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Investigations in data quality and uncertainty modeling are becoming key topics in geoinformation science. This paper models a collection of outcomes from a standard segmentation algorithm as a random set. It quantifies extensional uncertainties of extracted objects using statistical characteristics of random sets. The approach is applied to a synthetic data set and vegetation patches in the Poyang Lake area in China. These patches are of interest as they have both sharp and vague boundaries. Results show that random sets provide useful spatial information on uncertainties using their basic parameters like the mean, level sets, and variance. The number of iterations to achieve a stable covering function and the sum of the variances are good indicators of boundary sharpness. The coefficient of variation has a positive relation with the degree of uncertainty. An asymmetry ratio reflects the uneven gradual changes along different directions where broad boundaries exist. This paper shows that several characteristics of extensional uncertainty of segmented objects can be quantified numerically and spatially by random sets.