A Fuzzy Relation Based Algorithm for Segmenting Color Aerial Images of Urban Environment

Automated extraction of man-made objects such as buildings and roads using image analysis techniques for urban mapping and updating geographic information systems (GIS) databases has been an active research topic in photogrammetry and remote sensing community. Segmentation plays an important role in the process of digital image processing towards automatic extraction of GIS objects from aerial imagery. In digital image processing, clustering techniques are often used to segment images since segmentation is really pattern recognition, i.e., classifying each pixel. The clustering methods can be based on either crisp set or fuzzy set. The most popular fuzzy segmentation algorithm is the Fuzzy C-Means (FCM) and many of research work have been proposed to speed up the FCM algorithm. Although the FCM algorithm is powerful in image segmentation, there is still a drawback encountered, namely the desired number of clusters should be specified. This is a disadvantage whenever the clustered problem does not specify any desired number of clusters. The situation is often for the segmentation of remotely sensed images, because the ground truth is always not available for these images. In this paper, a fuzzy clustering method based on fuzzy equivalence relation is presented. The clustering technique is a hierarchical clustering method. First, a fuzzy compatibility relation is created in term of the Euclidean distance. In general, the fuzzy compatibility relation is not necessarily a fuzzy equivalence relation. Then, the transitive closure are computed and used as the fuzzy equivalence relation to cluster a given image. Finally, image segmentation is completed by computing α-cut on fuzzy equivalence relation.