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Extracting statistical moments

When the above image processing steps are completed, the resulting images (i.e. mosaicked, corrected, masked and co-registered), can be analyzed in various ways. In crop development studies, by bringing into the picture also the information obtained from a fieldwork campaign that has been conducted during the same time frame as the images have been acquired, one can study how images record crop development. Results from such study may help to address various purposes of studies of smallholder farming systems. We list a number of those here.

Many questions with a space/time characteristic appear to be, in principle, answerable from high-resolution images acquired in the growing season, yet in smallholder contexts they are currently open problems and/or have only been addressed in restricted study sites. One would want to have the functional capability to (a) distinguish between cropland and non-cropland, (b) identify the crop in a pixel or pixel cluster, (c) identify additional crops also grown, (d) delineate farm fields, (e) determine characteristics of farm management (irrigation, planting, application of fertilizer, weeding and other farmer activities), (f) determine whether the crop is stressed, and if so, what is the possible stress cause, (g) determine whether the field is optimally managed. Observe that solutions to earlier questions in this list will be needed to address later questions.

At landscape and regional scales, another batch of questions arises, and many of these have to do with accumulating information to feed policy and planning decisions, and in general such questions can be considered as bringing/improving agricultural statistics.

For these reasons, the STARS project has focused on studies of images in tandem with geometries of farm management units (FMU) to derive statistical moments of spectral responses for each FMU. The philosophy has been that the build-up of a library of image-derived crop characteristics will become an important information source for crop identification and other open problems. We have focused on statistics in the spectral, textural and temporal dimensions. The statistical moments calculated per FMU are: (1) the number of pixels with and without masking, (2) the average and variance of a substantial number of vegetation indices, (3) the reflectance average and skew for any spectral band in the image, and (4) the reflectance correlation between any pair of bands in the image. Statistics 2–4 have been obtained from multispectral images.  In addition, panchromatic images have been analysed for texture, again per FMU, giving (5) overall and local homogeneity, contrast, entropy, textural correlation, textural variance, local homogeneity, and (6) sum of average, of variance, and of entropy, as well as (7) another ten or so textural characteristics. Since the images come as a time-series acquired during the crop season, the results of these analytical procedures can be used to produce temporal profiles for each FMU and crop type, enriching the data set further with a time dimension. We are collecting the outcome of this work in a crop signature library, known as the CSSL. The CSSL will become a global public good.