Are fuzzy definitions of basic attributes of image objects really useful?

Computer vision applications often involve measuring properties of objects in images. Typically, thresholding or segmentation techniques are used to obtain crisp object boundaries before object properties are computed. In this correspondence, we explore the possibility of using fuzzy definitions for measuring object properties without having to make crisp decisions about object boundaries prematurely. We present theorems which indicate that the use of fuzzy definitions to measure properties in intensity-based image analysis almost always gives accurate results. We also present experimental evidence and reasoning which show that fuzzy definitions are not always useful in feature-based methods.