Pedro Martins

Bio: Pedro Martins is an academic researcher from University of Coimbra. The author has contributed to research in topics: Active appearance model & Point distribution model. The author has an hindex of 14, co-authored 32 publications receiving 6159 citations.

High-Speed Tracking with Kernelized Correlation Filters

Abstract: 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.

Exploiting the circulant structure of tracking-by-detection with kernels

Abstract: Recent years have seen greater interest in the use of discriminative classifiers in tracking systems, owing to their success in object detection. They are trained online with samples collected during tracking. Unfortunately, the potentially large number of samples becomes a computational burden, which directly conflicts with real-time requirements. On the other hand, limiting the samples may sacrifice performance. Interestingly, we observed that, as we add more and more samples, the problem acquires circulant structure. Using the well-established theory of Circulant matrices, we provide a link to Fourier analysis that opens up the possibility of extremely fast learning and detection with the Fast Fourier Transform. This can be done in the dual space of kernel machines as fast as with linear classifiers. We derive closed-form solutions for training and detection with several types of kernels, including the popular Gaussian and polynomial kernels. The resulting tracker achieves performance competitive with the state-of-the-art, can be implemented with only a few lines of code and runs at hundreds of frames-per-second. MATLAB code is provided in the paper (see Algorithm 1).

Beyond the shortest path: Unsupervised domain adaptation by Sampling Subspaces along the Spline Flow

Abstract: Recently, a particular paradigm [18] in the domain adaptation field has received considerable attention by introducing novel and important insights to the problem. In this case, the source and target domains are represented in the form of subspaces, which are treated as points on the Grassmann manifold. The geodesic curve between them is sampled to obtain intermediate points. Then a classifier is learnt using the projections of the data onto these subspaces. Despite its relevance and popularity, this paradigm [18] contains some limitations. Firstly, in real-world applications, that simple curve (i.e. shortest path) does not provide the necessary flexibility to model the domain shift between the training and testing data sets. Secondly, by using the geodesic curve, we are restricted to only one source domain, which does not allow to take fully advantage of the multiple datasets that are available nowadays. It is then, natural to ask whether this popular concept could be extended to deal with more complex curves and to integrate multi-sources domains. This is a hard problem considering the Riemannian structure of the space, but we propose a mathematically well-founded idea that enables us to solve it. We exploit the geometric insight of rolling maps [30] to compute a spline curve on the Grassmann manifold. The benefits of the proposed idea are demonstrated through several empirical studies on standard datasets. This novel concept allows to explicitly integrate multi-source domains while the previous one [18] uses the mean of all sources. This enables to model better the domain shift and take fully advantage of the training datasets.

A nonparametric Riemannian framework on tensor field with application to foreground segmentation

Abstract: Background modelling on tensor field has recently been proposed for foreground detection tasks. Taking into account the Riemannian structure of the tensor manifold, recent research has focused on developing parametric methods on the tensor domain e.g. gaussians mixtures (GMM) [7]. However, in some scenarios, simple parametric models do not accurately explain the physical processes. Kernel density estimators (KDE) have been successful to model, on Euclidean sample spaces the nonparametric nature of complex, time varying, and non-static backgrounds [8]. Founded on the mathematically rigorous KDE paradigm on general Riemannian manifolds [15], we define a KDE specifically to operate on the tensor manifold. We present a mathematically-sound framework for nonparametric modeling on tensor field to foreground segmentation. We endow the tensor manifold with two well-founded Riemannian metrics, i.e. Affine-Invariant and Log-Euclidean. Theoretical aspects are defined and the metrics are compared experimentally. Theoretic analysis and experimental results demonstrate the promise/effectiveness of the framework.

Accurate single view model-based head pose estimation

Abstract: A framework for automatic human head pose estimation from single view images is proposed The 6DOF head pose was estimated using pose from orthography and scaling with iterations (POSIT) where a statistical anthropometric 3D rigid model is used as an approximation of the human head, combined with active appearance models (AAM) for facial features extraction and tracking The overall performance of the proposed solution was evaluated comparing the results with a ground-truth data obtained by a pose planar approach The results show that orientations and head location were, on average, found within 2deg or 1 cm error standard deviations respectively

Pattern Recognition and Machine Learning

Abstract: Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

High-Speed Tracking with Kernelized Correlation Filters

Abstract: 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.

Online Object Tracking: A Benchmark

Abstract: Object tracking is one of the most important components in numerous applications of computer vision. While much progress has been made in recent years with efforts on sharing code and datasets, it is of great importance to develop a library and benchmark to gauge the state of the art. After briefly reviewing recent advances of online object tracking, we carry out large scale experiments with various evaluation criteria to understand how these algorithms perform. The test image sequences are annotated with different attributes for performance evaluation and analysis. By analyzing quantitative results, we identify effective approaches for robust tracking and provide potential future research directions in this field.

Object Tracking Benchmark

Abstract: Object tracking has been one of the most important and active research areas in the field of computer vision. A large number of tracking algorithms have been proposed in recent years with demonstrated success. However, the set of sequences used for evaluation is often not sufficient or is sometimes biased for certain types of algorithms. Many datasets do not have common ground-truth object positions or extents, and this makes comparisons among the reported quantitative results difficult. In addition, the initial conditions or parameters of the evaluated tracking algorithms are not the same, and thus, the quantitative results reported in literature are incomparable or sometimes contradictory. To address these issues, we carry out an extensive evaluation of the state-of-the-art online object-tracking algorithms with various evaluation criteria to understand how these methods perform within the same framework. In this work, we first construct a large dataset with ground-truth object positions and extents for tracking and introduce the sequence attributes for the performance analysis. Second, we integrate most of the publicly available trackers into one code library with uniform input and output formats to facilitate large-scale performance evaluation. Third, we extensively evaluate the performance of 31 algorithms on 100 sequences with different initialization settings. By analyzing the quantitative results, we identify effective approaches for robust tracking and provide potential future research directions in this field.

Fully-Convolutional Siamese Networks for Object Tracking

Abstract: The problem of arbitrary object tracking has traditionally been tackled by learning a model of the object’s appearance exclusively online, using as sole training data the video itself. Despite the success of these methods, their online-only approach inherently limits the richness of the model they can learn. Recently, several attempts have been made to exploit the expressive power of deep convolutional networks. However, when the object to track is not known beforehand, it is necessary to perform Stochastic Gradient Descent online to adapt the weights of the network, severely compromising the speed of the system. In this paper we equip a basic tracking algorithm with a novel fully-convolutional Siamese network trained end-to-end on the ILSVRC15 dataset for object detection in video. Our tracker operates at frame-rates beyond real-time and, despite its extreme simplicity, achieves state-of-the-art performance in multiple benchmarks.