Optical-digital incoherent system for image reconstruction by using Zernike moments

One of the main contributions of this paper is to show that contrary to the common belief Tchebichef moments are more sensitive to noise added to the image than Zernike moments. We show this by imposing different types and levels of noise on various images and measuring the error due to the added noise alone after image reconstruction. To calculate the error due to added noise alone, the image reconstruction error is subtracted from the total error, which initially includes both reconstruction and added noise errors. Another contribution of this paper is to present some analysis and compare the reconstruction capability of Tchebichef moments to that of Zernike and Legendre moments in noise free environments independent of the image used. We show this by spectrally analyzing the performance of Tchebichef, Legendre, and Zernike moments using single frequency images. Here the total reconstruction error of an arbitrary image is equal to the integration of the spectral errors, whose transfer functions are calculated using single frequency images, for all frequencies.

As an orthogonal moment, Zernike moment (ZM) is an attractive image feature in a number of application scenarios due to its distinguishing properties. However, we find that for digital images, the commonly used Cartesian method for ZM computation has compromised the advantages of ZMs because of their non-ideal accuracy stemming from two inherent sources of errors, i.e., the geometric error and the integral error. There exists considerable errors in image reconstruction using ZMs calculated with the Cartesian method. In this paper, we propose a polar coordinate based algorithm for the computation of ZMs, which avoids the two kinds of errors and greatly improves the accuracy of ZM computation. We present solutions to the key issues in ZM computation under polar coordinate system, including the derivation of computation formulas, the polar pixel arrangement scheme, and the interpolation-based image conversion etc. As a result, ZM-based image reconstruction can be performed much more accurately.

Finite precision error analysis of Zernike moments computation schemes and a new, efficient, robust recursive algorithm

Analysis of noise sensitivity of Tchebichef and Zernike moments with application to image watermarking

Compared to the classical VanderLugt correlator, optical-hybrid frequency plane correlator systems are more flexible, butalso more complicated. Implementation of the hybrid systems requires the use of addressable spatial light modulators todisplay contents of the input and filter planes and the use of the additional lenses to match the scalings in the system.Furthermore, hybrid systems use the optical elements such as quarter-wave plates, half-wave plates, and polarizers; which is all not needed for the classical setup. All these additional optical elements influence both amplitude and phase distortions of the wavefront that propagates throughout the system. For measuring the phase distortions of the opticalelements, we have used the holographic setup with one mirror mounted on a piezo-electric transducer and conirolled by adigital image processing system.Keywords: Interferometry, optical correlator, optical systems 1. INTRODUCTION Storage and display of information are key problems in optical correlator systems. Utilization of liquid crystal displays(LCDs) offers an improvement in the system possibilities but leads to implementation problems. Although the mainproblems are addressed to the characterization' of LCDs and further to the optimization of LCDs as correlation filters(CFs),46 the wavefront distortions throughout the optical system cannot be neglected.7The uniform plane wavefront after passing through an optical element is distorted in its amplitude and phase, where thephase distortions are much more severe than amplitude ones. The total phase distortion is defined by the total number ofthe optical elements in the system and by their particular flatness variations. The early systems have used photographicfilm or plates to introduce the images into the input and filter planes of the optical device, where the cojrelation filterswere produced holografically. Thus, a classical optical-analog frequency plane correlator was realized with two Fouriertransform (F7) lenses and two photo-plates but without an electronic computer support. Generally, such a system wassuffering from the lack of flexibility and practicability, but the wavefront modulation throughout the system was easy tocontrol. The development of addressable spatial light modulators enabled the possibility of calculating CFs as well as thepossibility for the fast exchange of data at the input and filter planes. The later system is generally more flexible, but thewavefront suffers because the additional optical elements (such as the polarization optics and enlarging lenses) togetherwith the two LCDs introduce an significant increase in the wavefront distortions.In this paper. we present the phase distortions of the optical elements used in our hybrid frequency plane correlator system.These distortions are measured by using a holographic setup and discussed in terms of the number of interferometricfringes and the regularity of the obtained fringe patterns. We also summarize the procedures of minimizing the wavefrontdistortions throughout the optical system.

Image analysis with logarithmic Zernike moments

This work proposes a new approach to find the generating function (GF) of the Zernike polynomials in two dimensional form. Combining the methods of GFs and discrete-time systems, we can develop two dimensional digital systems for systematic generation of entire orders of Zernike polynomials. We establish two different formulas for the GF of the radial Zernike polynomials based on both the degree and the azimuthal order of the radial polynomials. In this paper, we use four terms recurrence relation instead of the ordinary three terms recursion to calculate the radial Zernike polynomials and their GFs using unilateral 2D Z-transform. A spatio-temporal implementation scheme is developed for generation of the radial Zernike polynomials. Since Zernike moments (ZMs) are invariant with respect to rotation, translation and scaling, the experimental schemes show the image classification applications by using the proposed algorithm.

