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, Saha, Lotufo [15] and Saha, Udupa [14].) Our theory, which solves a problem of Udupa and Saha from [13], 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 [19], 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 [19]. On the other hand, the theoretical results from [19] 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.

Oriented relative fuzzy connectedness: theory, algorithms, and its applications in hybrid image segmentation methods

“…We performed the segmentation of the bones calcaneus and talus for all the methods (IRFC [9], RFC [26], OIFT [23], RFC+GC [29], OGC [11] the graph cut with boundary polarity, ORFC, and the proposed hybrid method ORFC+GC), for different seed sets automatically obtained by eroding and dilating the ground truth at different radius values. By varying the radius value, we can repeat the segmentation for different seed sets and trace accuracy curves using the dice coefficient of similarity and error curves of false positive (normalized by the object size).…”

“…After that, the seed's labels are propagated to all unlabeled regions by following some optimum criterion, such that a complete labeled image is constructed. This class encloses many of the most prominent methods for general purpose segmentation, which are usually easier to extend to multi-dimensional images, including frameworks, such as watershed from markers [6,7], random walks [8], fuzzy connectedness [9,10], graph cuts (GC) [11], distance cut [12], image foresting transform [13], and grow cut [14]. The study of the relations among different frameworks, including theoretical and empirical comparisons, has a vast literature [15][16][17][18][19], which allowed many algorithms to be described in a unified manner according to a common framework, which we refer to as generalized GC (GGC) [18,20].…”

Segmentação do lúmen em imagens de IOCT usando Fuzzy Connectedness e Reconstrução Binária Morfológica

“…Uma dessas técnicas é o método Fuzzy Connectedness, o qual apresenta bons resultados na segmentação em outras modalidades (Ciesielski et al, 2007;Moonis et al, 2002;Udupa e Saha, 2003;Zaidi e Naqa, 2010), mas ainda não se conhece nenhum trabalho em que esta seja direcionada para a segmentação do lúmen em imagens de IOCT.…”

GPU‐based relative fuzzy connectedness image segmentation

“…2 and 3, the graph cut methods 4 employ the 1 -norm while random walker 5 optimizes the 2 -norm. The fuzzy connectedness [6][7][8][9] and the shortest path (geodesics) (Refs. 10 and 11) use the ∞ -norm.…”