Vertex component analysis: a fast algorithm to unmix hyperspectral data

Given a set of mixed spectral (multispectral or hyperspectral) vectors, linear spectral mixture analysis, or linear unmixing, aims at estimating the number of reference substances, also called endmembers, their spectral signatures, and their abundance fractions. This paper presents a new method for unsupervised endmember extraction from hyperspectral data, termed vertex component analysis (VCA). The algorithm exploits two facts: (1) the endmembers are the vertices of a simplex and (2) the affine transformation of a simplex is also a simplex. In a series of experiments using simulated and real data, the VCA algorithm competes with state-of-the-art methods, with a computational complexity between one and two orders of magnitude lower than the best available method.

ECG Biometrics: A Template Selection Approach

Electrocardiography (ECG) biometrics is emerging as a viable biometric trait. Recent developments at the sensor level have shown the feasibility of performing signal acquisition at the fingers and hand palms, using one-lead sensor technology and dry electrodes. These new locations lead to ECG signals with lower signal to noise ratio and more prone to noise artifacts; the heart rate variability is another of the major challenges of this biometric trait. In this paper we propose a novel approach to ECG biometrics, with the purpose of reducing the computational complexity and increasing the robustness of the recognition process enabling the fusion of information across sessions. Our approach is based on clustering, grouping individual heartbeats based on their morphology. We study several methods to perform automatic template selection and account for variations observed in a person's biometric data. This approach allows the identification of different template groupings, taking into account the heart rate variability, and the removal of outliers due to noise artifacts. Experimental evaluation on real world data demonstrates the advantages of our approach.

Exact admission-control for integrated aperiodic and periodic tasks

Admission controllers are used to prevent overload in systems with dynamically arriving tasks. Typically, these admission controllers are based on suÆcient (but not necessary) capacity bounds in order to maintain a low computational complexity. In this paper we present how exact admission-control for aperiodic tasks can be eÆciently obtained. Our rst result is an admission controller for purely aperiodic task sets where the test has the same runtime complexity as utilization-based tests. Our second result is an extension of the previous controller for a baseload of periodic tasks. The runtime complexity of this test is lower than for any known exact admission-controller. In addition to presenting our main algorithm and evaluating its performance, we also discuss some general issues concerning admission controllers and their implementation.

H.264/AVC backward compatible Bit-Depth scalable video coding

As high dynamic range video is gaining popularity, video coding solutions able to efficiently provide both low and high dynamic range video, notably with a single bitstream, are increasingly important. While simulcasting can provide both dynamic range videos at the cost of some compression efficiency penalty, bit-depth scalable video coding can provide a better trade-off between compression efficiency, adaptation flexibility and computational complexity. Considering the widespread use of H.264/AVC video, this paper proposes a H.264/AVC backward compatible bit-depth scalable video coding solution offering a low dynamic range base layer and two high dynamic range enhancement layers with different qualities, at low complexity. Experimental results show that the proposed solution has an acceptable rate-distortion performance penalty regarding the HDR H.264/AVC single-layer coding solution.

NoC contention analysis using a branch-and-prune algorithm

“Many-core” systems based on a Network-on-Chip (NoC) architecture offer various opportunities in terms of performance and computing capabilities, but at the same time they pose many challenges for the deployment of real-time systems, which must fulfill specific timing requirements at runtime. It is therefore essential to identify, at design time, the parameters that have an impact on the execution time of the tasks deployed on these systems and the upper bounds on the other key parameters. The focus of this work is to determine an upper bound on the traversal time of a packet when it is transmitted over the NoC infrastructure. Towards this aim, we first identify and explore some limitations in the existing recursive-calculus-based approaches to compute the Worst-Case Traversal Time (WCTT) of a packet. Then, we extend the existing model by integrating the characteristics of the tasks that generate the packets. For this extended model, we propose an algorithm called “Branch and Prune” (BP). Our proposed method provides tighter and safe estimates than the existing recursive-calculus-based approaches. Finally, we introduce a more general approach, namely “Branch, Prune and Collapse” (BPC) which offers a configurable parameter that provides a flexible trade-off between the computational complexity and the tightness of the computed estimate. The recursive-calculus methods and BP present two special cases of BPC when a trade-off parameter is 1 or ∞, respectively. Through simulations, we analyze this trade-off, reason about the implications of certain choices, and also provide some case studies to observe the impact of task parameters on the WCTT estimates.

