Correlation Pattern Recognition

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Signal Processing Series. Theory and Application of Digital Signal Processing. The Econometrics of Financial Markets. NJ: Princeton University Press. Cambridge University Press. University of Pittsburgh, Master's Thesis. Outline Index. Descriptive statistics. Mean arithmetic geometric harmonic Median Mode.

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Central limit theorem Moments Skewness Kurtosis L-moments. Index of dispersion. Grouped data Frequency distribution Contingency table. Pearson product-moment correlation Rank correlation Spearman's rho Kendall's tau Partial correlation Scatter plot. Data collection.

Sampling stratified cluster Standard error Opinion poll Questionnaire. Scientific control Randomized experiment Randomized controlled trial Random assignment Blocking Interaction Factorial experiment. Adaptive clinical trial Up-and-Down Designs Stochastic approximation. Cross-sectional study Cohort study Natural experiment Quasi-experiment.

Statistical inference. Z -test normal Student's t -test F -test. Bayesian probability prior posterior Credible interval Bayes factor Bayesian estimator Maximum posterior estimator. Correlation Regression analysis. Pearson product-moment Partial correlation Confounding variable Coefficient of determination. Simple linear regression Ordinary least squares General linear model Bayesian regression.

Regression Manova Principal components Canonical correlation Discriminant analysis Cluster analysis Classification Structural equation model Factor analysis Multivariate distributions Elliptical distributions Normal. CPR owes its origins to the pioneering work of VanderLugt, 2 who showed how correlations between two images can be computed using coherent optical systems employing holographically-prepared complex masks in the frequency plane.

Pattern recognition

Another important development in this field 3 was the ability to create correlation filters that can represent multiple distortions e. Another major difference from the early work is that we now do correlations in digital hardware due to the high speed with which 2D fast Fourier transforms FFT can be implemented. Figure 1 schematically describes the use of CPR for face verification. During enrollment, a few face images of the authentic user are acquired. The 2D FTs of these images are then used to generate a 2D filter.

This filter array is stored perhaps on a smart card to identify that authentic user. When this authentic user presents his face image during verification, the 2D FFT of his live face image is multiplied pixel-wise by the stored filter array and the resulting product array is input to a 2D inverse FFT to produce a correlation output array. As illustrated in Figure 1 , the correlation output exhibits a sharp peak for the authentic user and no such discernible correlation peak for an impostor.

CPR offers other advantages as shown in Figure 2.

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In this example, the filter was designed using three training images representing the face of the subject with illumination-shadow in the left half, in the right half and no shadow of one subject retrieved from the well-known Carnegie Mellon University PIE pose, illumination and expression face database. The shifting of the image also shifted the correlation peak to a new position Figure 2 , bottom right , a result of the shift-invariance of the filter, but without affecting peak sharpness and thus the verification performance.

In contrast, many image-based algorithms fail completely when the live face image has one of the eyes closed or obscured, since they use the eye centers as a starting point to normalize the image.

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Face recognition is gaining increased importance. While this short summary focused on face recognition, CPR is proving equally applicable for other image biometrics. Sign In View Cart 0 Help.

News Menu. Vijayakumar Bhagavatula, Marios Savvides. Schematic of the use of correlation pattern recognition for biometrics. Left: Centered and full test image top and resulting correlation output bottom. Right: Shifted and partially occluded test image top and resulting correlation output bottom.

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  1. Cross-correlation.
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  6. You have no items in your shopping cart. Correlation Pattern Recognition. Add to cart Buy now. Sign in to add to Wish List. Details Author: Kumar, B. Correlation is a robust and general technique for pattern recognition and is used in many applications, such as automatic target recognition, biometric recognition and optical character recognition.

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    Correlation Pattern Recognition Correlation Pattern Recognition
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