Nonlinear Mixing Characteristics of Reflectance Spectra of Typical Mineral Pigments

Hyperspectral technology has been used to identify pigments that adhere to the surfaces of polychrome artifacts. However, the colors are often produced by the mixing of pigments, which requires that the spectral characteristics of the pigment mixtures be considered before pigment unmixing is conducted. Therefore, we proposed an experimental approach to investigate the nonlinear degree of spectral reflectance, using several mixing models, and to evaluate their performances in the study of typical mineral pigments. First, five mineral pigments of azurite, malachite, cinnabar, orpiment, and calcite were selected to form five groups of samples, according to their different mass ratios. Second, a fully constrained least squares algorithm based on the linear model and three algorithms based on the nonlinear model were employed to calculate the proportion of each pigment in the mixtures. We evaluated the abundance accuracy as well as the similarity between the measured and reconstructed spectra produced by those mixing models. Third, we conducted pigment unmixing on a Chinese painting to verify the applicability of the nonlinear model. Fourth, continuum removal was also introduced to test the nonlinearity of mineral pigment mixing. Finally, the results indicated that the spectral mixing of different mineral pigments was more in line with the nonlinear mixing model. The spectral nonlinearity of mixed pigments was higher near to the wavelength corresponding to their colors. Meanwhile, the nonlinearity increased with the wavelength increases in the shortwave infrared bands.

Regional Mapping of Vineyards Using Machine Learning and LiDAR Data

This study evaluates the use of LiDAR data and machine learning algorithms for mapping vineyards. Vineyards are planted in rows spaced at various distances, which can cause spectral mixing within individual pixels and complicate image classification. Four resolution where used for generating normalized digital surface model and intensity derivatives from the LiDAR data. In addition, texture measures with window sizes of 3x3 and 5x5 were generated from the LiDAR derivatives. The different combinations of the resolutions and window sizes resulted in eight data sets that were used as input to 11 machine learning algorithms. A larger window size was found to improve the overall accuracy for all the classifier–resolution combinations. The results showed that random forest with texture measures generated at a 5x5 window size outperformed the other experiments, regardless of the resolution used. The authors conclude that the random forest algorithm used on LiDAR derivatives with a resolution of 1.5m and a window size of 5x5 is the recommend configuration for vineyard mapping using LiDAR data.

Beyond Beer's Law: Spectral Mixing Rules

Based on Beer's law, it is assumed that the absorbance of a mixture is that of the neat materials weighted by their relative amounts (linear mixing rule). In this contribution, we show that this is an assumption that holds only under various approximations for which no change of the chemical interactions is just one among several. To understand these approximations, which lead incrementally to different well known mixing rules, we finally derive the linear mixing rule from the Lorentz–Lorenz relation, with the first approximation that the local electric field is correctly described in this relation. Further levels of approximation are that the local field equals the applied field (Newton–Laplace mixing rule) and that the change of the index of refraction and, equivalently, absorption is weak (Gladstone–Dale/Arago–Biot mixing rule). Even then the linear mixing rule is only strictly valid if the indices of refraction in the transparency region at higher frequency than the absorption have the same value and the mixing is homogeneous relative to the resolving power of the light (“micro-homogeneous”). Under these preconditions, linear mixing of the individual absorbances is established. We illustrate the spectral differences between the different mixing rules, all of which are based on volume and not on mass fractions, with examples. For micro-heterogeneous samples, a different linear mixing rule governs the optical properties, which refers to the experimental quantities, reflectance, and transmittance. As a result, for such samples, mixtures of already comparably high content give only weak signals due to band flattening, which are hard to distinguish from baseline effects.

Study on the Effect of Surface Roughness on the Spectral Unmixing of Mixed Pixels