Interação social entre agentes em ambientes de recursos limitados

Trabalho final de Mestrado para obtenção do grau de Mestre em Engenharia de Redes de Comunicação e Multimédia

Unmixing hyperspectral data: independent and dependent component analysis

The development of high spatial resolution airborne and spaceborne sensors has improved the capability of ground-based data collection in the fields of agriculture, geography, geology, mineral identification, detection [2, 3], and classification [4–8]. The signal read by the sensor from a given spatial element of resolution and at a given spectral band is a mixing of components originated by the constituent substances, termed endmembers, located at that element of resolution. This chapter addresses hyperspectral unmixing, which is the decomposition of the pixel spectra into a collection of constituent spectra, or spectral signatures, and their corresponding fractional abundances indicating the proportion of each endmember present in the pixel [9, 10]. Depending on the mixing scales at each pixel, the observed mixture is either linear or nonlinear [11, 12]. The linear mixing model holds when the mixing scale is macroscopic [13]. The nonlinear model holds when the mixing scale is microscopic (i.e., intimate mixtures) [14, 15]. The linear model assumes negligible interaction among distinct endmembers [16, 17]. The nonlinear model assumes that incident solar radiation is scattered by the scene through multiple bounces involving several endmembers [18]. Under the linear mixing model and assuming that the number of endmembers and their spectral signatures are known, hyperspectral unmixing is a linear problem, which can be addressed, for example, under the maximum likelihood setup [19], the constrained least-squares approach [20], the spectral signature matching [21], the spectral angle mapper [22], and the subspace projection methods [20, 23, 24]. Orthogonal subspace projection [23] reduces the data dimensionality, suppresses undesired spectral signatures, and detects the presence of a spectral signature of interest. The basic concept is to project each pixel onto a subspace that is orthogonal to the undesired signatures. As shown in Settle [19], the orthogonal subspace projection technique is equivalent to the maximum likelihood estimator. This projection technique was extended by three unconstrained least-squares approaches [24] (signature space orthogonal projection, oblique subspace projection, target signature space orthogonal projection). Other works using maximum a posteriori probability (MAP) framework [25] and projection pursuit [26, 27] have also been applied to hyperspectral data. In most cases the number of endmembers and their signatures are not known. Independent component analysis (ICA) is an unsupervised source separation process that has been applied with success to blind source separation, to feature extraction, and to unsupervised recognition [28, 29]. ICA consists in finding a linear decomposition of observed data yielding statistically independent components. Given that hyperspectral data are, in given circumstances, linear mixtures, ICA comes to mind as a possible tool to unmix this class of data. In fact, the application of ICA to hyperspectral data has been proposed in reference 30, where endmember signatures are treated as sources and the mixing matrix is composed by the abundance fractions, and in references 9, 25, and 31–38, where sources are the abundance fractions of each endmember. In the first approach, we face two problems: (1) The number of samples are limited to the number of channels and (2) the process of pixel selection, playing the role of mixed sources, is not straightforward. In the second approach, ICA is based on the assumption of mutually independent sources, which is not the case of hyperspectral data, since the sum of the abundance fractions is constant, implying dependence among abundances. This dependence compromises ICA applicability to hyperspectral images. In addition, hyperspectral data are immersed in noise, which degrades the ICA performance. IFA [39] was introduced as a method for recovering independent hidden sources from their observed noisy mixtures. IFA implements two steps. First, source densities and noise covariance are estimated from the observed data by maximum likelihood. Second, sources are reconstructed by an optimal nonlinear estimator. Although IFA is a well-suited