A zero-hit run-length probability model for image statistics is derived. The statistics are based on the lengths of runs of pixels that do not include any part of objects that define a scene model. The statistics are used to estimate the density and size of the discrete objects (modeled as disks) from images when the image pixel size is significant relative to the object size. Using different combinations of disk size, density, and image resolution (pixel size) in simulated images, parameter estimation may be used to investigate the essential invertibility of object size and density. Analysis of the relative errors and 95% confidence intervals indicates the accuracy and reliability of the estimates. An integrated parameter r, reveals relationships between errors and the combinations of the three basic parameters of object size, density, and pixel size. The method may be used to analyze real remotely sensed images if simplifying assumptions are relaxed to include the greater complexity found in real data.
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