Frequency and ridge estimation using structure tensor

Computing a reliable orientation map is a critical step in automatic fingerprint analysis and especially for analysis of fingermarks obtained at crime-scenes especially. Being the initial step of processing image information it may influence the further operations: registration, enhancement and matching. We suggest a new way of automatic frequency estimation improving the state-of-theart results [1], [2] favourably for noisy images. We suggest using frequency to steer Structure Tensor [3] which is used to obtain refined orientation maps. Fingermarks collected from crime scenes are usually low quality images, therefore lacking the support of automatic image analysis methods. Forensic expertise is utilized for the major part of the image analysis: registration of minutia, ridge frequency count, etc. It is desirable to support an expert by providing reliable orientation maps to ease the work. Having orientation maps estimated we can further provide suggestions for an expert (possible minutia location and orientation) to increase his/her efficiency. A structure tensor is a symmetric positive semidefinite matrix that can be utilized for building orientation maps of fingerprints. Response of the gradient filter, upon convolution with the image, is used for estimating frequency of the image. We provide mathematical descriptions to support the method. Suggested method provides maps of frequency that are continuous in the mathematical sense. We have tested suggested frequency estimation on the NIST SD27 database to perform ridge counting. The fingermark ridge count procedure is desirable but time consuming for an expert as it grows quadratically with the number of minutia we want to count ridges of. Also it is not fully reliable to be done automatically. The ridge count does not only depend on the frequency but also on the wave vector direction connecting two minutia points. We model a fingerprint image in the neighbourhood R around two minutiae with the planar wave cos(ω0r). Here, ω0 is a known constant wave vector (frequency of the image ridge flow calculated a forehead) and r is the line joining two minutia points.