In this paper

a scale space clustering algorithm based on mathematical morphology operators（MSCMO） is proposed. The data are firstly converted into a binary image

the noises are then deleted with close open operators. A scale space is constructed with the close operator and structure elements as well as increased size. The connected cells merge with each other with the increasing scale until all of them combine into one. We suggest this is just a multi scale hierarchy clustering process considering the data under the connected cells into one class. One of the biggest advantages is that we do not need to set the cluster number before hand

it is fixed in the end on the cluster number which spans the longest scale range （with the longest`scale survival time’）. Besides

less arguments the ability to extract clusters with arbitrary shapes

and the robustness against noises are also the advantages of MSCMO. The validity and practicality of the algorithm are validated with constructed data and earthquake data.