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.

Hyperspectral unmixing algorithm via dependent component analysis

This paper introduces a new method to blindly unmix hyperspectral data, termed dependent component analysis (DECA). This method decomposes a hyperspectral images into a collection of reflectance (or radiance) spectra of the materials present in the scene (endmember signatures) and the corresponding abundance fractions at each pixel. DECA assumes that each pixel is a linear mixture of the endmembers signatures weighted by the correspondent abundance fractions. These abudances are modeled as mixtures of Dirichlet densities, thus enforcing the constraints on abundance fractions imposed by the acquisition process, namely non-negativity and constant sum. The mixing matrix is inferred by a generalized expectation-maximization (GEM) type algorithm. This method overcomes the limitations of unmixing methods based on Independent Component Analysis (ICA) and on geometrical based approaches. The effectiveness of the proposed method is illustrated using simulated data based on U.S.G.S. laboratory spectra and real hyperspectral data collected by the AVIRIS sensor over Cuprite, Nevada.

Urban image classification with semisupervised multiscale cluster kernels

This paper presents a semisupervised support vector machine (SVM) that integrates the information of both labeled and unlabeled pixels efficiently. Method's performance is illustrated in the relevant problem of very high resolution image classification of urban areas. The SVM is trained with the linear combination of two kernels: a base kernel working only with labeled examples is deformed by a likelihood kernel encoding similarities between labeled and unlabeled examples. Results obtained on very high resolution (VHR) multispectral and hyperspectral images show the relevance of the method in the context of urban image classification. Also, its simplicity and the few parameters involved make the method versatile and workable by unexperienced users.

Active learning methods for remote sensing image classification

In this paper, we propose two active learning algorithms for semiautomatic definition of training samples in remote sensing image classification. Based on predefined heuristics, the classifier ranks the unlabeled pixels and automatically chooses those that are considered the most valuable for its improvement. Once the pixels have been selected, the analyst labels them manually and the process is iterated. Starting with a small and nonoptimal training set, the model itself builds the optimal set of samples which minimizes the classification error. We have applied the proposed algorithms to a variety of remote sensing data, including very high resolution and hyperspectral images, using support vector machines. Experimental results confirm the consistency of the methods. The required number of training samples can be reduced to 10% using the methods proposed, reaching the same level of accuracy as larger data sets. A comparison with a state-of-the-art active learning method, margin sampling, is provided, highlighting advantages of the methods proposed. The effect of spatial resolution and separability of the classes on the quality of the selection of pixels is also discussed.

Studies on the characterization of dental whitening process by using both hyperspectral imaging and colorimeter techniques

A beautiful smile is directly related with white teeth. Nowadays oral care has increased and developed processes for beautiful smiles. Dental bleaching is frequently used in odontology, not just for health care also for aesthetic treatment. With the possibility of teeth bleaching, now the importance is in, how white the tooth is? Because color is relate to an individual perception. In order to assets teeth correct color identification has been developed many color guides, models, spaces and analytical methods. Spite all of these useful tools the color interpretation depends on environmental factors, position of the sample in the data acquisition and most importantly the instrument sensitivity. The commons methods have proved to be useful. They are easy to handle, some are portable but they do not have a high sensitivity. The present work is based on the integration of a new analytical technique for color acquisition. High spectral Image (HSI) is able to performed image analysis with high quality and efficiency. HSI is used in many fields and we used it for color image analysis within the bleaching process. The main comparison was done with the HSI and the colorimeter through the processes of two different bleaching protocols. The results showed that HSI has higher sensitivity than the colorimeter. During the analysis the dental surface with the HSI we were able to notice surface changes. These changes were analyzed by roughness studies.

Nature-Inspired Framework for Hyperspectral Band Selection

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Bathymetric map of Heron Reef, Australia, derived from airborne hyperspectral data at 1 m resolution

A simple method for efficient inversion of arbitrary radiative transfer models for image analysis is presented. The method operates by representing the shape of the function that maps model parameters to spectral reflectance by an adaptive look-up tree (ALUT) that evenly distributes the discretization error of tabulated reflectances in spectral space. A post-processing step organizes the data into a binary space partitioning tree that facilitates an efficient inversion search algorithm. In an example shallow water remote sensing application, the method performs faster than an implementation of previously published methodology and has the same accuracy in bathymetric retrievals. The method has no user configuration parameters requiring expert knowledge and minimizes the number of forward model runs required, making it highly suitable for routine operational implementation of image analysis methods. For the research community, straightforward and robust inversion allows research to focus on improving the radiative transfer models themselves without the added complication of devising an inversion strategy.

