Dear Colleagues,

Soft computing and image processing have been long associated, especially since the golden age of image processing in 1980s. In the past years, there has been a continuous production of research efforts, which have been mainly characterized as the application of techniques from soft computing to problems in image processing. However, that is not the only possible case, since other authors have elaborated on fuzzy models for image representation, or even on the fuzzy reformulation of already-existing problems in image processing.

The connection between soft computing and image processing is not coincidental, and has a long history. Image processing has historically (although not uniquely) been treated as a signal processing problem, which was subsequently followed by some decisions regarding the presence, absence or measurement of visible artefacts. This schema is very similar to analogical system control, which is the field in which Prof. Zadeh excelled before presenting fuzzy sets in 1965. In fact, it can be said that Zadeh's early works on fuzzy sets were influenced by the need for modelling signal-based information for automated control and decision making. Hence, it is natural that soft computing is used to model the appearance of visual artefacts in image processing.

The coalescence of soft computing and image processing has been embodied in very different paradigms. One initial body of proposals includes the application of soft computing techniques to solve problems stated in terms of standard image processing. From the application of fuzzy sets to the modelling of areas, to the use of fuzzy-rule-based systems, the past years have seen many fuzzy-related techniques applied to the solution of image processing problems. A secondary body of research efforts is due to the reformulation of the basics in image processing in different terms, generally influenced by concepts of granularity, uncertainty modelling or tolerance to imprecision. Finally, a third group of researchers took advantage of the vast developments in mathematics due to fuzzy set theory, by applying those developments to specific tasks in image processing. Remarkable works in any of the three paradigms have been presented and continue to be presented.

One task that has been remarkably tackled from the perspective of soft computing is edge (or boundary) detection. This seems natural for diverse reasons. Edge detection is one of the fields in image processing in which definitions are more imprecise, to the point that there is arguably no definition for the task. Also, the evaluation of edge detection procedures is heavily based on the comparison of edge images to human-labelled edge images, which induces heavy quotas of uncertainty, ambiguity or contradiction to the task. Finally, the fact that edges are materialized as one-pixel-width lines on a discrete universe imposes the need to consider the tolerance for imprecision in terms of pixel- or region-wise information; sticking to the factual numerical information in an image, avoiding considering factors such as noise, shadows and image imperfections could never lead to acceptable results.

This Special Issue attempts to capture the state-of-the-art of edge detection, as tackled from the perspective of soft computing. In this regard, it considers different approximations to edge detection, which are rooted in the mathematical grounds, specific techniques or philosophical foundations of soft computing. This Special Issue is open to considering any approach which, at any stage of an image processing pipeline, attempts to improve the result of an edge detection procedure. It is also open to applications of soft computing procedures that, if not conducent to edge detection themselves, play a clear role in the evolution of the field,examples being edge image evaluation/comparison or edge image fusion.

Dr. Carlos Lopez-Molina
Guest Editor

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• Edge/boundary detection
• Edge quality evaluation
• Image differentiation
• Edge feature fusion
• Edge feature binarization