Two important factors that determine the efficiency and reliability of a rice sorting machine are the overall processing speed and the classification accuracy. In this paper, an efficient rice sorting process which uses a subset of Zernike moments (ZM) and a multilayer perceptron is presented. Since the falling rice grains during sorting process can be in any orientation, a rotational invariant feature set is crucial in this application. Hence, the set of ZM with its inherent rotational invariance property is chosen in this context. Nevertheless, one of the main drawbacks of ZM in real-time application is its long computation time. To overcome this, a subset of ZM is selected from its original full set of 12 orders, using the combination of fuzzy ARTMAP and genetic algorithm. To further reduce the computation time, the combination of q-recursive method and Zernike polynomials’ inherent symmetry property is utilized. Hence, the processing time of the subset of ZM is significantly reduced by almost 67% while maintaining the classification accuracy as compared to computing the original full set of ZMs.

Zernike Moments (ZMs) are used in many image processing applications, due to their resistance against various signal processing and geometric attacks. Digital image watermarking is one of those application areas, where ZMs are widely used to insert and extract the watermark bits for digital media authentication. In all the existing ZM based watermarking techniques, magnitude of moments is used to insert and extract the watermark. In this paper, the authors’ have proposed a semi blind watermarking technique in which phase of ZMs is used for watermark insertion and extraction. Due to the use of phase of ZMs, 100% detection ratio is achieved against any geometric and other signal processing attacks. To make the proposed technique fast, q-recursive method is used to compute the Zernike polynomials. The use of q-recursive method has also increased the transparency of watermark due to its better reconstruction ability as compared to traditional moment computation method. Through detailed experimentation, it has been confirmed that the proposed watermarking technique is fast, has more imperceptibility, less Bit Error Rate (BER) and more capacity as compared to traditional ZMs magnitude based watermarking technique.

Electro holography using LCD panels or AOMs is one of the techniques that can be used in 3D animation. The technique of using a light extracted from a white light laser or a white light source was developed asa way of using electro-holography in color reconstruction. However, it is difficult to adjust the image position of the RGB bands, because of the many focal lenses were used in real image reconstruction. Having said that, when using virtual image reconstruction, it is possible to remove the focal lenses. This is considered a simple optical setup. In this paper, we will examine a the simplification of an optical system in virtual image reconstruction.

Explicit invariance of Cartesian Zernike moments

The algorithm for reconstructing a 2D input signal (the image measured) by a finite realization of a 2D signal at the digital optical recording system output with the use of the fast Fourier transform is analyzed. The image reconstruction error is estimated.

Image reconstruction is very much concerned with the ability to reproduce image of possibly the same quality as original. This paper presents the comparison of Zernike Moment (ZM) and Discrete Cosine Transform (DCT) for image reconstruction in noise environment. Two types of images used are gray scale and binary. The original images are corrupted with three different noises that are Salt and Pepper, Gaussian and Random. Both original and corrupted images are reconstructed using Inverse Zernike Moment and Inverse Discrete Cosine Transform. The performance of each algorithm is measured by evaluating Peak Signal to Noise Ratio (PSNR) for the reconstructed gray scale of pixel size 64×64 and binary of pixel size 30×30 images. The comparison of PSNR values between the two techniques proves that Zernike Moment is less sensitive to noisy images compared to Discrete Cosine Transform.

Recent advances in electro-optics have brought into use communication and information theory to analyze performance in coherent and incoherent optical information processing systems. An optical information processsing system can be analyzed with many of the same concepts of linear system theory (e.g., spatial impulse response, spatial frequency and spatial domain synthesis, etc.), and the photographic images to be processed can be regarded in the same manner as time signals (e.g., spatial frequency content, spatial amplitude and phase modulation, space-bandwidth product, etc.). Both coherent and incoherent optical processing systems can be treated as linear systems, and the processing operation can generally be carried out by communication theory concepts. Although coherent optical information processing operations have been used for performing complex amplitude operations, complex processing can also be performed with incoherent or white-light illumination. The importance of optical information processing operations, either coherent or incoherent, is due to the basic Fourier transform properties of lenses. In this paper, we will discuss mostly the incoherent systems because they are of more recent interest and possess certain advantages, we feel, over the traditional coherent optical processors. Experimental illustrations of the results are provided. In view of the broad area in optical processing of photographic images, we will confine ourselves to a few applications that we consider of general interest. We apologize for the omission of other techniques and applications, and for neglecting the inclusion of their references.

