2.1

Analysed images

QuickBird is a commercial satellite, launched on October 18, 2001, in an heliosynchronous orbit (450 km and 482 km altitude). It has two CCD cameras - one panchromatic and one multispectral (blue, green, red and near infrared), with spatial resolutions of approximately 0.61 m and 2.50 m respectively. The sweeping width covered by these images is between 16.8 km and 18 km according to the orbital height. The radiometric resolution is 11 bits [8].

The analysed image covers an area of 4.63 km² and corresponds to the city of Azogues (Ecuador), including part of the Burgay river which runs north-south. Several characteristic spots such as the Central Plaza, the Cuenca-Azogues highway, the bus station and the municipal stadium can be distinguished in the image. The size of the panchromatic image is 5677 rows by 2267 columns.

IKONOS is a commercial Earth observation satellite launched on September 24, 1999. It was the first satellite to make high-resolution images available to the public, constituting a milestone in remote sensing. In orbit at 681 km altitude, the spatial resolution is one meter (panchromatic) and four meters (multispectral) with four bands (blue, green, red and near infrared). The width of this image is 11 km. The radiometric resolution is 11 bits [9]. In January 2015, DigitalGlobe, the owner of the satellite, announced that, due to problems with quality standards the satellite had been deactivated.

The analysed image covers the western part of the city and several rural villages. Land use basically corresponds to urban areas, crops, forests and shrubs. The size of the image is 12,217 rows per 10,599 columns, covering an area of 129.49 km².

Landsat 7 and 8 are part of a constellation of eight satellites that have provided Earth surface information since 1972. The Landsat project has been the most successful space remote sensing project developed so far [2]. The images used in this work are:

The Natmur-08 project was a technical assistance contracted by the Murcia Regional Administration (Region of Murcia - Spain), which consisted of digital photogrammetric images taken by airborne panchromatic and multispectral (R, G, B, NIR bands) sensors and a LiDAR survey for the generation of digital terrain models. The project generated panchromatic images with spatial resolutions of 0.45 m and 2 m respectively. The image used has an extension of 5451 rows by 8401 columns (9.27 km ²) and covers the hamlet of Archivel, belonging to the Municipality of Caravaca de la Cruz, in the Region of Murcia (Spain).

2.2

Image fusion methods

Ideally, a good image fusion method should not only increase the spatial resolution of multispectral data, but also preserve as far as possible its spectral integrity [10–13].

In the present study, three fusion algorithms have been implemented: High Pass Filter, Principal Component Analysis and Gram-Schmidt. The reason for choosing them are the good results reported in previous studies; in addition, they represent the main types of image fusion techniques [4, 14–18].

Despite the increasing use of image fusion techniques in remote sensing and the increasing use of R as a data analysis software, there is no R package that implements such techniques. The algorithms were implemented as R [7] functions. We are currently working on creating an R package that will include image fusion techniques, quality assessment methods, test images and a manual.

High Pass Filter (HPF) which is counted among space domain image fusion techniques, inserts high frequency components into images of low spatial resolution.

The HPF methodology was introduced by Schowengerdt (1980) [19] as a data reconstruction and compression technique, and has recently been extended to new datasets to fuse images of different spatial and spectral resolutions [10, 20, 21].

According to Gangkofner et al. (2008) [15], this technique has generally been implemented in a simplistic manner because the parameters used have not been optimized to achieve satisfactory spatial and radiometric results. The same author proposes an optimization and standardization of the method in order to guarantee its applicability to a wide range of images with different ratios between the multispectral and panchromatic spatial resolutions. Different parameter values were derived from this process. This standardisation method was applied in the research described. The algorithm implemented in R can be summarised in three simple steps [15]:

