Image moments are used extensively in various applications. Depending on the task at hand, the type as well as the order of moments to be implemented varies greatly. Simple geometric characteristics require the first few geometrical moments, while robust image watermarking employs high-order orthogonal moments. In this paper, we present an architecture which can be easily modified to implement various types of moments, including geometric, continuous as well as discrete orthogonal, in real-time. Although this architecture is optimized for hardware, software implementation is feasible and advantageous in some cases.

The angular radial transform (ART) is the region-based shape descriptor for MPEG-7. It is a compact descriptor that presents invariance to simple transformations, while presenting very low information redundancy. However, limited effort has been spent on the fast computation of ART, which is of the essence, especially in systems with sparse computational resources. In this paper, we present an efficient implementation of the descriptor, relating it to accumulation moments. The approximations used are shown not to affect the final 140-bit descriptor, and the architecture is capable of processing images up to one order of magnitude faster than the conventional method.

Image moments have been extensively used as feature descriptors. However, the quantization error introduced in discrete signals presents problems, especially when dealing with small-size images. This results in the fact that the invariant properties of moments are compromised. In this paper, we present a technique suitable for the calculation of moments from a continuous signal, derived by piecewise polynomial interpolation of the corresponding discrete one. The computed moments exhibit significantly increased accuracy while requiring trivial computational effort. Zernike moments are then computed using the proposed scheme and are shown to display increased stability to geometrical transformations.

In this paper, a one dimensional (1-d) cellular automaton (CA) for pseudorandom number generation (PRNG) and its reconfigurable hardware implementation are presented. The proposed 1-d CA based on the real time clock sequence (analytical time description) can generate high-quality random numbers which can pass all of the statistical tests of DIEHARD and NIST which seem to be the most powerfully complete general test suites for randomness. After describing our implementation in field-programmable gate array (FPGA), through experiments, we have identified the efficiency of the presented CA that performs exceptionally well compared to most known CA PRNGs reported in literature. More specifically, our CA implementation outperforms all the previous CA and LFSR PRNGs both in hardware implementation and timing characteristics. Such a CA can be efficiently implemented for PRNG reasons in every real time clock application with finally no silicon overhead.

Chebyshev moments were recently proposed to address problems of moments of continuous orthogonal basis. They are moments of a discrete basis and are orthogonal in the domain of the image coordinate space, a feature which presents a number of advantages over moments of continuous orthogonal basis. No effort has been devoted yet to the efficiency of their calculation. In this paper, we present a hardware architecture which enables real-time processing of binary and grayscale images of up to 4 Mpixels. This architecture is realized in a field-programmable gate array of typical clock frequency of 100 MHz

Zernike moments have been proven to be very powerful image descriptors. However, their computational complexity makes them unsuitable for real-time applications. In this paper, a mathematical relationship between geometric and Zernike moments is extracted. In this way, the computation of geometric moments is adequate to derive Zernike moments. Since geometric moments can be efficiently implemented in hardware and their calculation can be performed in real-time, we propose here a new real-time hardware architecture for the computation of Zernike moments. This method outperforms existing software approaches, especially for large images, allowing real-time processing of images up to 4 Mpixels.