In the spectrum measurement experiment, the roughness of the object surface is an essential factor that cannot be ignored. In this experiment, a group of mixed pixel samples with different mixing ratios were designed, and these samples were printed on four kinds of papers with different roughness. The spectral characteristics of mixed pixels with different roughness are quantitatively analyzed by using the measured spectral data. The linear spectral mixture model is used for spectral decomposition, and the effect of roughness on the unmixing precision of mixed pixels was studied. The surface roughness will affect the reflectivity of the mixed pixel. Specifically, the higher the roughness is, the higher the reflectivity of the sample is. This phenomenon is more noticeable when the proportion of white endmember (PWE) is large, and as the white area ratio decreases, the reflectance difference gradually decreases. When the surface roughness of the sample is less than 3.339 μm, the spectral decomposition is performed using a linear spectral mixing model in the visible light band. The average error of the unmixing is less than 0.53%, which is lower than the conventional standard spectral measurement error. In other words, when the surface roughness of the sample is controlled within a specific range, the effect of roughness on the unmixing accuracy of the mixed pixels is small, and this effect can be almost ignored. Multiple scattering within the pixels is the key to model selection and unmixing accuracy, when using the ASD FieldSpec3 spectrometer to perform spectral reflectance measurement and linear spectral unmixing experiments. If the surface roughness of the sample to be measured is less than the maximum wavelength of the spectrometer, the experimental results believe that the photon energy is mainly mirror reflection on the surface of the object and diffuse reflection. At this time, it is still a better choice to use a linear spectral mixing model to decompose the mixed pixels.

Variação Intra-Anual da Cobertura da Terra de Uma Ottobacia no Médio Curso do Rio Araguaia (Intra-Annual Variation in Land Cover of an Ottobacia in the Middle Course of the Araguaia River )

A Bacia do Rio Araguaia é uma região cujos ambientes mostram-se marcados pelas variações anuais de inundação. A caracterização da cobertura da terra tem o potencial de caracterização do funcionamento ecossistêmico, bem como, avaliar possíveis modificações antrópicas. O presente trabalho teve como objetivo avaliar as variações espectrais de classes de uso e cobertura da terra da Ottobacia 6951, localizada no Médio curso do Rio Araguaia, no ano de 2017. Foram utilizadas imagens de reflectância da superfície terrestre do sensor Operational Land Imager (OLI) do satélite Landsat 8, referente aos períodos de transição chuva-seca (maio), seca (julho) e transição seca-chuva (outubro) de 2017. Para cada data foram geradas imagens-fração, através da técnica de mistura espectral, considerando três membros finais (natural, pastagem e água), evidenciando as mudanças da cobertura. Também foram gerados índices de vegetação para cada período, evidenciado os aspectos biofísicos da cobertura da terra. Para essa avaliação foram estabelecidos 50 pontos aleatórios para cada classe considerando a bacia inteira, cada unidade geomorfológica e uso e cobertura da terra. A avaliação dos padrões temporais da cobertura da terra considerou, especialmente, as relações de significância entre os fatores “cobertura” e “período”, para a realização de Análise Multivariada de Permutação (PERMANOVA). A avaliação de agrupamentos foi realizada por meio da Análise de Componentes Principais (ACP), que proporciona a redução da dimensionalidade dos dados. A cobertura da terra foi a variável de maior significância das mudanças intra-anuais da Ottobacia. A classe pastagem apresentou a maior variação intra-anual, expressando um comportamento mais sensível à sazonalidade. A B S T R A C TThe Araguaia River Basin is an area whose environments are marked by annual flood variations. The characterization of the land cover has the potential to characterize the ecosystem functioning, as well as to evaluate possible anthropic changes. The objective of this work was to evaluate the spectral variations of land use and land cover classes of Ottobacia 6951, located in the middle course of the Araguaia River, in the year 2017. Land surface reflectance images of the Operational Land Imager (OLI) ) of the Landsat 8 satellite, referring to the rainy-dry (May), dry (July) and dry-rainy transition (October) periods of 2017. For each date fractional images were generated, using the spectral mixing technique, considering three final members (natural, pasture and water), evidencing changes in coverage. Vegetation indexes were also generated for each period, evidencing the biophysical aspects of the land cover. For this evaluation were established 50 random points for each class considering the entire basin, each geomorphological unit and land use and coverage. The evaluation of temporal patterns of land cover considered, especially, the relations of significance between the factors "coverage" and "period", for the realization of Multivariate Analysis of Permutation (PERMANOVA). The clustering evaluation was performed through the Principal Component Analysis (PCA), which provides a reduction in the dimensionality of the data. Land cover was the most significant variable of Ottobacia's intra-annual changes. The pasture class had the highest intra-annual variation, expressing a behavior more sensitive to seasonality.Keyworks: river geomorphology, land cover seasonality, spectral mixing, vegetation indices, land use and cover.