Spectral unmixing aims to determine the relative amount (so-called abundances) of raw materials (so-called endmembers) in hyperspectral images (HSI). Libraries of endmember spectra are often given. Since the linear mixing model assigns one spectrum to each raw material, the endmember variability is not considered. Computationally costly algorithms exist to still derive precise abundances. In the method proposed in this work, we use only the pseudoinverse of the matrix of the endmember spectra to estimate the abundances. As can be shown, this approach circumvents the necessity of acquiring a HSI and is less computationally costly. To become robust against model deviations, we iteratively estimate the abundances by modifying the matrix of the endmember spectra used to derive the pseudoinverse. The values to modify each endmember spectrum are derived involving the singular value decomposition and the grade of violation of physical constraints to the abundances. Unlike existing algorithms, we account for the endmember variability and force simultaneously to meet physical constraints. Evaluations of samples for material mixtures, such as mixtures of color powders and quartz sands, show that more accurate abundance estimates result. A physical interpretation of these estimates is enabled in most cases.
Regardless whether mosaics, material surfaces or skin surfaces are inspected their texture plays an important role. Texture is a property which is hard to describe using words but it can easily be described in pictures. Furthermore, a huge amount of digital images containing a visual description of textures already exists. However, this information becomes useless if there are no appropriate methods to browse the data. In addition, depending on the given task some properties like scale, rotation or intensity invariance are desired. In this paper we propose to analyze texture images according to their characteristic pattern. First a classification approach is proposed to separate regular from non-regular textures. The second stage will focus on regular textures suggesting a method to sort them according to their similarity. Different features will be extracted from the texture in order to describe its scale, orientation, texel and the texel’s relative position. Depending on the desired invariance of the visual characteristics (like the texture’s scale or the texel’s form invariance) the comparison of the features between images will be weighted and combined to define the degree of similarity between them. Tuning the weighting parameters allows this search algorithm to be easily adapted to the requirements of the desired task. Not only the total invariance of desired parameters can be adjusted, the weighting of the parameters may also be modified to adapt to an application-specific type of similarity. This search method has been evaluated using different textures and similarity criteria achieving very promising results.