Performance measures for correlation filters

Abstract

Several performance criteria are described to enable a fair comparison among the various correlation filter designs: signal-to-noise ratio, peak sharpness, peak location, light efficiency, discriminability, and distortion invariance. The trade-offs resulting between some of these criteria are illustrated with the help of a new family of filters called fractional power filters (FPFs). The classical matched filter, phase-only filter (POF), and inverse filter are special cases of FPFs. Using examples, we show that the POF appears to provide a good compromise between noise tolerance and peak sharpness.

Secure image encryption and authentication using the photon counting technique in the Gyrator domain

“…The authentication system is based on a nonlinear correlation technique [2,3]; in this system the decrypted image is compared with the original image to verify its authenticity. We show that the peak-to-correlation energy (PCE) [11] is improved for certain values of the rotation angle of the Gyrator transform (GT) and the nonlinearity applied in the correlation technique, in comparison with the previous results of the PCE for the integration of the PhTC with the DRPE in the Fourier domain (FD). This improvement over the PCE metric allows a better verification capability for the authentication system.…”

Invariant Nonlinear Correlations via Fourier Transform

“…I f we c on s i de r t h a t a n ob j e c t i s e m b e dde d i n a n oi s e b a c k gr ou n d, t h e di s c r i m i n a t i on coefficient that is a modified version of the discrimination ratio (Vijaya & Hassebrook, 1990) is given by…”

“…We use the scale transform and the k-th law nonlinear filter (Vijaya Kumar & Hassebrook, 1990) with a nonlinearity strength factor of k=0.3 (Coronel-Beltrán & Álvarez-Borrego, 2008). A kth law nonlinear filter is introduced to realize the digital invariant correlation that gives us information on the similarity between different objects.…”

Advances in Adaptive Composite Filters for Object Recognition

“…Negative values of DC indicate that the filter is unable to recognize any target. Note that other discrimination metrics can be used in the training procedure; for instance, the peak to correlation energy (PCE) (Vijaya-Kumar & Hassebrook, 1990) and the peak to sidelobe (PSR) ratio (Kerekes & Vijaya-Kumar, 2008). To measure the DC of the filter we carry out the correlation process between h sd f and a synthetic image of the background with similar statistical properties to those of the real background, then we calculate the DC using Eq.…”

“…An advantage of correlation filtering is that it possesses a strong mathematical foundation. Moreover, the design process of correlation filters usually considers the optimization of various performance criteria (Vijaya-Kumar & Hassebrook, 1990). As result, correlation filters have been used to develop reliable object recognition systems that exhibit robust performance even when used in highly noisy conditions (Javidi & Hormer, 1994;Javidi & Wang, 1997;Javidi et al, 1996).…”