Image Filter Design for Fingerprint Enhancement

Research on Palmprint Identification Method Based on Quantum Algorithms

“…For a given N dimension the traditional discrete Fourier transform [15] is a linear operator on C N mapping ( x 0 , x 1 ,…, x N −1 ) to ( y 0 , y 1 ,…, y N −1 ), where $\begin{array}{c}{y}_k=\frac{\mathrm{1}}{\sqrt{N}}\underset{i=\mathrm{normal0}}{\overset{N-\mathrm{normal1}}{{\displaystyle false\sum }}}{x}_j{e}^{\mathrm{2}\pi ikj/N}\hspace{1em}\left(k=\mathrm{0,1},\dots ,N-\mathrm{1}\right).\mathrm{\hspace{0.17em}\hspace{0.17em}}\end{array}$ The quantum Fourier transform (QFT) algorithm can be obtained from the traditional discrete Fourier transform [16] which is $\begin{array}{c}\text{QFT}:U_{\text{QFT}}|x\rangle =\frac{\mathrm{1}}{\sqrt{{\mathrm{normal2}}^m}}\underset{i=\mathrm{normal0}}{\overset{{\mathrm{normal2}}^m-\mathrm{normal1}}{{\displaystyle false\sum }}}{e}^{\mathrm{2}\pi itx/{\mathrm{2}}^m}|t\rangle .\end{array}$ QFT can be used in novel image encryption and decryption [17], where the quantum bit numbers of the quantum state | x 〉 are m , U QFT is a unitary operator, and QFT is a 2 m -dimensional unitary transformation [18, 19]. The effect of (11) is to transform a unit quantum state into a superposition state.…”

Estimation of the directional field anisotropy based on Mohr's Circle in fingerprint images

“…They have higher computational complexity. In the frequency domain [6] computed the optimal orientation using directional filters, taking into account the highest filter response and local smoothing. Short Time Fourier Transform (STFT) analysis was introduced by [7].…”