Unconstrained correlation filters

Abstract

A mathematical analysis of the distortion tolerance in correlation filters is presented. A good measure for distortion performance is shown to be a generalization of the minimum average correlation energy criterion. To optimize the filter's performance, we remove the usual hard constraints on the outputs in the synthetic discriminant function formulation. The resulting filters exhibit superior distortion tolerance while retaining the attractive features of their predecessors such as the minimum average correlation energy filter and the minimum variance synthetic discriminant function filter. The proposed theory also unifies several existing approaches and examines the relationship between different formulations. The proposed filter design algorithm requires only simple statistical parameters and the inversion of diagonal matrices, which makes it attractive from a computational standpoint. Several properties of these filters are discussed with illustrative examples.

Learning Detectors Quickly with Stationary Statistics

“…The algorithm of correlation filters [10] in its unconstrained form [11] is simply linear least-squares regression applied to the set of all circular shifts of every example. While including circular shifts in the training set may seem peculiar, it leads to a system of equations which can be constructed and solved in the Fourier domain.…”

“…Adopting this assumption within an LDA framework, comparable detection performance to HNM has been demonstrated [9]. The second method is that of correlation filters [10,11], in which all circular shifts of each example are incorporated into the training set (see Figure 2). This manifests in a covariance matrix which is not only Toeplitz, but circulant…”

Human tracking with multiple parallel metrics

“…This is known as a composite filter. There are a number different designs but we have incorporated the optimum trade off maximum average correlation height (OT-MACH) filter [15] due to its known performance. The filter works by attempting maximise the average correlation height (ACH) for all the templates.…”

<title>Standards-compatible compression for automated image recognition in sensor networks and surveillance systems</title>

“…The classical matched spatial filter (MSF) 1 is often not adequate for practical pattern recognition since its performance degrades rapidly when the reference object is distorted. Therefore, many improvements in correlation filters in the frequency domain [2][3][4][5] , and pre- [6][7][8] and post- [9][10][11] processing techniques in the spatial domain have been explored. Most of them involve the design of filters tolerable to various distortions such as noise, scale change, rotation and illumination.…”