Nonlinear Joint Transform Correlator Research Articles

Double Image Encryption System Using a Nonlinear Joint Transform Correlator in the Fourier Domain.

In this work, we present a new nonlinear joint transform correlator (JTC) architecture in the Fourier domain (FD) for the encryption and decryption of two simultaneous images. The main features of the proposed system are its increased level of security, the obtention of a single real-valued encrypted signal that contains the ciphered information of the two primary images and, additionally, a high image quality for the two final decrypted signals. The two images to be encrypted can be either related to each other, or independent signals. The encryption system is based on the double random phase encoding (DRPE), which is implemented by using a nonlinear JTC in the FD. The input plane of the JTC has four non-overlapping data distributions placed side-by-side with no blank spaces between them. The four data distributions are phase-only functions defined by the two images to encrypt and four random phase masks (RPMs). The joint power spectrum (JPS) is produced by the intensity of the Fourier transform (FT) of the input plane of the JTC. One of the main novelties of the proposal consists of the determination of the appropriate two nonlinear operations that modify the JPS distribution with a twofold purpose: to obtain a single real-valued encrypted image with a high level of security and to improve the quality of the decrypted images. The security keys of the encryption system are represented by the four RPMs, which are all necessary for a satisfactory decryption. The decryption system is implemented using a 4f-processor where the encrypted image and the security keys given by the four RPMs are introduced in the proper plane of the processor. The double image encryption system based on a nonlinear JTC in the FD increases the security of the system because there is a larger key space, and we can simultaneously validate two independent information signals (original images to encrypt) in comparison to previous similar proposals. The feasibility and performance of the proposed double image encryption and decryption system based on a nonlinear JTC are validated through computational simulations. Finally, we additionally comment on the proposed security system resistance against different attacks based on brute force, plaintext and deep learning.

Image Encryption System Based on a Nonlinear Joint Transform Correlator for the Simultaneous Authentication of Two Users

We propose a new encryption system based on a nonlinear joint transform correlator (JTC) using the information of two biometrics (one digital fingerprint for each user) as security keys of the encryption system. In order to perform the decryption and authentication in a proper way, it is necessary to have the two digital fingerprints from the respective users whose simultaneous authentication is pursued. The proposed security system is developed in the Fourier domain. The nonlinearity of the JTC along with the five security keys given by the three random phase masks and the two digital fingerprints of the two users allow an increase of the system security against brute force and plaintext attacks. The feasibility and validity of this proposal is demonstrated using digital fingerprints as biometrics in numerical experiments.

Optical Image Encryption Using a Nonlinear Joint Transform Correlator and the Collins Diffraction Transform

The Collins diffraction transform (CDT) describes the optical wave diffraction from the generic paraxial optical system. The CDT has as special cases the diffraction domains given by the Fourier, Fresnel and fractional Fourier transforms. In this paper, we propose to describe the optical double random phase encoding (DRPE) using a nonlinear joint transform correlator (JTC) and the CDT. This new description of the nonlinear JTC-based encryption system using the CDT covers several optical processing domains, such as Fourier, Fresnel, fractional Fourier, extended fractional Fourier and Gyrator domains, among others. The maximum number of independent design parameters or new security keys of the proposed encryption system using the CDT increases three times in comparison with the same encryption system that uses the Fourier transform. The proposed encryption system using the CDT preserves the shift-invariance property of the JTC-based encryption system in the Fourier domain, with respect to the lateral displacement of both the key random mask in the decryption process and the retrieval of the primary image. The viability of this encryption system is verified and analysed by numerical simulations.

Optimized swimmer tracking system by a dynamic fusion of correlation and color histogram techniques

