to m and creates two new individuals (X9 and Y9)

according to equation (14).

x0i y0i� �

~xi yið Þ if ivr

yi xið Þ otherwise

�ð14Þ

Arithmetic crossover produces two complimentary linear combinations of the

parents, where r5U(0, 1):

X0~rXz 1{rð ÞY ð15Þ

Y0~ 1{rð ÞXzrY ð16Þ

Heuristic crossover produces a linear extrapolation of the two individuals. This is

the only operator that uses fitness information. A new individual, X9, is created

using equation (17), where r is a random number r5U(0, 1) and X is better than Y in

terms of fitness. If X9 is not feasible, that is there is at least a new gene smaller than

ai or larger than bi, then generate a new random number r and create a new solution

using equation (17), otherwise stop. After t failures, the process is not repeated and

the children are set equal to the parents.

X0~Xzr X{Y

� �ð17Þ

Y0~X ð18Þ

3.4 Initialization, termination and fitness function

To start the search of the optimal solution by GA it is necessary to provide an initial

population as indicated in figure 1. The most common method is to randomly

generate solutions for the entire population. However, as GAs can iterativelyimprove existing solutions, the starting population can be seeded with potentially

good solutions, with the remainder of the population being randomly generated.

The GA moves from generation to generation selecting and reproducing parents

until a termination criterion is met. A maximum number of generations is

commonly used to stop the GA search. Another termination strategy involves

population convergence criteria. In general, GAs will force much of the entirepopulation to converge to a single solution. The algorithm can be terminated when

the sum of the deviations among individuals becomes smaller than some specified

threshold or due to a lack of improvement in the best solution over a specified

number of generations. Alternatively, a target value for the evaluation measure can

be established based on some arbitrarily ‘acceptable’ threshold. Several strategies

can be used in conjunction with each other.

Evaluation functions of many forms can be used in a GA, subject to the minimal

requirement that the function can map the population into a partially ordered set.


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As stated in section 2.3, the evaluation function to be optimized is Q4, which is

particularly suited for minimizing radiometric and spectral distortions.

3.5 Summary

The GA parameters selected for the optimization of Q4 are listed in table 1. The

initial random population is set to 50 and the maximum number of generations is

selected equal to 100. In section 5 we show that these two parameters are proper and

adequate to find the optimal solution in the sense of Q4 maximization. The first (or

unique, in some cases) value for the mutation/crossover operators indicates the

number of times that the operator is applied at each generation. The second and

third components of the non-uniform mutation and multi-non-uniform mutation

parameter vectors are the maximum number of generations and the shape factor

(b53), respectively. The second component of the heuristic crossover parameter

vector indicates the number of failures (t) and it is set to 3. In the reproduction

operator, the probability of selecting the best individual is set to 0.05. The interval of

variation for the gain parameters is the same for all bands and spans the interval

[210, 10] to ensure a wide state space. Each gain parameter gl is spatially constant

on the corresponding band l and will assume a positive value, typically lower than 3;

the interval [0, 3] would therefore be sufficient to ensure satisfactory results.

4. Data fusion

Figure 2 outlines a procedure based on ATWT, suitable for fusion of MS and PAN

image data whose scale ratio is 4. Both the higher resolution PAN image and the

lower resolution MS image dataset are decomposed by the two-level ATWT. The

MS images are previously interpolated by 4 along rows and columns to process MS

images having the same spatial scale as the PAN image. The interpolator and

decimator blocks are implemented by applying twice the up-sampling and down-

sampling operators with a 23-tap filter as described by Aiazzi et al. (2002).

To drive the injection of PAN data, the operator T [di(m, n)] reported in

equation (4) is applied, with g representing the best chromosome derived by the GA

search. The Q4 index, which is able to measure distortions but requires the fused and

the reference MS images as inputs, is calculated at coarser resolution, that is at a

resolution degraded by a factor equal to 4. The Q4N6N values are evaluated on

868 pixel blocks instead of 32632 as suggested by Alparone et al. (2004), as the GA

Table 1. GA parameters used for real-valued Q4 function optimization.

Operation Parameters

Initial population 50Normalized geometric selection 0.05Uniform mutation 4Non-uniform mutation [4, 100, 3]Multi-non-uniform mutation [6, 100, 3]Boundary mutation 4Simple crossover 2Arithmetic crossover 2Heuristic crossover [2, 3]Maximum generation 100Chromosomes bounds (for each band) [210, 10]


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is applied to MS images at a lower scale. The GA is finally applied with the

parameters described in table 1.

