  A comprehensive understanding of molecular clumps is essential for
investigating star formation. We present an algorithm for molecular clump
detection, called FacetClumps. This algorithm uses a morphological approach to
extract signal regions from the original data. The Gaussian Facet model is
employed to fit the signal regions, which enhances the resistance to noise and
the stability of the algorithm in diverse overlapping areas. The introduction
of the extremum determination theorem of multivariate functions offers
theoretical guidance for automatically locating clump centers. To guarantee
that each clump is continuous, the signal regions are segmented into local
regions based on gradient, and then the local regions are clustered into the
clump centers based on connectivity and minimum distance to identify the
regional information of each clump. Experiments conducted with both simulated
and synthetic data demonstrate that FacetClumps exhibits great recall and
precision rates, small location error and flux loss, a high consistency between
the region of detected clump and that of simulated clump, and is generally
stable in various environments. Notably, the recall rate of FacetClumps in the
synthetic data, which comprises $^{13}CO$ ($J = 1-0$) emission line of the
MWISP within $11.7^{\circ} \leq l \leq 13.4^{\circ}$, $0.22^{\circ} \leq b \leq
1.05^{\circ}$ and 5 km s$^{-1}$ $\leq v \leq$ 35 km s$^{-1}$ and simulated
clumps, reaches 90.2%. Additionally, FacetClumps demonstrates satisfactory
performance when applied to observational data.
