In recent years, advances in machine learning algorithms, cheap computational resources, and the availability of big data have spurred the deep learning revolution in various application domains. In particular, supervised learning techniques in image analysis have led to a superhuman performance in various tasks, such as classification, localization, and segmentation, whereas unsupervised learning techniques based on increasingly advanced generative models have been applied to generate high-resolution synthetic images indistinguishable from real images. In this letter, we consider a state-of-the-art machine learning model for image inpainting, namely, a Wasserstein Generative Adversarial Network based on a fully convolutional architecture with a contextual attention mechanism. We show that this model can be successfully transferred to the setting of digital elevation models for the purpose of generating semantically plausible data for filling voids. Training, testing, and experimentation are done on GeoTIFF data from various regions in Norway, made openly available by the Norwegian Mapping Authority.

We consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore well suited to floating‐point implementation in computer‐aided geometric design (CAGD) systems. We unify the approaches under the names of commonly known polynomial basis functions and consider various theoretical and practical aspects of the algorithms. We offer new methods for a least squares approach to approximate implicitization using orthogonal polynomials, which tend to be faster and more numerically stable than some existing algorithms. We propose several simple propositions relating the properties of the polynomial bases to their implicit approximation properties.