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The singular points of fingerprints, namely, core and delta, are important referential points for the classification of fingerprints. Several conventional approaches such as the Poincare index method have been proposed; however, these approaches cannot achieve the reliable detection of poor-quality fingerprints. In this paper, we propose a new core and delta detection method by singular candidate analysis using an extended relational graph. In order to use both the local and global features of the ridge direction patterns and to realize a method with high tolerance to local image noise, singular candidate analysis is adopted in the detection process; this analysis involves the extraction of locations in which the probability of the existence of a singular point is high. The experimental results show that the success rate of this approach is higher than that of the Poincare index method by 10% for singularity detection using the fingerprint image databases FVC2000 and FVC2002. These databases contain several poor quality images, even though the average computation time is 15%-30% greater than the Poincare index method.