Psychovisually tuned wavelet fingerprint compression

We present biorthogonal and orthonormal wavelets for embedded zerotree wavelet compression of fingerprint images. By simulated annealing over the wavelet filter coefficients, using a composite cost function dependent upon a parameter k 2 which weights the relative importance of the wavelet's bandwidth and time dispersion, a series of wavelets is obtained. Each of these is optimal in terms of a particular Heisenberg uncertainty 'footprint', i.e. a particular trade-off between bandwidth and time dispersion. The psychovisually optimal wavelet for fingerprint image compression is determined by fingerprint experts by examination of images compressed and recovered using the series of wavelets. Psychovisually tuned wavelets were found to yield superior visual fidelity to standard wavelets and also to wavelets optimized to produce minimum rms error on either fingerprint or general test images. Most large police forces use automated fingerprint identification systems (AFIS) to match fingerprints when seeking to identify individuals during criminal investigations. Fingerprint image compression is an essential component of AFIS systems because of the large sizes of data bases, which may contain several million fingerprint images. The U.S. Federal Bureau of Investigation has specified a wavelet method for use in its fingerprint data base [1]. Fingerprints have special local ridge properties [2, 3] which are well suited to processing via the discrete wavelet transform (DWT). In particular, the compact support of the basis functions implies an ability to adapt to local image structures. The well-known Heisenberg uncertainty relationship places a lower limit upon the time-frequency uncertainty of any signal. The aim of the present work was to determine the optimum trade-off between frequency and time resolution for wavelets when applied to the compression of fingerprint images for criminological identification purposes. The uncertainty principle in signal processing states that a linear filter with impulse response signal f(t) and whose Fourier transform is F(ω) has its time-frequency resolution restricted by ∆ω∆t ≥ 1 2 where ∆t 2 = ∫ τ 2 f(τ) 2 dτ ∫ f(τ) 2 dτ measures the pulse width, τ = t − t _ , and ∆ω 2 = ∫ ω 2  F(ω)  2 dω ∫ F(ω) 2 dω is the bandwidth. The uncertainty principle expresses the impossibility of obtaining arbitrarily small bandwidth and arbitrarily low time dispersion simultaneously. Our approach to defining a 'good' wavelet is to obtain a series of wavelets, each optimized for a different trade-off between ∆t 2 and ∆ω 2 , i.e. each …