Many questions may arise like what is a vague set, where does it come from,
500 WordsApr 23, 20192 Pages
Many questions may arise like what is a vague set, where does it come from, how to perform operations with vague sets, is there anything fuzzy about digital images, how can we obtain fuzzy images, how can we estimate their features, what is good about fuzziness in image processing, what can we do if, after all, we want crisp images again etc etc? Answers to these question will become cleaner afterwards.
Conventional approaches to image analysis and recognition [5-7] consist of segmenting the image into meaningful regions, extracting their edges and skeletons, computing various features/properties (e.g., area, perimeter, cen- troid etc.) and primitives (e.g., line, corner, curve etc.) of and relationships among the regions,…show more content…
primitive selection,) and this might, in turn. affect feature analysis and recognition. Consider, for example, the case of skeleton extraction of a region through medial axis transformation (MAT). The medial axis transformation of a region in a binary picture is determined with respect to its boundary. In a gray tone image, the boundaries are not well defined. Therefore,errors are likely, (and hence further increase uncertainty in the system), if we compute the MAT from the aforesaid hard-segmented version of the image.
Thus, it is convenient, natural and appropriate to avoid committing our- selves to a specific (hard) decision (e.g., segmentation/ thresholding, edge detection and skeletonization),by allowing the segments or skeletons or con- tours to be vague subsets of the image, the subsets being characterized by the possibility (degree) to which each pixel belongs to them and doesn’t belong to them. Similarly,for describing and interpreting ill-defined struc- tural information in a pattern, it is natural to define primitives (line, comer, curve etc.) and relations among them using labels of vague sets.
For example, primitives which do not lend themselves to precise defini- tion may be defined in terms of arcs with varying grades of membership from 0 to 1 representing their degree of belonging and not belonging to more than one class. The production rules of a grammar may similarly