Principal Components Analysis (PCA) is considered as a component replacement technique. It involves a linear transformation of the multispectral bands, the substitution of a variable in the transformed space, and the inverse transformation to the original space [22]. The justification for this substitution is that the panchromatic image is approximately equal to the first principal component, which contains information that is common to all the bands used as input in the PCA procedure, whereas the unique spectral information of each band is represented in the other components [10]. This substitution maximizes the effect of the high resolution panchromatic band on the fused bands resulting from the process [22]. In summary, to calculate PCA image fusion [23]:

Gram-Schmidt (GS), which is also considered a component substitution method [24] was invented by Laben and Brower in 1998 and patented by Eastman Kodak [12]. It is based on the Gram-Schmidt algorithm, a vector orthogonalization process. In the case of images, each band corresponds to a high-dimensional vector (equal to the number of pixels in the image), which are rotated to produce a new set of uncorrelated vectors (GS₁,…, GS_n)

[25].

The procedure for performing the GS fusion is summarized in five steps, which can be consulted in detail in Laben and Brower, 2000 [12]:

2.3

Image fusion evaluation

A visual comparison is made between the original and fused images. There are different criteria within the visual analysis [26], and our work takes into account spectral criteria and spatial criteria. As spectral criteria we considered:

The spatial criteria taken into account were as follows: the fused image should keep the sharpness of an objects’ edge and the spatial contrast between different elements without producing the veined textures in the form of small elongated distortions that can appear when a fusion algorithms is applied.

Five mosaics (Fig. 1 to 5), one for each platform used, containing a clip of the image in its original versions, HPF fusion, ACP fusion and GS fusion were composed to perform the evaluation presented in Tab. 1.

Figure 1.

Clip of the QuickBird image showing a highway roundabout to access the Azogues bus station. Original image (a); HPF fused (b); ACP fused (c) and GS fused (d).

Figure 2.

Clip of the IKONOS image showing the Cuenca University campus. Original image (a); HPF fused (b); ACP fused (c) and GS fused (d).

Figure 3.

Clip of the Landsat 7 image showing a segment of the River Chira and one of its tributaries, 10 km downstream

from Zapotillo. Original image (a); HPF fused (b); ACP fused (c) and GS fused (d).

Figure 4.

Clip of the Landsat 8 image showing the Mariscal La Mar Cuenca-Ecuador Airport. Original image (a); HPF fused (b); ACP fused (c) and GS fused (d).

Figure 5.

Clip of the Natmur-08 image showing agricultural plots in Archivel-Caravaca de la Cruz-Murcia-Spain. Original image (a); HPF fused (b); ACP fused (c) and GS fused GS (d).

Table 1.

Qualitative evaluation according to some criteria of visual interpretation in Fig. 1 a 5: 1=very bad; 2=bad; 3=acceptable; 4=good; 5=very good.

The images used in the mosaics correspond, in each case, to the best color composition to discriminate land cover. Such compositions are indicated in Tab. 1.

The quantitative evaluation was carried out using three algorithms: the universal image quality index (IQ), the ERGAS spatial index and the spectral ERGAS index.

The Q index, although initially proposed for other applications such as image compression, may be useful in image fusion to verify that there has been no significant alteration of the original radiometric values. It allows a quantitative evaluation of the quality of the fused images with respect to the original multispectral images, while calculating the distortions produced. It is expressed as a combination of three factors [27]: loss of correlation, the means of the two images and the contrast distortion [28]. The range of Q is [-1,1]. The best value is 1, which would be given if the two images are identical.

The ERGAS index, proposed by Wald (2000) [29], was used to compare the spectral quality of the fused images. It seeks to satisfy three main requirements:

To calculate this index, the original multispectral bands are rescaled to the spatial resolution of the fused bands. The value of ERGAS shows a strong tendency to decrease when the quality of the fused product increases. Values of less than 3 refer to good merge quality [29,30], which improves as it approaches zero. Since the ERGAS index only considers the spectral characteristics of the image, Lillo-Saavedra et al. (2005) [31] proposed a new spatial index, called the spatial ERGAS index, also introducing a spatial RMSE.