Due to complicated backgrounds and unclear target orientation, automated object detection is difficult in the field of archaeology. Most of the current convolutional neural network (CNN) object-oriented detection techniques are based on a faster region-based CNN (R-CNN) and other one-stage detectors that often lack adequate processing speeds and detection accuracies. Recently, the two-stage detector Mask R-CNN technique achieved impressive results in object detection and instance segmentation problems and was successfully applied in the analysis of archaeological airborne laser scanning (ALS) data. In this study, we outline a modified Mask R-CNN technique that reliably and efficiently detects relict charcoal hearth (RCH) sites on light detection and ranging (LiDAR) data-based digital elevation models (DEMs).Using image augmentation and image preprocessing steps combined with the deep learning-based adaptive gradient method with a dynamic bound on the learning rate (AdaBound) optimization technique, we could improve the model's accuracy and significantly reduce its training time. We use DEMs based on high-resolution LiDAR data and the visualization for archaeological topography (VAT) technique that give images with a very strong contrast of the terrain and the outline of the sites of interest in the North German Lowland. Therefore, the model can identify RCH sites with an average recall of 83% and an average precision of 87%. Techniques such as the modified Mask R-CNN method outlined here will help to greatly improve our knowledge about archaeological site densities in the realm of historical charcoal production and past human-landscape interactions. This method provides an accurate, time-efficient and bias-free large-scale site mapping option not only for the North German Lowland but potentially for other landscapes as well.

In this paper we study a modern, perspective model for shape from shading and its numerical approximation. We show that a new form of the classic concave/convex ambiguity is still present, although the model has been shown to be well-posed under particular assumptions. This analytical result is confirmed by various numerical tests. Moreover, we present convergence results for two iterative approximation schemes recently introduced in the literature. The first one is based on a finite difference discretization, whereas the second one is based on a semi-Lagrangian discretization. The convergence results are obtained in the general framework of viscosity solutions of the underlying partial differential equation. We also show that it is possible to obtain even in complex scenes results of reasonable quality. To this end we solve the constituting equation on a previously-segmented input image, where we use state constraints boundary conditions at the segment borders.

Dilation and erosion are the fundamental operations in morphological image processing. Algorithms that exploit the formulation of these processes in terms of partial differential equations offer advantages for non-digitally scalable structuring elements and allow sub-pixel accuracy. However, the widely-used schemes from the literature suffer from significant blurring at discontinuities. We address this problem by developing a novel, flux corrected transport (FCT) type algorithm for morphological dilation / erosion with a flat disc. It uses the viscosity form of an upwind scheme in order to quantify the undesired diffusive effects. In a subsequent corrector step we compensate for these artifacts by means of a stabilised inverse diffusion process that requires a specific nonlinear multidimensional formulation. We prove a discrete maximum-minimum principle in this multidimensional framework. Our experiments show that the method gives a very sharp resolution of moving fronts, and it approximates rotation invariance very well.

The integration of surface normals is a classic and fundamental task in computer vision. In this paper we deal with a highly efficient fast marching (FM) method to perform the integration. In doing this we build upon a previous work of Ho and his coauthors. Their FM scheme is based on an analytic model that incorporates the eikonal equation. Our method is also built upon this equation, but it makes use of a complete discrete formulation for constructing the FM integrator (DEFM). We not only provide a theoretical justification of the proposed method, but also illustrate at hand of a simple example that our approach is much better suited to the task. Several more sophisticated tests confirm the robustness and higher accuracy of the DEFM model. Moreover, we present an extension of DEFM that allows to integrate surface normals over non-trivial domains, e.g. featuring holes. Numerical results confirm desirable qualities of this method.

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In the present work, we consider the numerical approximation of pressureless gas dynamics in one and two spatial dimensions. Two particular phenomena are of special interest for us, namely ␦-shocks and vacuum states. A relaxation scheme is developed which reliably captures these phenomena. In one space dimension, we prove the validity of several stability criteria, i.e., we show that a maximum principle as well as the TVD property for the discrete velocity component and the validity of discrete entropy inequalities hold. Several numerical tests considering not only the developed first-order scheme but also a classical MUSCL-type second-order extension confirm the reliability and robustness of the relaxation approach. The article extends previous results on the topic: the stability conditions for relaxation methods for the pressureless case are refined, useful properties for the time stepping procedure are established, and two-dimensional numerical results are presented.

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