The singular points of fingerprints, viz. 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 are not reliable with poor-quality fingerprints. This paper proposes a new core and delta detection employing singular candidate analysis and an extended relational graph. Singular candidate analysis allows the use both the local and global features of ridge direction patterns and realizes high tolerance to local image noise; this involves the extraction of locations where there is high probability of the existence of a singular point. Experimental results using the fingerprint image databases FVC2000 and FVC2002, which include several poor-quality images, show that the success rate of the proposed approach is 10% higher than that of the Poincare index method for singularity detection, although the average computation time is 15%-30% greater.

In this paper, a novel Wold decomposition algorithm is proposed to address the issue of deterministic component extraction for texture images. This algorithm exploits the wavelet-based singularity detection theory to process both harmonic a nd evanescent features from frequency domain. This exploitation is based on the 2D Lebesgue decomposition theory. When applying multiresolution analysis techniq ue to the power spectrum density (PSD) of a regular homogeneous random field, its indeterministic component will be effectively smoothed, and its deterministic component will remain dominant at coarse scale. By means of propagating these positions to the finest scale, the deterministic component can be properly extracted. From experiment, the proposed algorithm can obtain results that satisfactorily ensure its robustness and efficiency.

Automatic image inspector inspects the quality of printed circuit boards using image-processing technology. In this study, we change an automatic inspection problem into a problem for detecting the signal singularities. Based on the wavelet theory that the wavelet transform can focus on localized signal structures with a zooming procedure, a novel singularity detection and measurement algorithm is proposed. Singularity positions are detected with the local wavelet transform modulus maximum (WTMM) line, and the Lipschitz exponent is estimated at each singularity from the decay of the wavelet transform amplitude along the WTMM line. According to the theoretical analysis and computer simulation results, the proposed algorithm is shown to be successful for solving the automatic inspection problem and calculating the Lipschitz exponents of signals. These Lipschitz exponents successfully characterize singular behavior of signals at singularities.