Gaussian Blur and Relative Edge Response

It is often convenient to use Gaussian blur in studying image quality or in data augmentation pipelines for training convoluional neural networks. Because of their convenience, Guassians are sometimes used as first order approximations of optical point spread functions. Here, we derive and evaluate closed form relationships between Gaussian blur parameters and relative edge response, finding good agreement with measured results. Additionally, we evaluate the extent to which Gaussian approximations of optical point spread functions can be used to predict relative edge response, finding that Gaussian relationships provide a reasonable approximation in limited circumstances but not across a wide range of optical parameters.

Hyperspectral Pigment Analysis of Cultural Heritage Artifacts Using the Opaque Form of Kubelka-Munk Theory

Kubelka-Munk (K-M) theory has been successfully used to estimate pigment concentrations in the pigment mixtures of modern paintings in spectral imagery. In this study the single-constant K-M theory has been utilized for the classification of green pigments in the Selden Map of China, a navigational map of the South China Sea likely created in the early seventeenth century. Hyperspectral data of the map was collected at the Bodleian Library, University of Oxford, and can be used to estimate the pigment diversity, and spatial distribution, within the map. This work seeks to assess the utility of analyzing the data in the K/S space from Kubelka-Munk theory, as opposed to the traditional reflectance domain. We estimate the dimensionality of the data and extract endmembers in the reflectance domain. Then we perform linear unmixing to estimate abundances in the K/S space, and following Bai, et al. (2017), we perform a classification in the abundance space. Finally, due to the lack of ground truth labels, the classification accuracy was estimated by computing the mean spectrum of each class as the representative signature of that class, and calculating the root mean squared error with all the pixels in that class to create a spatial representation of the error. This highlights both the magnitude of, and any spatial pattern in, the errors, indicating if a particular pigment is not well modeled in this approach.