This paper introduces a set of 2D transforms, based on a set of orthogonal projection bases, to generate a set of features which are invariant to rotation. We call these transforms Polar Harmonic Transforms (PHTs). Unlike the well-known Zernike and pseudo-Zernike moments, the kernel computation of PHTs is extremely simple and has no numerical stability issue whatsoever. This implies that PHTs encompass the orthogonality and invariance advantages of Zernike and pseudo-Zernike moments, but are free from their inherent limitations. This also means that PHTs are well suited for application where maximal discriminant information is needed. Furthermore, PHTs make available a large set of features for further feature selection in the process of seeking for the best discriminative or representative features for a particular application.

Two-Dimensional Polar Harmonic Transforms for Invariant Image Representation

Invariant character recognition with Zernike and orthogonal Fourier–Mellin moments

Chebyshev-Fourier moments for describing images were proposed. After definition of the moments, the multidistortion invariance of the moments was verified. The performance of the moments in describing images was investigated in terms of the normalized image-reconstruction error and the results of the experiments on the noise sensitivity are given.

https://www.intranet.copl.ulaval.ca/sheng/publications/JOSAA-Chebyshev.PDF

Image description with Chebyshev–Fourier moments

Minimizing a Euclidean distance in the complex plane optimizes a wide class of correlation metrics for filters implemented on realistic devices. The algorithm searches over no more than two real scalars (gain and phase). It unifies a variety of previous solutions for special cases (e.g., a maximum signal-to-noise ratio with colored noise and a real filter and a maximum correlation intensity with no noise and a coupled filter). It extends optimal partial information filter theory to arbitrary spatial light modulators (fully complex, coupled, discrete, finite contrast ratio, and so forth), additive input noise (white or colored), spatially nonuniform filter modulators, and additive correlation detection noise (including signaldependent noise). An appendix summarizes the algorithm as it is implemented in available computer code.

Optimal realizable filters and the minimum Euclidean distance principle. [for spatial light modulators]

Quaternion Fourier-Mellin moments for color images

We propose orthogonal Fourier–Mellin moments, which are more suitable than Zernike moments, for scaleand rotation-invariant pattern recognition. The new orthogonal radial polynomials have more zeros than do the Zernike radial polynomials in the region of small radial distance. The orthogonal Fourier–Mellin moments may be thought of as generalized Zernike moments and orthogonalized complex moments. For small images, the description by the orthogonal Fourier–Mellin moments is better than that by the Zernike moments in terms of image-reconstruction errors and signal-to-noise ratio. Experimental results are shown.

https://www.intranet.copl.ulaval.ca/sheng/publications/JosaA%20OFMM.pdf

Orthogonal Fourier–Mellin moments for invariant pattern recognition

We obtain continuous phase modulation with commercial twisted nematic liquid television. We present theory and experimental implementation of kinoforms, matched spatial filters, circular harmonic filters and synthetic discriminant functions with the phase-mostly filter approach.

Programmable phase-mostly holograms and correlation filters

Original experimental techniques for obtaining the phase-only modulation and the complex amplitude modulation with the commercial twisted nematic liquid crystal televisions (LCTV) are described. The techniques are based on the Jones matrix theoretical analysis. We use the programmable phase-mostly LCTV to optically implement the phase-only matched filters, phase-only circular harmonic filters, phase-only synthetic discriminant functions and the adaptive composite wavelet matched filters for pattern recognition. We also implement the phase-only computer generated holograms, speckle-free kinoforms and optical kinoform encryption using random phase encoding for security applications.

Phase-only SLMs for optical pattern recognition and security systems

The spatial light modulator (SLM) is a key element of an optical processor. The limitations of the currently availableSLM's are their limited phase and amplitude modulation capacity, limited space bandwidth product (SBWP) and limited speed.We use the commercial liquid crystal television (LCTV) as a SLM and build a real-time on-axis phase-only opticai correlator.This approach permits efficient use of the SBWP of the SLM (200 x 200 and 440 x 480 for new type of LCTV) and provideshigh light efficiency"2. Various continuous phase-only holograms, matched filters, circular harmonic filters and composite filtershave been implemented with this coupled mode modulation SLM.

Optical pattern-recognition with the real-time phase only filters and wavelet matched filters

The spatial light modulator (SLM) is a key element in an optical processor. The principle limitations of the currently available SLMs are the limited phase and amplitude modulation capacity, the limited space bandwidth product (SBWP) and the limited speed. We use the commercial liquid crystal television (LCTV) as the SLM and build a real-time on-axis phase-only optical correlator. This approach allows the efficient use of the SBWP of the LCTV (200 x 200 and 440 x 480 for new type of LCTV) and provides high light efficiency.

Lixin Shen

Papers

Orthogonal Fourier–Mellin moments for invariant pattern recognition

Programmable phase-mostly holograms and correlation filters

Phase-only SLMs for optical pattern recognition and security systems

Optical pattern-recognition with the real-time phase only filters and wavelet matched filters

Optical Real-Time Phase-Only Correlator Using Liquid Crystal Television