The core component of most modern trackers is a discriminative classifier, tasked with distinguishing between the target and the surrounding environment. To cope with natural image changes, this classifier is typically trained with translated and scaled sample patches. Such sets of samples are riddled with redundancies—any overlapping pixels are constrained to be the same. Based on this simple observation, we propose an analytic model for datasets of thousands of translated patches. By showing that the resulting data matrix is circulant, we can diagonalize it with the discrete Fourier transform, reducing both storage and computation by several orders of magnitude. Interestingly, for linear regression our formulation is equivalent to a correlation filter, used by some of the fastest competitive trackers. For kernel regression, however, we derive a new kernelized correlation filter (KCF), that unlike other kernel algorithms has the exact same complexity as its linear counterpart. Building on it, we also propose a fast multi-channel extension of linear correlation filters, via a linear kernel, which we call dual correlation filter (DCF). Both KCF and DCF outperform top-ranking trackers such as Struck or TLD on a 50 videos benchmark, despite running at hundreds of frames-per-second, and being implemented in a few lines of code (Algorithm 1). To encourage further developments, our tracking framework was made open-source.

High-Speed Tracking with Kernelized Correlation Filters

In this article, the authors present a new approach to building simpler, smaller, and cheaper digital cameras that can operate efficiently across a broader spectral range than conventional silicon-based cameras. The approach fuses a new camera architecture based on a digital micromirror device with the new mathematical theory and algorithms of compressive sampling.

/pdf/single-pixel-imaging-via-compressive-sampling-17xma709hr.pdf

Single-Pixel Imaging via Compressive Sampling

Although not commonly used, correlation filters can track complex objects through rotations, occlusions and other distractions at over 20 times the rate of current state-of-the-art techniques. The oldest and simplest correlation filters use simple templates and generally fail when applied to tracking. More modern approaches such as ASEF and UMACE perform better, but their training needs are poorly suited to tracking. Visual tracking requires robust filters to be trained from a single frame and dynamically adapted as the appearance of the target object changes. This paper presents a new type of correlation filter, a Minimum Output Sum of Squared Error (MOSSE) filter, which produces stable correlation filters when initialized using a single frame. A tracker based upon MOSSE filters is robust to variations in lighting, scale, pose, and nonrigid deformations while operating at 669 frames per second. Occlusion is detected based upon the peak-to-sidelobe ratio, which enables the tracker to pause and resume where it left off when the object reappears.

/pdf/visual-object-tracking-using-adaptive-correlation-filters-1xuhtpe358.pdf

Visual object tracking using adaptive correlation filters

Digital watermarking is a key ingredient to copyright protection. It provides a solution to illegal copying of digital material and has many other useful applications such as broadcast monitoring and the recording of electronic transactions. Now, for the first time, there is a book that focuses exclusively on this exciting technology. Digital Watermarking covers the crucial research findings in the field: it explains the principles underlying digital watermarking technologies, describes the requirements that have given rise to them, and discusses the diverse ends to which these technologies are being applied. As a result, additional groundwork is laid for future developments in this field, helping the reader understand and anticipate new approaches and applications.

Digital Watermarking

In this paper, we review most major filtering approaches to texture feature extraction and perform a comparative study. Filtering approaches included are Laws masks (1980), ring/wedge filters, dyadic Gabor filter banks, wavelet transforms, wavelet packets and wavelet frames, quadrature mirror filters, discrete cosine transform, eigenfilters, optimized Gabor filters, linear predictors, and optimized finite impulse response filters. The features are computed as the local energy of the filter responses. The effect of the filtering is highlighted, keeping the local energy function and the classification algorithm identical for most approaches. For reference, comparisons with two classical nonfiltering approaches, co-occurrence (statistical) and autoregressive (model based) features, are given. We present a ranking of the tested approaches based on extensive experiments.

Filtering for texture classification: a comparative study

The synthesis of a new category of spatial filters that produces sharp output correlation peaks with controlled peak values is considered. The sharp nature of the correlation peak is the major feature emphasized, since it facilitates target detection. Since these filters minimize the average correlation plane energy as the first step in filter synthesis, we refer to them as minimum average correlation energy filters. Experimental laboratory results from optical implementation of the filters are also presented and discussed.

Minimum average correlation energy filters

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.

Unconstrained correlation filters

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 The design, analysis and use of correlation pattern recognition algorithms requires background information, including linear systems theory, random variables and processes, matrix/vector methods, detection and estimation theory, digital signal processing and optical processing This 2005 book provides a needed review of this diverse background material and develops the signal processing theory, the pattern recognition metrics, and the practical application know-how from basic premises It shows both digital and optical implementations It also contains technology presented by the team that developed it and includes case studies of significant interest, such as face and fingerprint recognition Suitable for graduate students taking courses in pattern recognition theory, whilst reaching technical levels of interest to the professional practitioner

/pdf/correlation-pattern-recognition-1t3ibzhxl2.pdf

Correlation Pattern Recognition

A new correlation-filter design methodology is presented for achieving two objectives: synthetic discriminant function filters that can be implemented on arbitrary various criteria of interest. devices and that can provide optimal trade-off among various criteria of interest.

Optimal trade-off synthetic discriminant function filters for arbitrary devices

Anomaly localization is an important problem in computer vision which involves localizing anomalous regions within images with applications in industrial inspection, surveillance, and medical imaging. This task is challenging due to the small sample size and pixel coverage of the anomaly in real-world scenarios. Most prior works need to use anomalous training images to compute a class-specific threshold to localize anomalies. Without the need of anomalous training images, we propose Convolutional Adversarial Variational autoencoder with Guided Attention (CAVGA), which localizes the anomaly with a convolutional latent variable to preserve the spatial information. In the unsupervised setting, we propose an attention expansion loss where we encourage CAVGA to focus on all normal regions in the image. Furthermore, in the weakly-supervised setting we propose a complementary guided attention loss, where we encourage the attention map to focus on all normal regions while minimizing the attention map corresponding to anomalous regions in the image. CAVGA outperforms the state-of-the-art (SOTA) anomaly localization methods on MVTec Anomaly Detection (MVTAD), modified ShanghaiTech Campus (mSTC) and Large-scale Attention based Glaucoma (LAG) datasets in the unsupervised setting and when using only 2% anomalous images in the weakly-supervised setting. CAVGA also outperforms SOTA anomaly detection methods on the MNIST, CIFAR-10, Fashion-MNIST, MVTAD, mSTC and LAG datasets.

Abhijit Mahalanobis

Papers

Minimum average correlation energy filters

Unconstrained correlation filters

Correlation Pattern Recognition

Optimal trade-off synthetic discriminant function filters for arbitrary devices

Attention Guided Anomaly Localization in Images