Detection and quantification of peanut traces in wheat flour by near infrared hyperspectral imaging spectroscopy using principal-component analysis

The use of a common environment for processing different powder foods in the industry has increased the risk of finding peanut traces in powder foods. The analytical methods commonly used for detection of peanut such as enzyme-linked immunosorbent assay (ELISA) and real-time polymerase chain reaction (RT-PCR) represent high specificity and sensitivity but are destructive and time-consuming, and require highly skilled experimenters. The feasibility of NIR hyperspectral imaging (HSI) is studied for the detection of peanut traces down to 0.01% by weight. A principal-component analysis (PCA) was carried out on a dataset of peanut and flour spectra. The obtained loadings were applied to the HSI images of adulterated wheat flour samples with peanut traces. As a result, HSI images were reduced to score images with enhanced contrast between peanut and flour particles. Finally, a threshold was fixed in score images to obtain a binary classification image, and the percentage of peanut adulteration was compared with the percentage of pixels identified as peanut particles. This study allowed the detection of traces of peanut down to 0.01% and quantification of peanut adulteration from 10% to 0.1% with a coefficient of determination (r2) of 0.946. These results show the feasibility of using HSI systems for the detection of peanut traces in conjunction with chemical procedures, such as RT-PCR and ELISA to facilitate enhanced quality-control surveillance on food-product processing lines.

On independent component analysis applied to unmixing hyperspectral data

One of the most challenging task underlying many hyperspectral imagery applications is the spectral unmixing, which decomposes a mixed pixel into a collection of reectance spectra, called endmember signatures, and their corresponding fractional abundances. Independent Component Analysis (ICA) have recently been proposed as a tool to unmix hyperspectral data. The basic goal of ICA is to nd a linear transformation to recover independent sources (abundance fractions) given only sensor observations that are unknown linear mixtures of the unobserved independent sources. In hyperspectral imagery the sum of abundance fractions associated to each pixel is constant due to physical constraints in the data acquisition process. Thus, sources cannot be independent. This paper address hyperspectral data source dependence and its impact on ICA performance. The study consider simulated and real data. In simulated scenarios hyperspectral observations are described by a generative model that takes into account the degradation mechanisms normally found in hyperspectral applications. We conclude that ICA does not unmix correctly all sources. This conclusion is based on the a study of the mutual information. Nevertheless, some sources might be well separated mainly if the number of sources is large and the signal-to-noise ratio (SNR) is high.

Hyperspectral imaging and other optical techniques for (in-field/in-lab) physico-chemical attributes estimation of agri-food vegetal products

In the agri-food sector, measurement and monitoring activities contribute to high quality end products. In particular, considering food of plant origin, several product quality attributes can be monitored. Among the non-destructive measurement techniques, a large variety of optical techniques are available, including hyperspectral imaging (HSI) in the visible/near-infrared (Vis/NIR) range, which, due to the capacity to integrate image analysis and spectroscopy, proved particularly useful in agronomy and food science. Many published studies regarding HSI systems were carried out under controlled laboratory conditions. In contrast, few studies describe the application of HSI technology directly in the field, in particular for high-resolution proximal measurements carried out on the ground. Based on this background, the activities of the present PhD project were aimed at exploring and deepening knowledge in the application of optical techniques for the estimation of quality attributes of agri-food plant products. First, research activities on laboratory trials carried out on apricots and kiwis for the estimation of soluble solids content (SSC) and flesh firmness (FF) through HSI were reported; subsequently, FF was estimated on kiwis using a NIR-sensitive device; finally, the procyanidin content of red wine was estimated through a device based on the pulsed spectral sensitive photometry technique. In the second part, trials were carried out directly in the field to assess the degree of ripeness of red wine grapes by estimating SSC through HSI, and finally a method for the automatic selection of regions of interest in hyperspectral images of the vineyard was developed. The activities described above have revealed the potential of the optical techniques for sorting-line application; moreover, the application of the HSI technique directly in the field has proved particularly interesting, suggesting further investigations to solve a variety of problems arising from the many environmental variables that may affect the results of the analyses.

Determination Of Detergent And Dispensant Additives In Gasoline By Ring-oven And Near Infrared Hypespectral Imaging.