technique to unmix independent sources under noisy observations, the dependence among abundance fractions in hyperspectral imagery compromises, as in the ICA case, the IFA performance. Considering the linear mixing model, hyperspectral observations are in a simplex whose vertices correspond to the endmembers. Several approaches [40–43] have exploited this geometric feature of hyperspectral mixtures [42]. Minimum volume transform (MVT) algorithm [43] determines the simplex of minimum volume containing the data. The MVT-type approaches are complex from the computational point of view. Usually, these algorithms first find the convex hull defined by the observed data and then fit a minimum volume simplex to it. Aiming at a lower computational complexity, some algorithms such as the vertex component analysis (VCA) [44], the pixel purity index (PPI) [42], and the N-FINDR [45] still find the minimum volume simplex containing the data cloud, but they assume the presence in the data of at least one pure pixel of each endmember. This is a strong requisite that may not hold in some data sets. In any case, these algorithms find the set of most pure pixels in the data. Hyperspectral sensors collects spatial images over many narrow contiguous bands, yielding large amounts of data. For this reason, very often, the processing of hyperspectral data, included unmixing, is preceded by a dimensionality reduction step to reduce computational complexity and to improve the signal-to-noise ratio (SNR). Principal component analysis (PCA) [46], maximum noise fraction (MNF) [47], and singular value decomposition (SVD) [48] are three well-known projection techniques widely used in remote sensing in general and in unmixing in particular. The newly introduced method [49] exploits the structure of hyperspectral mixtures, namely the fact that spectral vectors are nonnegative. The computational complexity associated with these techniques is an obstacle to real-time implementations. To overcome this problem, band selection [50] and non-statistical [51] algorithms have been introduced. This chapter addresses hyperspectral data source dependence and its impact on ICA and IFA performances. The study consider simulated and real data and is based on mutual information minimization. Hyperspectral observations are described by a generative model. This model takes into account the degradation mechanisms normally found in hyperspectral applications—namely, signature variability [52–54], abundance constraints, topography modulation, and system noise. The computation of mutual information is based on fitting mixtures of Gaussians (MOG) to data. The MOG parameters (number of components, means, covariances, and weights) are inferred using the minimum description length (MDL) based algorithm [55]. We study the behavior of the mutual information as a function of the unmixing matrix. The conclusion is that the unmixing matrix minimizing the mutual information might be very far from the true one. Nevertheless, some abundance fractions might be well separated, mainly in the presence of strong signature variability, a large number of endmembers, and high SNR. We end this chapter by sketching a new methodology to blindly unmix hyperspectral data, where abundance fractions are modeled as a mixture of Dirichlet sources. This model enforces positivity and constant sum sources (full additivity) constraints. The mixing matrix is inferred by an expectation-maximization (EM)-type algorithm. This approach is in the vein of references 39 and 56, replacing independent sources represented by MOG with mixture of Dirichlet sources. Compared with the geometric-based approaches, the advantage of this model is that there is no need to have pure pixels in the observations. The chapter is organized as follows. Section 6.2 presents a spectral radiance model and formulates the spectral unmixing as a linear problem accounting for abundance constraints, signature variability, topography modulation, and system noise. Section 6.3 presents a brief resume of ICA and IFA algorithms. Section 6.4 illustrates the performance of IFA and of some well-known ICA algorithms with experimental data. Section 6.5 studies the ICA and IFA limitations in unmixing hyperspectral data. Section 6.6 presents results of ICA based on real data. Section 6.7 describes the new blind unmixing scheme and some illustrative examples. Section 6.8 concludes with some remarks.