5. Experimental results and comparisons

Evaluation of the efficiency and robustness of the proposed fusion algorithm was

carried out on three different dataset acquired by the Quickbird spaceborne MS

scanner on the urban and suburban areas of Pavia (Italy), Rome (Italy) and Ceuta

(Spain). The four MS bands span the visible and NIR wavelengths with blue

(B15450–520 nm), green (B25520–600 nm), red (B35630–690 nm) and NIR

(B45760–900 nm); the PAN band is acquired on the wavelength interval 450–

900 nm. All the data were radiometrically calibrated from digital counts,

orthorectified (i.e. resampled to uniform ground resolutions of 2.8 m and 0.7 m

Ground Spatial Distance (GSD) for MS and PAN, respectively), and packed in 16-

bit words. The full scale of all the bands is 2047 (11 bits) and is reached in the NIR

wavelengths. The original sizes of the PAN and MS images were:

N 204862048 and 5126512 for the PAN and MS area of Pavia;

N 102461024 and 2566256 for the PAN and MS area of Rome;

N 153661536 and 3846384 for the PAN and MS area of Ceuta.

To obtain a good fusion of the injected PAN data, that is with low distortion, the

fused MS images should be as similar as possible to the MS set of images that the

corresponding sensor would observe with the highest spatial resolution (0.7 m), if it

existed. Unfortunately, those images are not available; therefore, PAN and MS data

are first spatially degraded by a factor equal to the ratio between MS and PAN

Figure 2. Flowchart of PAN-sharpening based on GA with 1 : 4 scale ratio.


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resolutions (Wald et al. 1997). Thus, 2.8 m PAN and 11.2 m MS are synthetically

generated and processed to enhance MS images up to 2.8 m. The true MS data at

2.8 m used as reference images are available for objective distortion measurements.

Table 2 lists the values of the chromosomes after 100 iterations, providing the best

values of Q4. For each result, it is shown that equalization gains are between 0 and

1.3, hence validating the conservative choice of limiting the state space between 210

and 10. The gains change considerably depending on the data set and on the MS

band; in particular, they are lower on the blue band (B1) than on the other three

bands, especially on NIR (B3). It is worth noting that the gains determined by the

GA are not derivable from the equivalent gains computed by any statistical injection

model (CBD, RWM, SDM, etc.), because the GA injection process is driven by the

minimization of not only radiometric (through intraband processing) but also

spectral (through interband processing) distortions. Figure 3 reports the trend of Q4

for the best chromosome between a population of 50 individuals vs. the generation

step. The three curves show that 100 iterations are sufficient to reach the asymptotic

value for optimum search. Note that after 20 iterations the variations in Q4 are

extremely low. Thus, if necessary, CPU time can be sensibly reduced from 100

iterations to 20–30 iterations without compromising the fusion quality. In our

simulations the number of iterations have not been reduced as the CPU

requirements were not prohibitive.

The proposed method was compared to some very efficient fusion methods, listed

below:

N Synthetic Variable Ratio (SVR) as proposed by Zhang (1999);

N SDM (Alparone et al. 2003), with a 23-taps filter as reported by Aiazzi et al.

(2002);

N RWM, as described by Ranchin et al. (2003);

N CBD (Aiazzi et al. 2002) with a 23-tap filter;

N Gram Schmidt (GS) as implemented by ENVIr software (Laben and Brower

1998).

The distortion measures of simply resampled MS bands, referred to as EXP, are also

presented for comparison.

Mean bias values were calculated on each band and are listed in table 3. All values

are low and tend to zero except those related to the SVR method, which shows

significant bias values. In the MRA methods and also in the GS method the results

are acceptable; in particular, GA and GS methods are designed to maintain bias

equal to the corresponding values of the resampled MS images (EXP). Table 4

reports, for each band, the CC on the left and the universal quality index on the

right. CC measures how much the texture of the fused MS images reflects that of the

reference MS images, but it does not take into account mean bias and contrast

deviation. The values of CC and Q on the blue band (B1) are lower than those

Table 2. Best chromosomes (g) computed from degraded data (PAVIA, ROME andCEUTA) after 100 iterations.