To design a robust swimmer tracking system, we took into account two well-known tracking techniques: the nonlinear joint transform correlation (NL-JTC) and the color histogram. The two techniques perform comparably well, yet they both have substantial limitations. Interestingly, they also seem to show some complementarity. The correlation technique yields accurate detection but is sensitive to rotation, scale and contour deformation, whereas the color histogram technique is robust for rotation and contour deformation but shows low accuracy and is highly sensitive to luminosity and confusing background colors. These observations suggested the possibility of a dynamic fusion of the correlation plane and the color scores map. Before this fusion, two steps are required. First is the extraction of a sub-plane of correlation that describes the similarity between the reference and target images. This sub-plane has the same size as the color scores map but they have different interval values. Thus, the second step is required which is the normalization of the planes in the same interval so they can be fused. In order to determine the benefits of this fusion technique, first, we tested it on a synthetic image containing different forms with different colors. We thus were able to optimize the correlation plane and color histogram techniques before applying our fusion technique to real videos of swimmers in international competitions. Last, a comparative study of the dynamic fusion technique and the two classical techniques was carried out to demonstrate the efficacy of the proposed technique. The criteria of comparison were the tracking percentage, the peak to correlation energy (PCE), which evaluated the sharpness of the peak (accuracy), and the local standard deviation (Local-STD), which assessed the noise in the planes (robustness).

Binary Nonlinear Joint Transform Correlator with Sinusoidal Iterative Filter in Spectrum Domain

The joint transform correlator (JTC) has been the best known technique for pattern recognition and identification. This paper proposes a new technique of fringe adjustment by adopting a sinusoidal amplitude-modulated iterative filter convolved with an interference fringe pattern in the joint power spectrum (JPS) domain. The comparison of our new technique and other techniques is presented to show that the newly proposed technique can successfully improve both the correlation peaks and the peak signal-to-noise ratio (PSNR). Simulated results of enhanced interference fringes are also presented.

Analysis of Fingerprint Recognition Characteristics Based on New CGH Direct Comparison Method and Nonlinear Joint Transform Correlator

Fingerprint recognition using a joint transform correlator (JTC) is the most well-known technology among optical fingerprint recognition methods. The JTC method optically compares the reference fingerprint image with the sample fingerprint image then examines match or non-match by acquiring a correlation peak. In contrast to the JTC method, this paper presents a new method to examine fingerprint recognition by producing a computer generated hologram (CGH) of those two fingerprint images and directly comparing them. As a result, we present some parameters to show that fingerprint recognition capability of the CGH direct comparison method is superior to that of the JTC method.

Optodigital implementation of multiple information hiding and extraction system

A new optodigital multiple information hiding and real-time ex- traction system is suggested. In the proposed system, multiple informa- tion is hidden in a cover image by using stego keys, which are generated by combining use of a random sequence and Hadamard matrix. This hidden data is then extracted in real time by using an optical nonlinear joint transform correlator (NJTC)-based decoding system. In the experi- ment, 50, 30, and 20 combination sets of three letters selected from the English and Korean alphabets, and Arabic numerals are used as the multiple message data and they are formulated into 838 blocks, in which each block is composed of 64364 pixels and multiplied with the corre- sponding stego keys of 64364 pixels one by one. Then, by adding these modulated data to the cover image of Lena of 5123512 pixels, a stego image is generated. To extract the hidden data from this stego image in real time, an optical NJTC is employed, in which optical correlation be- tween the stego image and each of the stego keys is performed, and from these correlation outputs the hidden data can be extracted. Com- puter simulations and optical experiments reveal that the proposed opti- cal NJTC-based decoding system has a highly improved signal-to-noise ratio (SNR) performance of the correlation outputs under the condition of k,0.6, and these experimental results finally confirm the feasibility of the