Vertex component analysis: a geometric-based approach to unmix hyperspectral data

Hyperspectral remote sensing exploits the electromagnetic scattering patterns of the different materials at specific wavelengths [2, 3]. Hyperspectral sensors have been developed to sample the scattered portion of the electromagnetic spectrum extending from the visible region through the near-infrared and mid-infrared, in hundreds of narrow contiguous bands [4, 5]. The number and variety of potential civilian and military applications of hyperspectral remote sensing is enormous [6, 7]. Very often, the resolution cell corresponding to a single pixel in an image contains several substances (endmembers) [4]. In this situation, the scattered energy is a mixing of the endmember spectra. A challenging task underlying many hyperspectral imagery applications is then decomposing a mixed pixel into a collection of reflectance spectra, called endmember signatures, and the corresponding abundance fractions [8–10]. Depending on the mixing scales at each pixel, the observed mixture is either linear or nonlinear [11, 12]. Linear mixing model holds approximately when the mixing scale is macroscopic [13] and there is negligible interaction among distinct endmembers [3, 14]. If, however, the mixing scale is microscopic (or intimate mixtures) [15, 16] and the incident solar radiation is scattered by the scene through multiple bounces involving several endmembers [17], the linear model is no longer accurate. Linear spectral unmixing has been intensively researched in the last years [9, 10, 12, 18–21]. It considers that a mixed pixel is a linear combination of endmember signatures weighted by the correspondent abundance fractions. Under this model, and assuming that the number of substances and their reflectance spectra are known, hyperspectral unmixing is a linear problem for which many solutions have been proposed (e.g., maximum likelihood estimation [8], spectral signature matching [22], spectral angle mapper [23], subspace projection methods [24,25], and constrained least squares [26]). In most cases, the number of substances and their reflectances are not known and, then, hyperspectral unmixing falls into the class of blind source separation problems [27]. Independent component analysis (ICA) has recently been proposed as a tool to blindly unmix hyperspectral data [28–31]. ICA is based on the assumption of mutually independent sources (abundance fractions), which is not the case of hyperspectral data, since the sum of abundance fractions is constant, implying statistical dependence among them. This dependence compromises ICA applicability to hyperspectral images as shown in Refs. [21, 32]. In fact, ICA finds the endmember signatures by multiplying the spectral vectors with an unmixing matrix, which minimizes the mutual information among sources. If sources are independent, ICA provides the correct unmixing, since the minimum of the mutual information is obtained only when sources are independent. This is no longer true for dependent abundance fractions. Nevertheless, some endmembers may be approximately unmixed. These aspects are addressed in Ref. [33]. Under the linear mixing model, the observations from a scene are in a simplex whose vertices correspond to the endmembers. Several approaches [34–36] have exploited this geometric feature of hyperspectral mixtures [35]. Minimum volume transform (MVT) algorithm [36] determines the simplex of minimum volume containing the data. The method presented in Ref. [37] is also of MVT type but, by introducing the notion of bundles, it takes into account the endmember variability usually present in hyperspectral mixtures. The MVT type approaches are complex from the computational point of view. Usually, these algorithms find in the first place the convex hull defined by the observed data and then fit a minimum volume simplex to it. For example, the gift wrapping algorithm [38] computes the convex hull of n data points in a d-dimensional space with a computational complexity of O(nbd=2cþ1), where bxc is the highest integer lower or equal than x and n is the number of samples. The complexity of the method presented in Ref. [37] is even higher, since the temperature of the simulated annealing algorithm used shall follow a log( ) law [39] to assure convergence (in probability) to the desired solution. Aiming at a lower computational complexity, some algorithms such as the pixel purity index (PPI) [35] and the N-FINDR [40] still find the minimum volume simplex containing the data cloud, but they assume the presence of at least one pure pixel of each endmember in the data. This is a strong requisite that may not hold in some data sets. In any case, these algorithms find the set of most pure pixels in the data. PPI algorithm uses the minimum noise fraction (MNF) [41] as a preprocessing step to reduce dimensionality and to improve the signal-to-noise ratio (SNR). The algorithm then projects every spectral vector onto skewers (large number of random vectors) [35, 42,43]. The points corresponding to extremes, for each skewer direction, are stored. A cumulative account records the number of times each pixel (i.e., a given spectral vector) is found to be an extreme. The pixels with the highest scores are the purest ones. N-FINDR algorithm [40] is based on the fact that in p spectral dimensions, the p-volume defined by a simplex formed by the purest pixels is larger than any other volume defined by any other combination of pixels. This algorithm finds the set of pixels defining the largest volume by inflating a simplex inside the data. ORA SIS [44, 45] is a hyperspectral framework developed by the U.S. Naval Research Laboratory consisting of several algorithms organized in six modules: exemplar selector, adaptative learner, demixer, knowledge base or spectral library, and spatial postrocessor. The first step consists in flat-fielding the spectra. Next, the exemplar selection module is used to select spectral vectors that best represent the smaller convex cone containing the data. The other pixels are rejected when the spectral angle distance (SAD) is less than a given thresh old. The procedure finds the basis for a subspace of a lower dimension using a modified Gram–Schmidt orthogonalizati on. The selected vectors are then projected onto this subspace and a simplex is found by an MV T pro cess. ORA SIS is oriented to real-time target detection from uncrewed air vehicles using hyperspectral data [46]. In this chapter we develop a new algorithm to unmix linear mixtures of endmember spectra. First, the algorithm determines the number of endmembers and the signal subspace using a newly developed concept [47, 48]. Second, the algorithm extracts the most pure pixels present in the data. Unlike other methods, this algorithm is completely automatic and unsupervised. To estimate the number of endmembers and the signal subspace in hyperspectral linear mixtures, the proposed scheme begins by estimating sign al and noise correlation matrices. The latter is based on multiple regression theory. The signal subspace is then identified by selectin g the set of signal eigenvalue s that best represents the data, in the least-square sense [48,49 ], we note, however, that VCA works with projected and with unprojected data. The extraction of the end members exploits two facts: (1) the endmembers are the vertices of a simplex and (2) the affine transformation of a simplex is also a simplex. As PPI and N-FIND R algorithms, VCA also assumes the presence of pure pixels in the data. The algorithm iteratively projects data on to a direction orthogonal to the subspace spanned by the endmembers already determined. The new end member signature corresponds to the extreme of the projection. The algorithm iterates until all end members are exhausted. VCA performs much better than PPI and better than or comparable to N-FI NDR; yet it has a computational complexity between on e and two orders of magnitude lower than N-FINDR. The chapter is structure d as follows. Section 19.2 describes the fundamentals of the proposed method. Section 19.3 and Section 19.4 evaluate the proposed algorithm using simulated and real data, respectively. Section 19.5 presents some concluding remarks.

