Analysis of kernel distortion-invariant filters

Abstract

Kernel techniques have been used in support vector machines (SVMs), feature spaces, etc. In kernel methods, the wellknown kernel trick is used to implicitly map the input data to a higher-dimensional feature space. If all terms can be written as a kernel function, one can then use data in higher-dimensional space without actually computing the higherdimensional features or knowing the mapping function Φ. In this paper, we address kernel distortion-invariant filters (DIFs). Standard DIFs are synthesized in a linear feature space (in the image or Fourier domain). They are fast since they use FFT-based correlations. If the data is mapped to a higher-dimensional feature space before filter synthesis and before performing correlations, kernel filters result and performance can be improved. Kernel versions of several DIFs (OTF, SDF, and Mace) have been presented in prior work. However, several key issues were ignored in all prior work. These include : the unrealistic assumption of centered data in tests, the significantly larger storage and on-line computation time required, and the proper type of energy minimization in filter synthesis to reduce false peaks is necessary when the filters are applied to target scenes and has yet to be done. In addition, prior kernel DIF work used test set data to select the value of the kernel parameter. In this paper, we analyze these issues, present supporting test results on two face databases, and present several improvements to prior kernel DIF work.

High-Speed Tracking with Kernelized Correlation Filters

“…A few studies go in that direction, and attempt to apply kernel methods to correlation filters [24], [25], [26], [27]. In these works, a distinction must be drawn between two types of objective functions: those that do not consider the power spectrum or image translations, such as Synthetic Discriminant Function (SDF) filters [25], [26], and those that do, such as Minimum Average Correlation Energy [28], Optimal Trade-Off [27] and Minimum Output Sum of Squared Error (MOSSE) filters [9].…”

“…Since the spatial structure can effectively be ignored, the former are easier to kernelize, and Kernel SDF filters have been proposed [26], [27], [25]. However, lacking a clearer relationship between translated images, non-linear kernels and the Fourier domain, applying the kernel trick to other filters has proven much more difficult [25], [24], with some proposals requiring significantly higher computation times and imposing strong limits on the number of image shifts that can be considered [24].…”

A Novel Image Fusion Scheme using Wavelet Transform for Concealed Weapon Detection

“…Another challenge is to track a person in a cluttered and dynamic background. The techniques employed for tracking can be classified in three groups: filtering techniques, statistical models, and multi-agents systems [13]- [14]. Filtering techniques such as Kalman filtering have been successfully employed in surveillance systems.…”

“…Wavelet transform includes various frequency subbands. In [14], the authors introduced Multi-sensor image fusion utilizing empirical wavelet transform, showing high performance through experimentation of images came from different sensors. Normalized convolution framework through a multi-frame super resolution of digitized videos is introduced in [16].…”

An Experimental Survey on Correlation Filter-based Tracking

“…There have already been some studies [36]- [38] to apply kernel methods in correlation filters. According to [36], [37], it has been found that filters which do not use the power spectrum or image translations are easier to be kernelized. Different from these studies, Henriques et al [16], [20] proposed that correlation filters can be effectively kernelized with the introduction of Ridge Regression problem and circulant matrix.…”