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Abstract-Quantifying ambiguities in images using fuzzy set theory has been of utmost interest to researchers in the field of image processing. In this paper, we present the use of rough set theory and its certain generalizations for quantifying ambiguities in images and compare it to the use of fuzzy set theory. We propose classes of entropy measures based on rough set theory and its certain generalizations, and perform rigorous theoretical analysis to provide some properties which they satisfy. Grayness and spatial ambiguities in images are then quantified using the proposed entropy measures. We demonstrate the utility and effectiveness of the proposed entropy measures by considering some elementary image processing applications. We also propose a new measure called average image ambiguity in this context.

Sickle cell nephropathy characterized by proteinuria and predominantly glomerular lesions has not been studied as extensively as renal tubular alterations in sickle cell disease. We reviewed our experience with this entity over a 14-year period. Of 13 children with either proteinuria or the nephrotic syndrome, 8 showed focal and segmental glomerulosclerosis, and 5 had mesangial proliferation. Children with focal and segmental glomerulosclerosis were older at onset of nephropathy and presented with the nephrotic syndrome more frequently than those with mesangial proliferation (p < 0.05). All patients with mesangial proliferation and half of the focal and segmental glomerulosclerosis patients had supranormal renal clearances at onset of nephropathy suggesting hyperfiltration. Hyperfiltration seen in animals with reduced renal mass, and in human diabetic nephropathy before reduction in nephron units leads to mesangial proliferation and sclerosis. Our study suggests that sickle cell disease produces similar lesions in patients with sickle cell nephropathy.

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