Fast unsupervised extraction of endmembers spectra from hyperspectral data

Linear unmixing decomposes an hyperspectral image into a collection of re ectance spectra, called endmember signatures, and a set corresponding abundance fractions from the respective spatial coverage. This paper introduces vertex component analysis, an unsupervised algorithm to unmix linear mixtures of hyperpsectral data. VCA exploits the fact that endmembers occupy vertices of a simplex, and assumes the presence of pure pixels in data. VCA performance is illustrated using simulated and real data. VCA competes with state-of-the-art methods with much lower computational complexity.

Combining open and closed world reasoning for the semantic web

Dissertação para obtenção do Grau de Doutor em Informática

Hand gesture recognition for human computer interaction : a comparative study of different image features

Hand gesture recognition for human computer interaction, being a natural way of human computer interaction, is an area of active research in computer vision and machine learning. This is an area with many different possible applications, giving users a simpler and more natural way to communicate with robots/systems interfaces, without the need for extra devices. So, the primary goal of gesture recognition research is to create systems, which can identify specific human gestures and use them to convey information or for device control. For that, vision-based hand gesture interfaces require fast and extremely robust hand detection, and gesture recognition in real time. In this study we try to identify hand features that, isolated, respond better in various situations in human-computer interaction. The extracted features are used to train a set of classifiers with the help of RapidMiner in order to find the best learner. A dataset with our own gesture vocabulary consisted of 10 gestures, recorded from 20 users was created for later processing. Experimental results show that the radial signature and the centroid distance are the features that when used separately obtain better results, with an accuracy of 91% and 90,1% respectively obtained with a Neural Network classifier. These to methods have also the advantage of being simple in terms of computational complexity, which make them good candidates for real-time hand gesture recognition.

