Peak-to-correlation Energy Research Articles

Three-Dimensional Image Visualization under Photon-Starved Conditions Using N Observations and Statistical Estimation.

In this paper, we propose a method for the three-dimensional (3D) image visualization of objects under photon-starved conditions using multiple observations and statistical estimation. To visualize 3D objects under these conditions, photon counting integral imaging was used, which can extract photons from 3D objects using the Poisson random process. However, this process may not reconstruct 3D images under severely photon-starved conditions due to a lack of photons. Therefore, to solve this problem, in this paper, we propose N-observation photon-counting integral imaging with statistical estimation. Since photons are extracted randomly using the Poisson distribution, increasing the samples of photons can improve the accuracy of photon extraction. In addition, by using a statistical estimation method, such as maximum likelihood estimation, 3D images can be reconstructed. To prove our proposed method, we implemented the optical experiment and calculated its performance metrics, which included the peak signal-to-noise ratio (PSNR), structural similarity (SSIM), peak-to-correlation energy (PCE), and the peak sidelobe ratio (PSR).

Signal detection in turbid water using temporally encoded polarimetric integral imaging.

To improve signal detection in a turbid medium, we propose temporally encoded single shot polarimetric integral imaging. An optical signal is temporally encoded using gold coded sequences and transmitted through a turbid medium. The encoded signals are captured as a sequence of elemental images by two orthogonal polarized image sensor arrays. Polarimetric and polarization difference imaging are used to suppress the partially polarized and unpolarized background noise such that only the polarized ballistic signal photons are captured at the sensor. Multidimensional integral imaging is used to obtain 4D reconstructed data, and multidimensional nonlinear correlation is performed on the reconstructed data to detect the optical signal. We compare the effectiveness of the proposed polarimetric underwater optical signal detection approach to conventional (non-polarimetric) integral imaging-based and 2D imaging-based signal detection systems. The underwater signal detection capabilities are measured through performance metrics such as receiver operating characteristic (ROC) curves, the area under the curve (AUC), and the number of detection errors. Furthermore, statistical measures, including the Kullback-Leibler divergence, signal-to-noise ratio (SNR), and peak-to-correlation energy (PCE), are also calculated to show the improved performance of the proposed system. Our experimental results show that the proposed polarimetric integral-imaging approach significantly outperforms the conventional imaging-based methods. To the best of our knowledge, this is the first report on temporally encoded single shot polarimetric integral imaging for signal detection in turbid water.

Optical correlation assists to enhance underwater polarization imaging performance

Polarization imaging is a promising technology with great potential. Besides light intensity, it provides information in another dimension, polarization. When imaging through water, two frames of the target at two orthogonally polarized states, Imax and Imin, are needed. In most experiments, they are determined by searching for the darkest and brightest moments during polarizer rotation. But in cases where no noticeable difference can be observed, the final detection may fail. To cope with this problem, this study exploits optical correlation to assist to determine the optimal image pair. It provides reference information by comparing the similarity between two images and quantify it with parameter PCE (Peak-to-correlation energy). Final determination is based upon the fact that the optimal image pair should be in the least similarity. Experiments demonstrate that the location of optimal images can be accurately indicated through the method. Final recovery with the selected images presents the best contrast and image quality. The established strategy will enhance performance of underwater polarization imaging with better vision, higher resolution and accuracy.

Fractional Fourier Transform for Digital Image Recognition

In the image recognition field, there are several techniques that allow identifying patterns in digital images, correlation being one of them. In a correlation, you have to obtain an output plane that is as clean as possible. To measure the sharpness of the correlation peak and the cleanliness of the output plane, a performance metric called Peak to Correlation Energy (PCE) is used. In this paper, the fractional correlation is applied to recognize real phytoplankton images. This fractional correlation guarantees a higher PCE compared to the conventional correlation. The results of PCE are two-orders of magnitude higher than those obtained with the conventional correlation and manage to identify 91.23% of the images, while the conventional correlation only manages to identify 87.42% of them. This methodology was tested using images in salt and pepper or Gaussian noise, and the fractional correlation output plane always is cleaner and generates a better-defined correlation peak when compared with the classical correlation.

Efficient Correlation Tracking via Center-Biased Spatial Regularization.

Correlation filters (CFs) have been applied to visual tracking with success providing excellent performance in terms of accuracy and efficiency. The underlying periodic assumption of the training samples results in their great efficiency when using the fast Fourier transform (FFT), yet it also brings unwanted boundary effects. To address this issue, the recently proposed spatially-regularized discriminative CF (SRDCF) method introduces a Gaussian weight function to regularize the learning filter, yielding favorable performances in accuracy but high computational complexity because the objective of the SRDCF cannot achieve a closed solution via the FFT. Motivated by SRDCF, we present an efficient and effective CF-based tracker using center-biased constraint weights (CBCWs), which improve simultaneously speed and accuracy. Specifically, we first construct a CBCW function by exploiting the symmetry of the Fourier transform. The values of the constraint weights are real in both time and frequency domains, so that the optimization can be directly solved in the frequency domain without any data transformation, thereby greatly reducing its computational complexity. Moreover, according to the average peak-tocorrelation energy value of the CF response, we propose an efficient and effective filter update strategy to handle occlusions during tracking. Extensive experiments on the OTB-2013, OTB- 2015, and VOT2016 benchmarks demonstrate that the proposed tracker significantly outperforms the baseline SRDCF in terms of accuracy and efficiency. Moreover, the proposed method performs favorably against 16 other representative state-of-the-art methods regarding robustness and success rate.

