Peter Alleine Fletcher

A coherent framework for fingerprint analysis: are fingerprints Holograms?

We propose a coherent mathematical model for human fingerprint images. Fingerprint structure is represented simply as a hologram - namely a phase modulated fringe pattern. The holographic form unifies analysis, classification, matching, compression, and synthesis of fingerprints in a self-consistent formalism. Hologram phase is at the heart of the method; a phase that uniquely decomposes into two parts via the Helmholtz decomposition theorem. Phase also circumvents the infinite frequency singularities that always occur at minutiae. Reliable analysis is possible using a recently discovered two-dimensional demodulator. The parsimony of this model is demonstrated by the reconstruction of a fingerprint image with an extreme compression factor of 239.

Direct Embedding and Detection of RST Invariant Watermarks

A common goal of many watermarking techniques is to produce a mark that remains detectable after the geometric transformations of Rotation, Scale and Translation; also known as RST invariance. We present a simple approach to achieving RST invariance using pixel-by-pixel addition of oscillating homogeneous patterns known as Logarithmic Radial Harmonic Functions [LRHFs]. LRHFs are the basis functions of the Fourier-Mellin transform and have perfect correlation, orthogonality, and spread-spectrum properties. Once the patterns have been embedded in an image they can be detected directly regardless of RST and with great sensitivity by correlation with the corresponding complex LRHFs. In contrast to conventional methods our approach is distinguished by the utilization of signal phase information and the absence of interpolation artifacts. Data encoding is based on the information in the relative centre positions of multiple spatially overlapping patterns.

Affine-Invariant Image Watermarking Using the Hyperbolic Chirp

Image watermarking is the robust, imperceptible embedding of a small quantity of data into a digital image, and the subsequent recovery of this data, perhaps after the watermarked image has been distorted. We present a new watermarking technique which is robust to many image distortions, in particular arbitrary affine transformations of the image. The method achieves its robustness through the use of one-dimensional chirp functions. An affine-invariant detection method exists for such functions using a Radon transform, yet they are not detected trivially by a malicious attacker. The method also provides a way to determine any affine transformation applied to the watermarked image by using an affine-invariant property of groups of intersecting lines.

Extreme Compression of Fingerprint Images: Squeezing Fingerprints until the Spirals Pop Out

We propose a new mathematical model for human fingerprint images. The model can be summarized by the phrase “fingerprints are holograms”. The model unifies the analysis, compression, classification, matching, and re‐synthesis of fingerprints, in a self‐consistent formalism. The parsimony of this model is demonstrated by the reconstruction of fingerprint images with extreme compression ratios (typically >200x). At the heart of the method is a recently proposed method for demodulating two‐dimensional fringe patterns, such as holograms. Demodulation uses a spiral‐phase quadrature transform combined with a two‐dimensional orientation estimator that also uses spiral‐phase Fourier operators. Finally, the fingerprint decomposition itself achieves compactness by splitting the phase modulation into two unique parts, one of which is a pure spiral‐phase function. Spiral‐phase inexorably emerges as a central theme of the work.