Accuracy vs. simplicity: a complex trade-off

Inductive learning aims at finding general rules that hold true in a database. Targeted learning seeks rules for the predictions of the value of a variable based on the values of others, as in the case of linear or non-parametric regression analysis. Non-targeted learning finds regularities without a specific prediction goal. We model the product of non-targeted learning as rules that state that a certain phenomenon never happens, or that certain conditions necessitate another. For all types of rules, there is a trade-off between the rule's accuracy and its simplicity. Thus rule selection can be viewed as a choice problem, among pairs of degree of accuracy and degree of complexity. However, one cannot in general tell what is the feasible set in the accuracy-complexity space. Formally, we show that finding out whether a point belongs to this set is computationally hard. In particular, in the context of linear regression, finding a small set of variables that obtain a certain value of R2 is computationally hard. Computational complexity may explain why a person is not always aware of rules that, if asked, she would find valid. This, in turn, may explain why one can change other people's minds (opinions, beliefs) without providing new information.

Object recognition for autonomous objects: comparison of two approaches

Report for the scientific sojourn at the Swiss Federal Institute of Technology Zurich, Switzerland, between September and December 2007. In order to make robots useful assistants for our everyday life, the ability to learn and recognize objects is of essential importance. However, object recognition in real scenes is one of the most challenging problems in computer vision, as it is necessary to deal with difficulties. Furthermore, in mobile robotics a new challenge is added to the list: computational complexity. In a dynamic world, information about the objects in the scene can become obsolete before it is ready to be used if the detection algorithm is not fast enough. Two recent object recognition techniques have achieved notable results: the constellation approach proposed by Lowe and the bag of words approach proposed by Nistér and Stewénius. The Lowe constellation approach is the one currently being used in the robot localization project of the COGNIRON project. This report is divided in two main sections. The first section is devoted to briefly review the currently used object recognition system, the Lowe approach, and bring to light the drawbacks found for object recognition in the context of indoor mobile robot navigation. Additionally the proposed improvements for the algorithm are described. In the second section the alternative bag of words method is reviewed, as well as several experiments conducted to evaluate its performance with our own object databases. Furthermore, some modifications to the original algorithm to make it suitable for object detection in unsegmented images are proposed.

Comparison of topography- and aperture-dependent motion compensation algorithms for airborne SAR

This letter presents a comparison between threeFourier-based motion compensation (MoCo) algorithms forairborne synthetic aperture radar (SAR) systems. These algorithmscircumvent the limitations of conventional MoCo, namelythe assumption of a reference height and the beam-center approximation.All these approaches rely on the inherent time–frequencyrelation in SAR systems but exploit it differently, with the consequentdifferences in accuracy and computational burden. Aftera brief overview of the three approaches, the performance ofeach algorithm is analyzed with respect to azimuthal topographyaccommodation, angle accommodation, and maximum frequencyof track deviations with which the algorithm can cope. Also, ananalysis on the computational complexity is presented. Quantitativeresults are shown using real data acquired by the ExperimentalSAR system of the German Aerospace Center (DLR).

Location models for airline hubs behaving as M/D/c queues

Models are presented for the optimal location of hubs in airline networks, that take into consideration the congestion effects. Hubs, which are the most congested airports, are modeled as M/D/c queuing systems, that is, Poisson arrivals, deterministic service time, and {\em c} servers. A formula is derived for the probability of a number of customers in the system, which is later used to propose a probabilistic constraint. This constraint limits the probability of {\em b} airplanes in queue, to be lesser than a value $\alpha$. Due to the computational complexity of the formulation. The model is solved using a meta-heuristic based on tabu search. Computational experience is presented.