Perimeter and Area Estimations of Digitized Objects with Fuzzy Borders

Abstract

Abstract. Fuzzy segmentation methods have been developed in order to reduce the negative effects of the unavoidable loss of data in the digitization process. These methods require the development of new image analysis methods, handling grey-level images. This paper describes the first step in our work on developing shape analysis methods for fuzzy images: the investigation of several measurements on digitized objects with fuzzy borders. The performance of perimeter, area, and the P 2 A measure estimators for digitized disks and digitized squares with fuzzy borders is analyzed. The method we suggest greatly improves the results obtained from crisp (hard) segmentation, especially in the case of low resolution images.

Fuzzy sets for image processing and understanding

“…This point of view leads to definitions as fuzzy numbers [68]. It has been shown in [145,146] that using fuzzy representations of digital objects allows deriving more robust measures than using crisp representations, and in particular dealing properly with the imprecision induced by the digitization process. Such geometrical measures can typically be used in shape recognition, where geometrical attributes of the objects are taken into account (e.g.…”

Fuzzy methods in medical imaging

“…It has been shown in [65,66] that using fuzzy representations of digital objects allow deriving more robust measures than using crisp representations, and in particular dealing properly with the imprecision induced by the digitization process.…”

Measurements of digitized objects with fuzzy borders in 2D and 3D

“…[2] is restricted to locally convex shapes), and its accuracy is increased by incorporating a more accurate binary perimeter estimation method then the one used in Ref. [2]. In addition, this paper extends the proposed perimeter estimation method to 3D.…”

“…In Ref. [2], we presented in initial study on area and perimeter estimation of disks and squares, digitized at low resolutions and fuzzy segmented. An analysis of the P 2 /A compactness measure, often referred to as 'roundness factor', or 'roundness index', was done, as well.…”

“…In this paper, we present an improved perimeter estimator; it is applicable to any fuzzy shape (the method presented in Ref. [2] is restricted to locally convex shapes), and its accuracy is increased by incorporating a more accurate binary perimeter estimation method then the one used in Ref. [2].…”