A local variance based approach to alleviate the scene content interference for source camera identification

Identifying the source camera of images is becoming increasingly important nowadays. A popular approach is to use a type of pattern noise called photo-response non-uniformity (PRNU). The noise of image contains the patterns which can be used as a fingerprint. Despite that, the PRNU-based approach is sensitive towards scene content and image intensity. The identification is poor in areas having low or saturated intensity, or in areas with complicated texture. The reliability of different regions is difficult to model in that it depends on the interaction of scene content and the characteristics of the denoising filter used to extract the noise. In this paper, we showed that the local variance of the noise residual can measure the reliability of the pixel for PRNU-based source camera identification. Hence, we proposed to use local variance to characterize the severeness of the scene content artifacts. The local variance is then incorporated to the general matched filter and peak to correlation energy (PCE) detector to provide an optimal framework for signal detection. The proposed method is tested against several state-of-art methods. The experimental results show that the local variance based approach outperformed other state-of-the-art methods in terms of identification accuracy.

A comprehensive statistical investigation of schlieren image velocimetry (SIV) using high-velocity helium jet

A detailed statistical assessment of seedless velocity measurement using Schlieren Image Velocimetry (SIV) was explored using open source Robust Phase Correlation (RPC) algorithm. A well-known flow field, an axisymmetric turbulent helium jet, was analyzed near and intermediate region $$(0\le x/d\le 20)$$ for two different Reynolds numbers, Re d = 11,000 and Re d = 22,000 using schlieren with horizontal knife-edge, schlieren with vertical knife-edge and shadowgraph technique, and the resulted velocity fields from SIV techniques were compared to traditional Particle Image Velocimetry (PIV) measurements. A novel, inexpensive, easy to setup two-camera SIV technique had been demonstrated to measure high-velocity turbulent jet, with jet exit velocities 304 m/s (Mach = 0.3) and 611 m/s (Mach = 0.6), respectively. Several image restoration and enhancement techniques were tested to improve signal to noise ratio (SNR) in schlieren and shadowgraph images. Processing and post-processing parameters for SIV techniques were examined in detail. A quantitative comparison between self-seeded SIV techniques and traditional PIV had been made using correlation statistics. While the resulted flow field from schlieren with horizontal knife-edge and shadowgraph showed excellent agreement with PIV measurements, schlieren with vertical knife-edge performed poorly. The performance of spatial cross-correlations at different jet locations using SIV techniques and PIV was evaluated. Turbulence quantities like turbulence intensity, mean velocity fields, Reynolds shear stress influenced spatial correlations and correlation plane SNR heavily. Several performance metrics such as primary peak ratio (PPR), peak to correlation energy (PCE), the probability distribution of signal and noise were used to compare capability and potential of different SIV techniques.

Designing a composite correlation filter based on iterative optimization of training images for distortion invariant face recognition

We present a novel method to optimize the discrimination ability and noise robustness of composite filters. This method is based on the iterative preprocessing of training images which can extract boundary and detailed feature information of authentic training faces, thereby improving the peak-to-correlation energy (PCE) ratio of authentic faces and to be immune to intra-class variance and noise interference. By adding the training images directly, one can obtain a composite template with high discrimination ability and robustness for face recognition task. The proposed composite correlation filter does not involve any complicated mathematical analysis and computation which are often required in the design of correlation algorithms. Simulation tests have been conducted to check the effectiveness and feasibility of our proposal. Moreover, to assess robustness of composite filters using receiver operating characteristic (ROC) curves, we devise a new method to count the true positive and false positive rates for which the difference between PCE and threshold is involved.

Phase-only Wavelet Matched Filtering for Two- Dimensional Image Recognition and Classification

Objectives: The adaptability of the Wavelet Matched Filtering which uses wavelets along with Fourier transforms is applied for the recognition and classification of two-dimensional objects. In image processing and pattern recognition, phase information is very relevant as it contains the features of the visual scene. Methods/Statistical Analysis: The paper describes the design for the phase-only wavelet matched filtering. The performance of the phase-only wavelet matched filter is compared with that of wavelet matched filter, the classical Matched Filter and the Phase-only Matched Filter for classifying four objects in a 2D scene. The comparison is done using the MATLAB simulation tool. Findings: Two metrics - the Peak to Correlation Energy (PCE) and the Discrimination Ratio (DR), were used to study the performance of Phase-only Wavelet Matched Filtering (PWMF), Wavelet Matched Filtering (WMF), Phase-only Matched Filtering (PMF) and classical Matched Filtering (MF). It is found that the Phase-only Wavelet Matched Filtering (PWMF) gives better discrimination capability and the proof of the concept is demonstrated here. Applications: The method finds its application in pattern or object recognition and classification.

