The C++ language is often used for implementing functionality that is performance and/or resource sensitive. While the standard C++ library provides many useful algorithms (such as sorting), in its current form it does not provide direct handling of linear algebra (matrix maths).Armadillo is an open source linear algebra library for the C++ language, aiming towards a good balance between speed and ease of use. Its high-level application programming interface (function syntax) is deliberately similar to the widely used Matlab and Octave languages [4], so that mathematical operations can be expressed in a familiar and natural manner. The library is useful for algorithm development directly in C++, or relatively quick conversion of research code into production environments.Armadillo provides efficient objects for vectors, matrices and cubes (third order tensors), as well as over 200 associated functions for manipulating data stored in the objects. Integer, floating point and complex numbers are supported, as well as dense and sparse storage formats. Various matrix factorisations are provided through integration with LAPACK [3], or one of its high performance drop-in replacements such as Intel MKL [6] or OpenBLAS [9]. It is also possible to use Armadillo in conjunction with NVBLAS to obtain GPU-accelerated matrix multiplication [7].Armadillo is used as a base for other open source projects, such as MLPACK, a C++ library for machine learning and pattern recognition [2], and RcppArmadillo, a bridge between the R language and C++ in order to speed up computations [5]. Armadillo internally employs an expression evaluator based on template meta-programming techniques [1], to automatically combine several operations in order to increase speed and efficiency. An overview of the internal architecture is given in [8].

The R statistical environment and language has demonstrated particular strengths for interactive development of statistical algorithms, as well as data modelling and visualisation. Its current implementation has an interpreter at its core which may result in a performance penalty in comparison to directly executing user algorithms in the native machine code of the host CPU. In contrast, the C++ language has no built-in visualisation capabilities, handling of linear algebra or even basic statistical algorithms; however, user programs are converted to highperformance machine code, ahead of execution. A new method avoids possible speed penalties in R by using the Rcpp extension package in conjunction with the Armadillo C++ matrix library. In addition to the inherent performance advantages of compiled code, Armadillo provides an easy-to-use template-based meta-programming framework, allowing the automatic pooling of several linear algebra operations into one, which in turn can lead to further speedups. With the aid of Rcpp and Armadillo, conversion of linear algebra centered algorithms from R to C++ becomes straightforward. The algorithms retains the overall structure as well as readability, all while maintaining a bidirectional link with the host R environment. Empirical timing comparisons of R and C++ implementations of a Kalman filtering algorithm indicate a speedup of several orders of magnitude.

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Abstract. Recent advances suggest that a wide range of computer vision problems can be addressed more appropriately by considering non-Euclidean geometry. This paper tackles the problem of sparse coding and dictionary learning in the space of symmetric positive definite matrices, which form a Riemannian manifold. With the aid of the recently introduced Stein kernel (related to a symmetric version of Bregman matrix divergence), we propose to perform sparse coding by embedding Riemannian manifolds into reproducing kernel Hilbert spaces. This leads to a convex and kernel version of the Lasso problem, which can be solved efficiently. We furthermore propose an algorithm for learning a Riemannian dictionary (used for sparse coding), closely tied to the Stein kernel. Experiments on several classification tasks (face recognition, texture classification, person reidentification) show that the proposed sparse coding approach achieves notable improvements in discrimination accuracy, in comparison to state-of-the-art methods such as tensor sparse coding, Riemannian locality preserving projection, and symmetry-driven accumulation of local features.

A convenient way of dealing with image sets is to represent them as points on Grassmannian manifolds. While several recent studies explored the applicability of discriminant analysis on such manifolds, the conventional formalism of discriminant analysis suffers from not considering the local structure of the data. We propose a discriminant analysis approach on Grassmannian manifolds, based on a graphembedding framework. We show that by introducing withinclass and between-class similarity graphs to characterise intra-class compactness and inter-class separability, the geometrical structure of data can be exploited. Experiments on several image datasets (PIE, BANCA, MoBo, ETH-80) show that the proposed algorithm obtains considerable improvements in discrimination accuracy, in comparison to three recent methods: Grassmann Discriminant Analysis (GDA), Kernel GDA, and the kernel version of Affine Hull Image Set Distance. We further propose a Grassmannian kernel, based on canonical correlation between subspaces, which can increase discrimination accuracy when used in combination with previous Grassmannian kernels. * Acknowledgements: NICTA is funded by the Australian Government as represented by the Department of Broadband, Communications and the Digital Economy, as well as the Australian Research Council through the ICT Centre of Excellence program. The second and third authors contributed equally. We thank Prof. Terry Caelli for useful discussions.

Abstract. We propose a scalable face matching algorithm capable of dealing with faces subject to several concurrent and uncontrolled factors, such as variations in pose, expression, illumination, resolution, as well as scale and misalignment problems. Each face is described in terms of multi-region probabilistic histograms of visual words, followed by a normalised distance calculation between the histograms of two faces. We also propose a fast histogram approximation method which dramatically reduces the computational burden with minimal impact on discrimination performance. Experiments on the Labeled Faces in the Wild (LFW) dataset (unconstrained environments) as well as FERET and VidTIMIT (controlled variations) show that the proposed algorithm obtains performance on par with a more complex method and displays a clear advantage over predecessor systems. Furthermore, the use of multiple regions (as opposed to a single overall region) improves accuracy in most cases, especially when dealing with illumination changes and very low resolution images. The experiments also show that normalised distances can noticeably improve robustness by partially counteracting the effects of image variations.

In video based face recognition, face images are typically captured over multiple frames in uncontrolled conditions, where head pose, illumination, shadowing, motion blur and focus change over the sequence. Additionally, inaccuracies in face localisation can also introduce scale and alignment variations. Using all face images, including images of poor quality, can actually degrade face recognition performance. While one solution it to use only the 'best' subset of images, current face selection techniques are incapable of simultaneously handling all of the abovementioned issues. We propose an efficient patch-based face image quality assessment algorithm which quantifies the similarity of a face image to a probabilistic face model, representing an 'ideal' face. Image characteristics that affect recognition are taken into account, including variations in geometric alignment (shift, rotation and scale), sharpness, head pose and cast shadows. Experiments on FERET and PIE datasets show that the proposed algorithm is able to identify images which are simultaneously the most frontal, aligned, sharp and well illuminated. Further experiments on a new video surveillance dataset (termed ChokePoint) show that the proposed method provides better face subsets than existing face selection techniques, leading to significant improvements in recognition accuracy.

Shadow detection and removal is an important step employed after foreground detection, in order to improve the segmentation of objects for tracking. Methods reported in the literature typically have a significant trade-off between the shadow detection rate (classifying true shadow areas as shadows) and the shadow discrimination rate (discrimination between shadows and foreground). We propose a method that is able to achieve good performance in both cases, leading to improved tracking in surveillance scenarios. Chromacity information is first used to create a mask of candidate shadow pixels, followed by employing gradient information to remove foreground pixels that were incorrectly included in the mask. Experiments on the CAVIAR dataset indicate that the proposed method leads to considerable improvements in multiple object tracking precision and accuracy.