광학적 상관관계를 기반으로 하는 지문인식 방법에 관한 연구

지문 인식은 보통 지문 영상의 획득과 획득된 지문 영상을 비교하는 단계로 구분해서 생각할 수 있다. 본 논문에서는 지문 영상을 획득하는 단계에서 지문 입력 센서를 사용하여 연구의 초점을 지문의 비교 방법에 맞추었다. 지문 입력 센서에서 는 지문 영상이 영상처리되어 출력되기 때문에 지문을 획득할 때 발생할 수 있는 잡음들에 대해서는 고려하지 않았고 사용자가 임의적으로 여러 번 지문을 입력하게 하여 회전과 이동이 복합적으로 존재하는 영상 왜곡을 고려하였다. 사용자의 지문 인식을 위한 방법으로 광학적 상관관계(Optical Correlation)를 출력하는 Non-linear Joint Transform Correlator(NRC)를 컴퓨터 상에서 구현하였고, 지문 입력 시에 발생할 수 있는 왜곡에 불변적인 특징을 갖도록 지문의 중심점을 찾는 알고리즘을 추가하여 지문 인식의 정확도를 보완하였다. 또한, 찾아진 지문 영상의 중심점을 가지고 100<TEX>$\times$</TEX>100픽셀 크기의 중심 영역만을 추출하여 지문 인식에 필요한 시간과 입력 영상의 정보를 줄이면서 높은 정확도를 갖는 매칭 기법을 제시하였다 Fingerprint recognition is concerned with fingerprint acquisition and matching. Our research was focused on a fingerprint matching method using an inkless fingerprint input sensor at the fingerprint acquisition step. Since an inkless fingerprint sensor produces a digital-image-processed fingerprint image, we did not consider noise that can happen while acquiring the fingerprint. And making the user attempt fingerprint input as random, we considered image distortion that translation and rotation are included as complex. NJTC algorithm is used for fingerprint identification and verification. The method to find the center of the fingerprint is added in the NJTC algorithm to supplement discrimination of fingerprint recognition. From this center point, we decided the optimum cropping size for effective matching with pixels and demonstrated that the proposed method has high discrimination and high efficiency.

Phase encoding the input scene of an optical correlator in the presence of nonoverlapping noise

We study the influence of phase encoding the input image of an optical correlator. We show that if the object to be located is perturbed by nonoverlapping noise, phase encoding can improve the correlation performance compared to amplitude encoding. We provide a phenomenological interpretation of this fact, taking into account the graylevel histograms of the target and of the noisy background. Using numerical simulations, we show that in some realistic situations, phase encoding can significantly improve the probability of correct location of a nonlinear joint-transform correlator (NLJTC).

Bayesian theory for target location in noise with unknown spectral density

A Bayesian approach adapted to practical detection and location tasks of a target in additive Gaussian noise with unknown spectral density is developed and studied. The relevance of this theory is first discussed in comparison with a maximum a posteriori solution that has been recently developed [J. Opt. Soc. Am. A15, 61 (1998)]. The analysis is first performed without considering a particular prior for the spectral density of the noise. General results of the Bayesian approach are thus provided as well as properties of its first-order development, which corresponds to the so-called nonlinear joint-transform correlation frequently used in optical correlators. It is demonstrated that the kernel of the nonlinear filtering is an increasing function of the sum of the spectral density of the reference object and of the input image. Furthermore, it is shown that a power-law mathematical form of the nonlinear filtering is directly related to assumptions on the asymptotic behavior of the prior density probabilities of the unknown spectral density of the noise. These properties constitute new theoretical results in the context of statistical theory concerning the use of nonlinearities in optical correlators.

Micro-displacement by Means of Optoelectronic Nonlinear Joint Transform Correlation of Speckle Pattern

Two objective speckle patterns are obtained—one before and one after the object has been moved—and are placed in the input plane of an optoelectronic nonlinear joint transform correlator.Nonlinear transformation of the joint power spectrum permits a sharper correlation peak and a high signal-to-noise ratio. The autocorrelation peak coordinates of the first pattern are set as a reference for measuring displacements of the cross-correlation peak, and also, the calibration of the measurement system is performed.It is well known that speckle can be regarded as a random spatial carrier in which information on the shape and position of the diffusing surface is encoded. The correlation of speckle patterns is highly appropriate for measuring displacements of tens of micrometers.1,2 In this work, an alternative technique based on the correlation between two speckle patterns by means of a digital bipolar joint transform correlator3 is presented. Initially the technique is described and then experimental results are shown.

Nonlinear joint transform correlator using one-dimensional Fourier transformation

We present a new method for processing the data in a nonlinear joint transform correlator (NJTC). The output of the NJTC is obtained after two steps. The first step consists of the acquisition of the joint power spectrum (JPS) of the images to be correlated. The JPS is in principle a bidimensional image. The second step is the calculation of the cross-correlation function. To do this, the JPS image is compressed to one dimension and a 1-D Fourier transform is performed. This significantly reduces the number of operations required to evaluate the crosscorrelation. To improve the cross-correlation sensitivity, a degree of nonlinearity is introduced using an illumination level above the saturation threshold of the camera used to acquire the JPS.

