Change of spatial information under rescaling: A case study using multi-resolution image series

Spatial structure in imagery depends on a complicated interaction between the observational regime and the types and arrangements of entities within the scene that the image portrays. Although block averaging of pixels has commonly been used to simulate coarser resolution imagery, relatively little attention has been focused on the effects of simple rescaling on spatial structure and the explanation and a possible solution to the problem. Yet, if there are significant differences in spatial variance between rescaled and observed images, it may affect the reliability of retrieved biogeophysical quantities. To investigate these issues, a nested series of high spatial resolution digital imagery was collected at a research site in eastern Nebraska in 2001. An airborne Kodak DCS420IR camera acquired imagery at three altitudes, yielding nominal spatial resolutions ranging from 0.187 m to 1 m. The red and near infrared (NIR) bands of the co-registered image series were normalized using pseudo-invariant features, and the normalized difference vegetation index (NDVI) was calculated. Plots of grain sorghum planted in orthogonal crop row orientations were extracted from the image series. The finest spatial resolution data were then rescaled by averaging blocks of pixels to produce a rescaled image series that closely matched the spatial resolution of the observed image series. Spatial structures of the observed and rescaled image series were characterized using semivariogram analysis. Results for NDVI and its component bands show, as expected, that decreasing spatial resolution leads to decreasing spatial variability and increasing spatial dependence. However, compared to the observed data, the rescaled images contain more persistent spatial structure that exhibits limited variation in both spatial dependence and spatial heterogeneity. Rescaling via simple block averaging fails to consider the effect of scene object shape and extent on spatial information. As the features portrayed by pixels are equally weighted regardless of the shape and extent of the underlying scene objects, the rescaled image retains more of the original spatial information than would occur through direct observation at a coarser sensor spatial resolution. In contrast, for the observed images, due to the effect of the modulation transfer function (MTF) of the imaging system, high frequency features like edges are blurred or lost as the pixel size increases, resulting in greater variation in spatial structure. Successive applications of a low-pass spatial convolution filter are shown to mimic a MTF. Accordingly, it is recommended that such a procedure be applied prior to rescaling by simple block averaging, if insufficient image metadata exist to replicate the net MTF of the imaging system, as might be expected in land cover change analysis studies using historical imagery.