In this paper we introduce the concept of Fuzzy Image Segmentation, providing an algorithm to build fuzzy boundaries based on the existing relations between the fuzzy boundary set problem and the (crisp) hierarchical image segmentation problem. In particular, since a crisp image segmentation can be characterized in terms of the set of edges that separates the adjacent regions of the segmentation, from these edges we introduce the concept of fuzzy image segmentation. Hence, each fuzzy image segmentation is characterized by means of a fuzzy set over the set of edges, which can be then understood as the fuzzy boundary of the image. Some computational experiences are included in order to show the obtained fuzzy boundaries of some digital images.
In this paper we discuss some main image processing techniques in order to propose a classification based upon the output these methods provide. Because despite a particular image analysis technique can be supervised or unsupervised, and can allow or not the existence of fuzzy information at some stage, each technique has been usually designed to focus on a specific objective, and their outputs are in fact different according to each objective. Thus, they are in fact different methods. But due to the essential relationship between them they are quite often confused. In particular, this paper pursues a clarification of the differences between image segmentation and edge detection, among other image processing techniques.
Traditionally, the edge detection process requires one final step that is known as scaling. This is done to decide, pixel by pixel, if these will be selected as final edge or not. This can be considered as a local evaluation method that presents practical problems, since the edge candidate pixels should not be considered as independent. In this article, we propose a strategy to solve these problems through connecting pixels that form arcs, that we have called segments. To accomplish this, our edge detection algorithm is based on a more global evaluation inspired by actual human vision. Our paper further develops ideas 1 first proposed in Venkatesh and Rosin (Graph Models Image Process 57(2):146-160, 1995). These segments contain visual features similar to those used by humans, which lead to better comparative results against humans. In order to select the relevant segments to be retained, we use fuzzy clustering techniques. Finally, this paper shows that this fuzzy clustering of segments presents a higher performance compared to other standard edge detection algorithms.
KeywordsEdge detection • Global evaluation • Supervised classification • Fuzzy clustering • Edge segments Edge detection is quite useful in many fields. For instance, for the recognition of different pathologies in medical diagnoses (Sonka 2014), a field has grown in recent years. It is also used in images taken by satellites or drones-remote sensing-for agricultural purposes. Some other relevant fields of application are the military industry, law enforcement, among others (Monga et al. 1991; Fathy and Siyal 1995; Zielke et al. Communicated by I. Perfilieva.
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