  Open clusters (OCs) are common in the Milky Way, but most of them remain
undiscovered. There are numerous techniques (e.g., machine-learning algorithms)
available for the exploration of OCs. However, each method has its limitations
and therefore, different approaches to discovering OCs hold significant value.
We develop a comprehensive approach method to automatically explore the data
space and identify potential OC candidates with relatively reliable membership
determination. This approach combines the techniques of HDBSCAN, GMM, and a
novel cluster member identification technique, color excess constraint. The new
method exhibits efficiency in detecting OCs while ensuring precise
determination of cluster memberships. It is called Blind Search-Extra
Constraint (BSEC) method. It is successfully applied to the Gaia DR3, and 83
new OCs are found. This study also reports 621 new OC candidates with
discernible main sequence or red giant branch. The BSEC technique can discard
some false negatives of previous works, which takes about 3 percentage of known
clusters. As an extra constraint, color excess (or 2-color) constraint is
useful for removing fake cluster member stars from the clusters that are
identified from the positions and proper motions of stars, and getting more
precise CMDs, when differential reddening of member stars of a cluster is not
large (e.g., \DeltaE(G_BP -G_RP)<0.5 mag). It makes the CMDs of 15 percent
clusters clearer (in particular for the region near turnoff) and therefore is
helpful for CMD and stellar population studies. Our result suggests that color
excess constraint is more appropriate for clusters with small differential
reddening, such as globular clusters or older OCs, and clusters that the
distances of member stars cannot be determined accurately.
