DSCOKRI: A library of computer programs for downscaling cokriging in support of remote sensing applications $ Eulogio Pardo-Iguzquiza a,n , Peter M. Atkinson b , Mario Chica-Olmo c a Instituto Geolo ´gico y Minero de Espan ˜a (IGME), Calle Rı ´os Rosas 23, 28003, Madrid Spain b School of Geography, University of Southampton, Highfield, Southampton SO17 1BJ, UK c Departamento de Geodina ´mica, Universidad de Granada, Avenida Fuentenueva, 18071, Granada, Spain article info Article history: Received 1 June 2009 Received in revised form 2 October 2009 Accepted 8 October 2009 Keywords: Image fusion Image sharpening Super-resolution Spatial resolution Spectral bands Variograms Geostatistics Landsat Enhanced Thematic Mapper abstract The main purpose of this paper is to describe and provide a suite of computer programs for performing downscaling cokriging with satellite sensor images. The usual setting of downscaling cokriging is to increase the spatial resolution of multispectral images with coarse spatial resolution by fusing them with a fine spatial resolution image of a different band from the same or a different sensor. This problem has also been described as image sharpening and commonly the spatial resolution of the fused image is equal to the finest spatial resolution used in the fusion. Nevertheless, downscaling cokriging allows the spatial resolution of the predicted image to be increased beyond that of any of the input data sets, a procedure usually referred to as super-resolution sharpening. The programs provided here support all the required stages for image fusion and super-resolution sharpening by downscaling cokriging. These stages are: (i) compute the empirical variogram of each spectral band and empirical cross-variograms for each pair of spectral bands; (ii) estimate and fit a model to the point-support variogram of each spectral band and cross-variogram of each pair of spectral bands; (iii) set up the cokriging system and obtain the set of downscaling cokriging weights and (iv) obtain the sharpened image by application of the weights to the empirical remote sensing images. A case study with Landsat ETM+ images is provided to demonstrate the implementation of the method and to allow checking of the programs. & 2010 Elsevier Ltd. All rights reserved. 1. Introduction A typical problem in remote sensing image processing is the merging of coregistered images with different spatial resolutions in different spectral bands. The task of the fusion process is usually to produce images at the finest spatial resolution amongst those of the different available spectral bands. Thus, the objective of image fusion is to increase the spatial resolution (decrease the pixel size) of the coarse spatial resolution image band(s) of interest by merging them with other bands of a finer spatial resolution. Classic examples are the merging of Landsat satellite sensor images such as to increase the spatial resolution of the thermal infrared band and the merging of coarse spatial resolution multispectral images and a fine spatial resolution panchromatic image such as to increase the spatial resolution of the multispectral bands. It is also possible to produce images with a spatial resolution that is finer than that of any of the available input bands if working in super-resolution mode (Atkinson et al., 2008). Different methods have been proposed for image fusion. One of them is cokriging, the geostatistical multivariate prediction method (Niishii et al., 1996; Memarsadeghi et al., 2005; Pardo-Iguzquiza et al., 2006). Although an exhaustive comparison between the methods has not been undertaken, cokriging has several advan- tages for image fusion (Pardo-Iguzquiza et al., 2006):  The autocorrelation within the image and the cross-correlation between images is taken into account explicitly.  The different pixel sizes (spatial resolutions) of the images are taken into account explicitly.  The point spread function of the sensor is explicitly taken into account.  The cokriged fused image has the property of prediction coherence (Wald, 1999; Kyriakidis, 2004).  Ancillary images (as thematic maps) and sparse field experi- mental data can be included in the merging process. Without loss of generality, the simplest case to consider is the cokriging merging of two images with different spatial resolutions in two different spectral bands: ^ Z k u ðx 0 Þ¼ X N i ¼ 1 l i Z k V ðx i Þþ X M j ¼ 1 b j Z ‘ v ðx j Þ ð1Þ ARTICLE IN PRESS Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/cageo Computers & Geosciences 0098-3004/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.cageo.2009.10.006 $ Code available from server at http://www.iamg.org/CGEditor/index.htm. n Corresponding author. Tel.: + 34 91 349 5914; fax: + 34 91 349 5951. E-mail addresses: pardoiguzquiza@yahoo.es, e.pardo@igme.es (E. Pardo-Iguzquiza). Computers & Geosciences 36 (2010) 881–894