B1 B2 B3 B4

PAVIA 0.160 0.446 0.688 1.282ROME 0.376 0.788 0.792 1.186CEUTA 0.449 0.930 0.899 0.893


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calculated on the other bands, especially for the Pavia data set. Note that the GA

method generally provides the best results for all the data sets. A performance

ranking of algorithms indicates that the GA method is followed by RWM, CBD and

GS methods, whose performances depend highly on the particular data set being

considered. As an example, the Q index of CBD is higher than that of RWM and GS

for all bands in Pavia but this is not true for the Rome data set, and it is lower than

that of RWM on all bands of the Ceuta MS image. Table 5 reports other distortion

measures that are not band dependent:

N Relative dimensionless global error in synthesis, ERGAS, to measure radio-

metric distortions (Wald 2000);

N Spectral Angle Mapper (SAM), to measure spectral distortions (Alparone et al.

2003);

N Q4 index, to measure radiometric and spectral distortions jointly (Alparone et

al. 2004).

An excellent fusion quality is obtained when the values of ERGAS and SAM

converge to 0. A unique index can be useful for determining whether one fusion

method is globally better than another. The GA results are the best for all three data

sets analysed. The validity of the optimization process driven by the Q4 index,

jointly minimizing spectral and radiometric distortions, is confirmed by the

reduction in the single-band distortion indexes, i.e. ERGAS and SAM. The GA

method shows the best performance, while the RWM, CBD and GS methods have

similar behaviour but are strongly dependent on the particular data set. This result

proves the robustness of the GA method: when the statistical properties of the MS

Figure 3. Plot of optimal Q4 values at each generation step. The three curves refer toPAVIA data (solid line), ROME data (dotted line) and CEUTA data (dash-dot line). Theiteration steps are visualized in logarithmic scale.


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images change, the fusion quality is still very satisfactory. Note also that the

computational burden of GA is lower than that in the RWM or CBD methods,

which use a local injection model, and is comparable to that of the GS method.

Figure 4 shows, on the left, the fusion results obtained by the GA method at 2.8 m,

and, on the right, the reference images. The sizes of the MS images in figure 4 are set

according to the spatial dimensions of the original data, as listed at the beginning of

this section. Figure 5 reports 2566256 tiles of the GA fused data at 0.7 m on the left,

and the corresponding tiles of the resampled data on the right side. In all figures,

true colour (B3–B2–B1) composites, instead of false colour (B4–B3–B2) composites,

are shown because fusion methods typically fail on the blue band (B1). The fused

images of figure 4 are very similar to the reference MS images and they give a very

accurate result in the colour representation. Figure 5 demonstrates that PAN

accurately sharpens and does not overenhance the MS images. Finally, a

comparison between fused and lower-scale original images shows that evident

chromatic distortions are avoided completely.

6. Conclusion

A novel GA fusion method has been proposed for PAN-sharpening of MS images.

The algorithm is based on undecimated multiresolution analysis, which adopts

injection-model parameters derived at coarser scales by means of a GA.

Table 3. Mean bias between fused and reference 2.8 m MS bands.

BIAS

B1 B2 B3 B4

PAVIAEXP 0.002 0.007 0.011 0.027GA 0.002 0.007 0.012 0.027SVR 0.590 0.624 0.097 20.398SDM 20.255 20.310 20.134 20.097RWM 20.080 20.127 20.118 20.024CBD 20.027 20.058 20.117 0.204GS 0.002 0.007 0.012 0.023

ROMEEXP 0.066 0.005 0.001 0.020GA 0.066 0.005 0.001 0.020SVR 3.208 2.310 20.162 20.973SDM 20.800 21.090 20.765 20.790RWM 20.002 0.025 0.013 0.060CBD 20.067 20.049 20.022 0.220GS 0.006 0.006 0.001 0.020

CEUTAEXP 0.013 0.032 0.026 0.034GA 0.013 0.032 0.026 0.034SVR 2.939 2.468 20.280 21.387SDM 20.501 20.644 20.394 20.377RWM 0.061 0.052 0.019 0.043CBD 20.094 20.147 0.007 0.321GS 0.013 0.032 0.026 0.034

EXP, MS image expanded to PAN scale; GA, genetic algorithm; SVR, Synthetic VariableRatio; SDM, Spectral Distortion Minimizing; RWM, Ranchin, Wald, Mangolini; CBD,Context Based Decision; GS, Gram Schmidt.


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Table 5. Unique (not band-dependent) quality indexes measuring spectral, radiometric andgeometric distortions between fused and original 2.8 m MS bands.