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).

Decision optimization for face recognition based on an alternate correlation plane quantification metric

We consider a new approach for enhancing the discrimination performance of the VanderLugt correlator. Instead of trying to optimize the correlation filter, or propose a new decision correlation peak detection criterion, we propose herein to denoise the correlation plane before applying the peak-to-correlation energy (PCE) criterion. For that purpose, we use a linear functional model to express a given correlation plane as a linear combination of the correlation peak, noise, and residual components. The correlation peak is modeled using an orthonormalized function and the singular value decomposition method. A set of training correlation planes is then selected to create the correlation noise components. Finally, an optimized correlation plane is reconstructed while discarding the noise components. Independently of the filter correlation used, this technique denoises the correlation plane by lowering the correlation noise magnitude in case of true correlation and decreases the false alarm rate when the target image does not belong to the desired class. Test results are presented, using a composite filter and a face recognition application, to verify the effectiveness of the proposed technique.

Enhancing Source Camera Identification Performance With a Camera Reference Phase Sensor Pattern Noise

Sensor pattern noise (SPN) extracted from digital images has been proved to be a unique fingerprint of digital cameras. However, SPN can be contaminated largely in the frequency domain by image content and nonunique artefacts of JPEG compression, on-sensor signal transfer, sensor design, color interpolation. The source camera identification (CI) performance based on SPN needs to be improved for small sizes of images and especially in resisting JPEG compression. Because the SPN is modelled as an additive white Gaussian noise (AWGN) in its extraction process from an image, it is reasonable to assume the camera reference SPN to be a white noise signal in order to remove the interference mentioned above. The noise residues (SPN) extracted from the original images are whitened first, then they are averaged to generate the camera reference SPN. Motivated by Goljan 's test statistic peak to correlation energy (PCE), we propose to use correlation to circular correlation norm (CCN) as the test statistic, which can lower the false positive rate to be a half of that with PCE. Theoretical analysis shows that the proposed CI method can remove the interference and raise the CCN value of a positive sample and thus achieve greater CI performance, CCN values of the negative sample class with the proposed method follow the normal distribution <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> (0,1) and the false positive rate can be calculated. Compared with the existing state of the art on seven cameras, 1400 photos totally (200 for each camera), the experimental results show that the proposed CI method achieves the best receiver operating characteristic (ROC) performance among all CI methods in all cases and especially achieves much better resistance to JPEG compression than all of the existing state-of-the-art CI methods.

New spectral image compression method based on an optimal phase coding and the RMSduration principle

By using only phase information, this paper describes a new spectral lossy compressionmethod which can: reduce required memories; adaptively retrieve original images by usingonly spectral phase information; increase the peak-to-correlation energy (PCE) at theoutput of the correlator; and be easily employed in major encryption techniques. Toincrease the compression ratio of the proposed method, an optimal phase codingbased on ‘a fading grid’ is performed. In fact, a variable number of quantizationbits has been used to quantize phase information depending on the importanceof the spectral phases. The phase information could be classified according tothe concept of ‘RMS duration’. Many simulations have been carried out. Ourexperimental results corroborate the performance of the proposed new method.

Comparative analysis between different font types and letter styles using a nonlinear invariant digital correlation

We present, in this paper, a comparative analysis of the letters in Times New Roman (TNR), Courier New (CN) and Arial (Ar) font types in plain and italic style and the effects of five foreground/background color combinations using an invariant digital correlation system with a nonlinear filter with k = 0.3. The evaluation of the output plane with this filter is given by the peak-to-correlation energy (PCE) metric. The results show that the letters in TNR font have a better mean PCE value when compared with the CN and Ar fonts. This result is in agreement with some studies on text legibility and for readability where the reaction time (RT) of some participant individuals reading a text is measured. We conclude that the PCE metric is proportional to 1/RT.

Non-zero order joint transform correlator with multi-level quantized reference function

A novel method for optical pattern recognition based on the multi-level quantized reference function (MQRF) is presented. The reference function with finite levels is a spatial domain filter, which can be used in the input of a non-zero order joint transform correlator (NOJTC). It is suitable to the current spatial light modulator (SLM). The system has distortion tolerant capability. The desired correlation outputs indicate the success of the technique. In this paper, we have shown that the measurement criteria including peak to correlation energy (PCE), peak to sidelobe ratio (PSR), and discrimination ratio (DR) meliorate as the quantization level increases.

Improved cross-correlation for template matching on the Laplacian pyramid

Template matching 1 1 Following Duda and Hart (1973), we use template matching to describe a technique used in order to decide if a previously specified template is present in an image. Cross-correlation is adopted here as a measure of similarity between template and a region of the image edge maps. via cross-correlation on Laplacian pyramid image architectures has been traditionally performed in a “coarse” to “fine” fashion. In the present paper, we show that by computing cross-correlation within each level of the pyramid independently, and considering the sum across (expanded) levels, a significant improvement in Peak to Correlation Energy (PCE) ( Kumar and Hassebrook, 1992) is obtained. This result is illustrated with a number of numerical examples.