Iterative relative fuzzy connectedness for multiple objects with multiple seeds

Abstract

In this paper we present a new theory and an algorithm for image segmentation based on a strength of connectedness between every pair of image elements. The object definition used in the segmentation algorithm utilizes the notion of iterative relative fuzzy connectedness, IRFC. In previously published research, the IRFC theory was developed only for the case when the segmentation was involved with just two segments, an object and a background, and each of the segments was indicated by a single seed. (See Udupa et al. [J.K. Udupa, P.K. Saha, R.A. Lotufo, Relative fuzzy connectedness and object definition: theory, algorithms, and applications in image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 24 (2002) 1485–1500] and Saha and Udupa [P.K. Saha, J.K. Udupa, Iterative relative fuzzy connectedness and object definition: theory, algorithms, and applications in image segmentation, in: Proceedings of IEEE Workshop on Mathematical Methods in Biomedical Image Analysis, Hilton Head, South Carolina, 2002, pp. 28–35].) Our theory, which solves a problem of Udupa and Saha from [J.K. Udupa, P.K. Saha, Fuzzy connectedness in image segmentation, Proc. IEEE 91 (10) (2003) 1649–1669], allows simultaneous segmentation involving an arbitrary number of objects. Moreover, each segment can be indicated by more than one seed, which is often more natural and easier than a single seed object identification. The first iteration step of the IRFC algorithm gives a segmentation known as relative fuzzy connectedness, RFC, segmentation. Thus, the IRFC technique is an extension of the RFC method. Although the RFC theory, due to Saha and Udupa [P.K. Saha, J.K. Udupa, Relative fuzzy connectedness among multiple objects: theory, algorithms, and applications in image segmentation, Comput. Vis. Image Understand. 82 (1) (2001) 42–56], is developed in the multi object/multi seed framework, the theoretical results presented here are considerably more delicate in nature and do not use the results from [P.K. Saha, J.K. Udupa, Relative fuzzy connectedness among multiple objects: theory, algorithms, and applications in image segmentation, Comput. Vis. Image Understand. 82 (1) (2001) 42–56]. On the other hand, the theoretical results from [P.K. Saha, J.K. Udupa, Relative fuzzy connectedness among multiple objects: theory, algorithms, and applications in image segmentation, Comput. Vis. Image Understand. 82 (1) (2001) 42–56] are immediate consequences of the results presented here. Moreover, the new framework not only subsumes previous fuzzy connectedness descriptions but also sheds new light on them. Thus, there are fundamental theoretical advances made in this paper. We present examples of segmentations obtained via our IRFC-based algorithm in the multi-object/multi-seed environment, and compare it with the results obtained with the RFC-based algorithm. Our results indicate that, in many situations, IRFC outperforms RFC, but there also exist instances where the gain in performance is negligible.