If we have spatial points randomly distributed in 2D space, then we clustered those points according to some parameters, say location x,y. Can we use the same clustering algorithm and apply it on finding a geographical area borders? . In another words , If a set of points with the same characteristics are clustered according to their geographical relationship , can we say that we have found the area borers that contains those points ? For example this paper
Yes, people have successfully used clustering algorithms such as DBSCAN for this.
I don't have references for you, but look for image segmentation by clustering.
I don't think it is the best way to do this (in particular on images, you really should exploit the pixel grid for performance) and I really do not recommend k-means for this. But a well built generalized DBSCAN in a special implementation for your data may work well, and give you good control over the desired outcome. Generalized DBSCAN is much superior here, because you can specify both adjacency and similarity thresholds.