A method using the ring-oven technique for pre-concentration in filter paper discs and near infrared hyperspectral imaging is proposed to identify four detergent and dispersant additives, and to determine their concentration in gasoline. Different approaches were used to select the best image data processing in order to gather the relevant spectral information. This was attained by selecting the pixels of the region of interest (ROI), using a pre-calculated threshold value of the PCA scores arranged as histograms, to select the spectra set; summing up the selected spectra to achieve representativeness; and compensating for the superimposed filter paper spectral information, also supported by scores histograms for each individual sample. The best classification model was achieved using linear discriminant analysis and genetic algorithm (LDA/GA), whose correct classification rate in the external validation set was 92%. Previous classification of the type of additive present in the gasoline is necessary to define the PLS model required for its quantitative determination. Considering that two of the additives studied present high spectral similarity, a PLS regression model was constructed to predict their content in gasoline, while two additional models were used for the remaining additives. The results for the external validation of these regression models showed a mean percentage error of prediction varying from 5 to 15%.

Comparing Near-infrared Conventional Diffuse Reflectance Spectroscopy And Hyperspectral Imaging For Determination Of The Bulk Properties Of Solid Samples By Multivariate Regression: Determination Of Mooney Viscosity And Plasticity Indices Of Natural Rubber.

Conventional reflectance spectroscopy (NIRS) and hyperspectral imaging (HI) in the near-infrared region (1000-2500 nm) are evaluated and compared, using, as the case study, the determination of relevant properties related to the quality of natural rubber. Mooney viscosity (MV) and plasticity indices (PI) (PI0 - original plasticity, PI30 - plasticity after accelerated aging, and PRI - the plasticity retention index after accelerated aging) of rubber were determined using multivariate regression models. Two hundred and eighty six samples of rubber were measured using conventional and hyperspectral near-infrared imaging reflectance instruments in the range of 1000-2500 nm. The sample set was split into regression (n = 191) and external validation (n = 95) sub-sets. Three instruments were employed for data acquisition: a line scanning hyperspectral camera and two conventional FT-NIR spectrometers. Sample heterogeneity was evaluated using hyperspectral images obtained with a resolution of 150 × 150 μm and principal component analysis. The probed sample area (5 cm(2); 24,000 pixels) to achieve representativeness was found to be equivalent to the average of 6 spectra for a 1 cm diameter probing circular window of one FT-NIR instrument. The other spectrophotometer can probe the whole sample in only one measurement. The results show that the rubber properties can be determined with very similar accuracy and precision by Partial Least Square (PLS) regression models regardless of whether HI-NIR or conventional FT-NIR produce the spectral datasets. The best Root Mean Square Errors of Prediction (RMSEPs) of external validation for MV, PI0, PI30, and PRI were 4.3, 1.8, 3.4, and 5.3%, respectively. Though the quantitative results provided by the three instruments can be considered equivalent, the hyperspectral imaging instrument presents a number of advantages, being about 6 times faster than conventional bulk spectrometers, producing robust spectral data by ensuring sample representativeness, and minimizing the effect of the presence of contaminants.

Tradução, adaptação cultural e validação do questionário Body image After Breast Cancer para a língua portuguesa do Brasil

Universidade Estadual de Campinas . Faculdade de Educação Física

Tradução, adaptação transcultural e validação do "Body Image Avoidance Questionnaire (BIAQ)" e do "Body Checking Questionnaire (BCQ)" para lingua portuguesa no Brasil

Universidade Estadual de Campinas . Faculdade de Educação Física

Juvenile idiopathic arthritis with involvement of the temporomandibular joint: the role of image examinations

PURPOSE: Juvenile idiopathic arthritis (JIA) has unknown etiology, and the involvement of the temporomandibular joint (TMJ) is rare in the early phase of the disease. The present article describes the use of computed tomography (CT) and magnetic resonance (MRI) images for the diagnosis of affected TMJ in JIA. CASE DESCRIPTION: A 12-year-old, female, Caucasian patient, with systemic rheumathoid arthritis and involvement of multiple joints was referred to the Imaging Center for TMJ assessment. The patient reported TMJ pain and limited opening of the mouth. The helical CT examination of the TMJ region showed asymmetric mandibular condyles, erosion of the right condyle and osteophyte-like formation. The MRI examination showed erosion of the right mandibular condyle, osteophytes, displacement without reduction and disruption of the articular disc. CONCLUSION: The disorders of the TMJ as a consequence of JIA must be carefully assessed by modern imaging methods such as CT and MRI. CT is very useful for the evaluation of discrete bone changes, which are not identified by conventional radiographs in the early phase of JIA. MRI allows the evaluation of soft tissues, the identification of acute articular inflammation and the differentiation between pannus and synovial hypertrophy.