Decision theory approach to nonlinear joint-transform correlation

We propose a new decision theory approach adapted to practical target detection and location tasks in which the spectral density of Gaussian additive noise is unknown. We determine the maximum likelihood and the maximum a posteriori solutions for that problem. We demonstrate that the nonlinear joint-transform correlation, which is frequently used in optical correlators, can be considered an approximation of these optimal processors. This new result constitutes a theoretical support in the context of detection theory for the use of nonlinearities in optical correlators.

An improved photorefractive joint-transform correlator utilizing beam-fanning in a high-gain barium titanate crystal

A photorefractive nonlinear joint-transform correlator is demonstrated by utilizing the nonlinear intensity-dependent behavior of beam-fanning in a photorefractive barium titanate crystal. The results obtained reveal a narrowing of the correlation profile, and improved peak-to-side lobe ratio resulting in a better discrimination ability of the correlator. The compressional beam-fanning nonlinearity is modelled for a simulation study in order to give a comparison with the experimental observation.

Effects of saturation on the nonlinear incoherent-erasure joint-transform correlator

A photorefractive nonlinear joint-transform correlator based on the incoherent-to-coherent conversion is presented and analyzed. The nonlinearity of this incoherent-erasure joint-transform correlator (IEJTC) is tunable from the classical-matched to the phase-extraction limit. Correlation peak intensity, sharpness, and discrimination ability increase with the incoherent beam intensity. At easily achievable incoherent-to-coherent beam intensity ratios the IEJTC has its optimal performance, at which the IEJTC approaches the performance of the inverse filter for clean inputs and surpasses the inverse filter performance for noisy inputs. We examine this nonlinearity by using the transform method of analysis and computer simulations. Our study focuses on the effect of saturation on the correlation ability. Our results provide an explanation of why extending the severity of saturation by increasing the incoherent-to-coherent intensity ratio beyond a turning point results in lower optical efficiency, degraded correlation peak, and increased higher-order harmonics.

A BPEJTC-based segmentation for a non-stationary image

This paper presents a correlator-based segmentation algorithm applied to a non-stationary image. We show that in this algorithm, a moving target's signature residing in the image sequence can be extracted via monitoring the levels of correlation peaks between two adjacent images. We also present an electro-optical system to implement the algorithm. It is shown that the performance of this method depends to a great extent on the correlation results and thus the proposed system uses a non-linear JTC called BPEJTC that has a much higher peak-to-sidelobe ratio than a conventional JTC. Moreover, we show that this system effectively distributes the required computations over an optical unit and a digital unit to reduce the processing time, and the inclusion of optical processing enables the system to work well even for massive input data size. Experimental results obtained with a real image sequence are demonstrated.

Incoherent-erasure joint-transform correlator

We propose a nonlinear joint-transform correlator that is produced from the erasure of a real-time hologram by the joint-transform spectrum. Our analysis of this incoherent-erasure correlator with a four-wave-mixing readout arrangement indicates that the performance of this correlator exceeds that of the phase-only correlator.

Photorefractive two-beam-coupling nonlinear joint-transform correlator

An all-optical nonlinear joint-transform correlator that is based on a square-law receiver has been implemented for the first time to our knowledge without the use of a spatial light modulator and digital processing in the Fourier plane. The correlator uses energy transfer from two-beam coupling in the Fourier plane. We implement compressional nonlinearity in the hard-clipped regime by pumping a weak plane wave with the intense joint spectrum of the reference and the signal images. Operation of this device rivals or exceeds that of the phase-only filter for detecting objects in cluttered noise. Experimental results are compared with both plane-wave and beam-propagation simulations.

Theoretical analysis for the nonlinear frequency-selective joint-transform correlator

The theoretical analysis for a nonlinear and bipolar frequency-selective joint-transform correlator is reported without any impractical assumptions and verifield. The theoretical results are similar to those for a nonlinear and bipolar joint-transform correlator. In addition, the optimal threshold value for a bipolar frequency-selective joint-transform correlator is found to be zero. Moreover, a bipolar frequency-selective joint-transform correlator can provide a phase-only correlation signal with delta-function shape. The theoretical study for a DC-block bipolar frequency-selective joint-transform correlator is also given. It is shown that its autocorrelation peak remains the same as that without a DC block.

Characterization of an Optimized Nonlinear Joint Transform Correlator

Characterization of an Optimized Nonlinear Joint Transform Correlator