Carbon black photo-resist (CB PR), containing CB, CB dispersant, photo-curable resins, adhesion promoter, photo-initiator, and solvent, was developed for production of high resolution of black matrix (BM) which is an important light-shielding element on the color filter in liquid crystal display (LCD) industry. This work was divided into two parts: (1) the synthesis and function of each ingredient in CB PR and (2) the kinetic behaviors of photo-polymerization and TEMPO-mediated polymerization related to the compounds synthesized in the first part. In the first part, CB was first treated by CB dispersant in order to prepare a high loading of CB dispersion in an organic solvent (propylene glycol monomethyl ether acetate, PGMEA) up to 10 wt%. Three different kinds of dispersants were taken separately to disperse CB, a commercialized dispersant and two newly synthesized dispersants. These three CB dispersants were effectively adsorbed onto CB by the interaction between amino-containing anchoring groups of dispersant and carboxylic acid group on CB surface. They had a moderate chain length to provide a steric repulsion for CB. In addition, the influences of amount and structure of these dispersants on the stability and light-shielding property of CB were discussed. Among these dispersants, one of the newly synthesized dispersants having (meth)acrylate group is an UV-curable CB dispersant, which was synthesized by a two-step process. First, a styrene-(meth)acrylate living copolymer was synthesized as a CB dispersant by TEMPO-mediated living polymerization. In the second step, to render the UV-curable property, additional (meth)acrylate groups were grafted onto the prepared CB dispersant by an urethane linkage reaction. The other newly synthesized CB dispersant was also interesting because it exhibited both UV-curable and alkali-soluble properties, which was capable of forming micro-patterns through an UV-lithographic process. This dispersant was also synthesized by a two-step process. First, UV-curable and alkali-soluble resins were synthesized by the reaction of bisphenol-A epoxy diacrylate with benzophenone tetracarboxylic dianhydride at different molar ratios. Second, to be able to disperse CB particles, these resins were further reacted with an isocyanate-containing methacrylate monomer to produce effective dispersants. Afterwards, CB PRs were prepared by adding photo-initiator and with or without photo-curable resins into the above CB dispersions. However, it was not easy to prepare a BM with both a high opacity and a good resolution upon a low irradiation energy of UV light. This is because CB is a strong light-shielding material which would reduce the photo-sensitivity of CB PR. Besides, the developability of CB PR was strongly retarded by CB since CB can not be soluble in any solvent. In view of this, the selections of photo-initiator and photo-curable resins are critical because they affect the lithographic performance of CB PR. Several photo-initiators were evaluated with respect to their light absorbance and the rate of photo-polymerization in the presence of CB. In addition, several new photo-curable resins were synthesized in this work. UV-curable and alkali-soluble resins were tailored because they can form patterns by an environmental-friendly alkali developer. The influences of photo-sensitivities and concentration of carboxylic acid groups of these resins on the appearance of BM patterns and the energy consumption of UV light were discussed. Finally, a BM with both a high optical density of 4μm-1 and resolution of 10 μm in size upon irradiation of 50-200 mJ/cm2 was successfully produced by using the aforementioned CB PRs through an UV-lithographic process. In addition, the adhesion strength between BM and glass substrate was studied. In the manufacturing process of color filter, the adhesion strength between the BM and glass substrate largely decreased after the ITO sputtering process. To overcome this problem, in this work, a newly synthesized UV-curable silane coupling agent as an adhesion promoter was added into a CB PR. This adhesion promoter was synthesized by the reaction between the hydroxyl group of bisphenol A epoxy diacrylate and the isocyanate group of 3-(isocyanatopropyl)-triethoxysilane. This adhesion promoter containing both acrylate and triethoxysilane groups can be cured upon UV irradiation and form a strong covalent bond with the glass substrate at high temperature, respectively. The influence of this adhesion promoter on the adhesion strength between BM and glass substrate before and after ITO sputtering process was discussed. In the second part, the kinetic behaviors of photo-polymerization of UV-curable resins with carboxylic acid and amino functional groups were investigated. The rate of polymerization and extent of reaction were monitored by using a photo differential scanning calorimeter. A new method combining dark polymerization with pseudo steady state assumption of growing radicals was presented in order to calculate the kinetic constants for propagation, bimolecular termination, monomolecular termination, and the concentration of growing radicals of each resin as a function of extent of reaction. According to the experimental results, it was found that the photo-polymerization was strongly influenced by both functional groups of resins and photo-initiators. The influences of functional groups on the kinetic rate constants and initiator efficiency were discussed in depth. For the CB dispersant synthesized by TEMPO-mediated copolymerization of styrene and (meth)acrylate monomers, the successful living character was observed only at high styrene molar fraction in feed. In view of this, a new kinetic model was established in order to explain the retardant mechanism of the living polymerization of (meth)acrylate. Besides, it was found that TEMPO-mediated polymerization of acrylate could be improved by adding a small amount of polar solvent, DMF (N,N-dimethylformamide) as a rate-enhancement agent. Finally, by using this kinetic model and experimental results, the kinetic rate constants in the TEMPO-mediated polymerization were then calculated and discussed.