EXP GA SVR SDM RWM CBD GS

PAVIAERGAS 1.760 1.250 1.589 1.676 1.694 1.429 1.388SAM 2.142 1.661 2.143 2.142 2.075 1.886 1.823Q4 0.750 0.906 0.841 0.864 0.865 0.889 0.874

ROMEERGAS 4.907 3.162 3.744 3.724 3.376 3.366 3.468SAM 4.050 3.597 4.050 4.051 3.747 3.735 3.715Q4 0.791 0.929 0.899 0.916 0.919 0.917 0.911

CEUTAERGAS 3.065 2.021 2.433 2.360 2.109 2.211 2.280SAM 1.765 1.621 1.765 1.765 1.700 1.843 1.981Q4 0.809 0.931 0.916 0.914 0.923 0.915 0.922


Table 4. CC and Q between fused and reference MS bands at 2.8 m.

CC Q

B1 B2 B3 B4 B1 B2 B3 B4

PAVIAEXP 0.860 0.843 0.852 0.819 0.749 0.740 0.757 0.684GA 0.898 0.906 0.916 0.925 0.842 0.873 0.886 0.898SVR 0.531 0.735 0.912 0.924 0.413 0.693 0.867 0.848SDM 0.598 0.771 0.912 0.929 0.387 0.659 0.883 0.897RWM 0.794 0.829 0.837 0.898 0.705 0.785 0.801 0.873CBD 0.862 0.878 0.889 0.916 0.802 0.841 0.856 0.889GS 0.884 0.894 0.905 0.908 0.801 0.830 0.848 0.859

ROMEEXP 0.851 0.847 0.855 0.857 0.785 0.782 0.792 0.787GA 0.931 0.941 0.945 0.946 0.899 0.917 0.918 0.932SVR 0.780 0.903 0.945 0.955 0.731 0.867 0.909 0.921SDM 0.843 0.916 0.945 0.951 0.763 0.883 0.924 0.940RWM 0.921 0.932 0.932 0.941 0.882 0.905 0.898 0.927CBD 0.918 0.931 0.934 0.941 0.884 0.905 0.905 0.925GS 0.926 0.936 0.940 0.941 0.868 0.888 0.890 0.918

CEUTAEXP 0.913 0.913 0.928 0.936 0.790 0.784 0.788 0.760GA 0.957 0.963 0.971 0.974 0.902 0.914 0.916 0.907SVR 0.867 0.936 0.970 0.973 0.802 0.882 0.917 0.906SDM 0.907 0.948 0.970 0.973 0.809 0.884 0.916 0.905RWM 0.949 0.958 0.969 0.971 0.888 0.904 0.911 0.896CBD 0.943 0.954 0.967 0.969 0.873 0.893 0.903 0.888GS 0.955 0.959 0.964 0.963 0.891 0.902 0.902 0.885



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Experimental results obtained on co-registrated MS and PAN images acquired by

Quickbird satellite sensors confirm that the proposed approach significantly

increases the spectral fidelity of the fused images, with respect to the most

promising fusion techniques in the literature, also maintaining very good properties

in terms of spatial enhancement. A peculiar property of the proposed GA-based

Figure 4. True colour (bands 3–2–1) MS images at 2.8 m resolution: (a), (c), (e) GA fusionresults; (b), (d), (f) reference images, for PAVIA data (first row, 5126512 pixels), ROME data(second row, 2566256 pixels) and CEUTA data (third row, 3846384 pixels).


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Figure 5. True colour (band 3–2–1) MS details (2566256): (a), (c), (e), GA fusion results at0.7 m; (b), (d), (f) 2.8 m original images resampled to 0.7 m for PAVIA data (first row), ROMEdata (second row) and CEUTA data (third row).


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fusion algorithm is the robustness to different data characteristics, while the

performances of other state-of-the-art fusion methods often depend on global and

local band statistics. The global injection model provides excellent results and even ifthe local-model approach adopted by several algorithms seems more suitable for

context representation, the GA performances are not limited by numerical

instabilities on the model parameters that may produce, in pure statistical fusion

methods, some relevant artefacts in the fused products. The maximization of Q4 at

coarser scales and the application of the derived solution at finer scales are allowed

by the ARSIS concept and are demonstrated by the excellent results.

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3292 PAN-sharpening by genetic algorithm

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pan‐sharpening of very high resolution multispectral images using genetic algorithms

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