Fingerprint analysis is typically based on the location and pattern of detected singular points in the images. These singular points (cores and deltas) not only represent the characteristics of local ridge patterns but also determine the topological structure (i.e., fingerprint type) and largely influence the orientation field. In this paper, we propose a novel algorithm for singular points detection. After an initial detection using the conventional Poincaré Index method, a so-called DORIC feature is used to remove spurious singular points. Then, the optimal combination of singular points is selected to minimize the difference between the original orientation field and the model-based orientation field reconstructed using the singular points. A core-delta relation is used as a global constraint for the final selection of singular points. Experimental results show that our algorithm is accurate and robust, giving better results than competing approaches. The proposed detection algorithm can also be used for more general 2D oriented patterns, such as fluid flow motion, and so forth.