  The problem of multiple surface clustering is a challenging task,
particularly when the surfaces intersect. Available methods such as Isomap fail
to capture the true shape of the surface nearby the intersection and result in
incorrect clustering. The Isomap algorithm uses the shortest path between
points. The main draw back of the shortest path algorithm is due to the lack of
curvature constrained where causes to have a path between points on different
surfaces. In this paper, we tackle this problem by imposing a curvature
constraint to the shortest path algorithm used in Isomap. The algorithm chooses
several landmark nodes at random and then checks whether there is a curvature
constrained path between each landmark node and every other node in the
neighbourhood graph. We build a binary feature vector for each point where each
entry represents the connectivity of that point to a particular landmark. Then
the binary feature vectors could be used as an input of conventional clustering
algorithm such as hierarchical clustering. We apply our method to simulated and
some real datasets and show, it performs comparably to the best methods such as
K-manifold and spectral multi-manifold clustering.
