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.