A flexible lag definition for experimental variogram calculation

Inferring the experimental variogram used in geostatistics commonly relies on the method-of-moments approach.Ideally,the available data-set used for calculating the experimental variogram should be drawn from a regular pattern.However,in practice the available data-set is typically sampled over a sparse pattern at irregularly spaced locations.Hence,some binning of the variogram cloud is required to obtain fair estimates of the experimental variogram.Grouping of the variogram data pairs as a result of conventional binning depends on parameters such as the main anisotropic directions and a regular definition of the lag vectors.These parameters are not based on the configuration of the variogram data pairs in the variogram cloud but on a segment of it that is arbitrarily predefined.Therefore,the conventional experimental variogram estimation approach is biased because of the strict configuration of the bins over the variogram cloud.In this paper,a new method of estimating experimental variograms is proposed.Lag vectors and their tolerances are decided in the proposed method from information in the variogram cloud：they are not influenced by any predefined directions.The proposed methodology is a well-founded,practicable and easy-to-automate approach for experimental variogram calculation using an irregularly sampled data-set.Comparison of results from the new method to those from the traditional approach is very encouraging.

Characterizing Landscape Spatial Heterogeneity in Multisensor Images with Variogram Models

Most evaluation of the consistency of multisensor images have focused on Normalized Difference Vegetation Index （NDVI） products for natural landscapes, often neglecting less vegetated urban landscapes. This gap has been filled through quantifying and evaluating spatial heterogeneity of urban and natural landscapes from QuickBird, Satellite pour l＇observation de la Terre （SPOT）, Ad- vanced Spacebome Thermal Emission and Reflection Radiometer （ASTER） and Landsat Thematic Mapper （TM） images with variogram analysis. Instead of a logarithmic relationship with pixel size observed in the corresponding aggregated images, the spatial variability decayed and the spatial structures decomposed more slowly and complexly with spatial resolution for real multisensor im- ages. As the spatial resolution increased, the proportion of spatial variability of the smaller spatial structure decreased quickly and only a larger spatial structure was observed at very coarse scales. Compared with visible band, greater spatial variability was observed in near infrared band for both densely and less densely vegetated landscapes. The influence of image size on spatial heterogeneity was highly dependent on whether the empirical sernivariogram reached its sill within the original image size. When the empirical semivariogram did not reach its sill at the original observation scale, spatial variability and mean characteristic length scale would increase with image size; otherwise they might decrease. This study could provide new insights into the knowledge of spatial heterogeneity in real multisen- sor images with consideration of their nominal spatial resolution, image size and spectral bands.

Relationship between spatial heterogeneity and wavelength in multisensor airborne images

Variogram has been utilized to exploring the spatial heterogeneity of remote sensing images,especially its association with spatial resolution.However,very few attentions have been drawn on evaluating the spatial heterogeneity of multisensor airborne imagery and its relationship with spectral wavelength.Therefore,an investigation was carried out on multisensor airborne images to determine the relation between spatial heterogeneity and spectral wavelength for woodland,grass,and urban landscapes by applying variogram modeling.The airborne thematic mapper(ATM),compact airborne spectrographic imager(CASI),and Specim AISA Eagle airborne images at Harwood Forest,Monks wood,Cambridge,and River Frome areas,UK,were utilized.Results revealed that(1)the red band contained greater spatial variability than near-infrared wavelengths and other visible wavebands;(2)there was a steep gradient at the red edge in reference to its spatial variability of multisensor airborne images;(3)only for natural landscape such as woodland and grass,near-infrared waveband contains greater within-scene variations than the blue and green bands;(4)compared with the discrepancy of spatial resolution introduced by multisensor images(ATM,CASI,and Eagle),the specific landscape and spectral bands were more important in determining heterogeneity by means of original visible,near-infrared bands,and normalized difference vegetation index(NDVI).These findings remained us to be caution when combining and interpreting spatial variability and spatial structures derived from airborne images with different spatial resolution and spectral wavelength.Additionally,the outcomes of this study also have considerable implications in terms of designing and choosing suitable images for different applications.

Comparative spatio-spectral heterogeneity analysis using multispectral and hyperspectral airborne images

Knowledge of spatio-spectral heterogeneity within multisensor remote sensing images across visible,near-infrared and short wave infrared spectra is important.Till now,little comparative research on spatio-spectral heterogeneity has been conducted on real multisensor images,especially on both multispectral and hyperspectral airborne images.In this study,four airborne images,Airborne Thematic Mapper,Compact Airborne Spectrographic Imager,Specim AISA Eagle and AISI Hawk hyperspectral airborne images of woodland and heath landscapes at Harwood,UK,were applied to quantify and evaluate the differences in spatial heterogeneity through semivariogram modelling.Results revealed that spatial heterogeneity of multisensor airborne images has a close relationship with spatial and spectral resolution and wavelength.Within the visible,near-infrared spectra and short wave infrared spectra,greater spatial heterogeneity is generally observed from the relatively longer wavelength in short wave infrared spectra.There are dramatic changes across the red and red edge spectra,and the peak value is generally examined in the red middle or red edge wavelength across the visible and near-infrared spectra for vegetation or non-vegetation landscape respectively.In all,for real multisensor airborne images,the change in spatial heterogeneity with spatial resolution will accord with the change of support theory depending on whether dramatic change exists across the corresponding wavelength.Besides,if with close spatial resolution,the spatial heterogeneity of multispectral images might be far from the overall integration of these bands from the hyperspectral images involved.A comparative assessment of spatio-spectral heterogeneity using real hyperspectral and multispectral airborne images provides practical guidance for designing the placement and width of a spectral band for different applications and also makes a contribution to the understanding of how to reconcile spatial patterns generated by multisensors.