Density-based clustering has the advantages for (i) allowing arbitrary shape of cluster and (ii) not requiring the number of clusters as input. However, when clusters touch each other, both the cluster centers and cluster boundaries (as the peaks and valleys of the density distribution) become fuzzy and difficult to determine. In higher dimension, the boundaries become wiggly and over-fitting often occurs. We introduce the notion of cluster intensity function (CIF) which captures the important characteristics of clusters. When clusters are well-separated, CIFs are similar to density functions. But as clusters touch each other, CIFs still clearly reveal cluster centers, cluster boundaries, and, degree of membership of each data point to the cluster that it belongs. Clustering through bump hunting and valley seeking based on these functions are more robust than that based on kernel density functions which are often oscillatory or over-smoothed. These problems of kernel density estimation are resolved using Level Set Methods and related techniques. Comparisons with two existing density-based methods, valley seeking and DBSCAN, are presented to illustrate the advantages of our approach.