An important task of pattern recognition and map generalization is to partition a set of disjoint polygons into groups and to aggregate the polygons within each group to a representative output polygon. We introduce a new method for this task called bicriteria shapes. Following a classical approach, we define the output polygons by merging the input polygons with a set of triangles that we select from a conforming Delaunay triangulation of the input polygons’ exterior. The innovation is that we control the selection of triangles with a bicriteria optimization model that is efficiently solved via graph cuts. In particular, we minimize a weighted sum that combines the total area of the output polygons and their total perimeter. In a basic problem, we ask for a single solution that is optimal for a preset parameter value. In a second problem, we ask for a set containing an optimal solution for every possible value of the parameter. We discuss how this set can be approximated with few solutions and show that it is hierarchically nested. Hence, the output is a hierarchical clustering that corresponds to multiple levels of detail. An evaluation with building footprints as input and a comparison with α-shapes that are based on the same underlying triangulation conclude the article. An advantage of bicriteria shapes compared to α-shapes is that the sequence of solutions for decreasing values of the parameter is monotone with respect to the total perimeter of the output polygons, resulting in a monotonically decreasing visual complexity.

Euler diagrams are an intuitive and popular method to visualize set-based data. In a Euler diagram, each set is represented as a closed curve, and set intersections are shown by curve overlaps. However, Euler diagrams are not visually scalable and automatic layout techniques struggle to display real-world data sets in a comprehensible way. Prior state-of-the-art approaches can embed Euler diagrams by splitting a closed curve into multiple curves so that a set is represented by multiple disconnected enclosed areas. In addition, these methods typically result in multiple curve segments being drawn concurrently. Both of these features significantly impede understanding. In this paper, we present a new and scalable method for embedding Euler diagrams using set merges. Our approach simplifies the underlying data to ensure that each set is represented by a single, connected enclosed area and that the diagram is drawn without curve concurrency, leading to well formed and understandable Euler diagrams.

This article presents an approach for the automatic semantic segmentation of floorplan images, predicting room boundaries (walls, doors, windows) and semantic labels of room types. A multi-task network was designed to represent and learn inherent dependencies by combining a Convolutional Neural Network to generate suitable features with a Graph Convolutional Network (GCN) to capture long-range dependencies. In particular, a Self-Constructing Graph module is applied to automatically induce an input graph for the GCN. Experiments on different datasets demonstrate the superiority and effectiveness of the multi-task network compared to state-of-the-art methods. The accurate results not only allow for subsequent vectorization of the existing floorplans but also for automatic inference of layout graphs including connectivity and adjacency relations. The latter could serve as basis to automatically sample layout graphs for architectural planning and design, predict missing links for unobserved parts for as-built building models and learn important latent topological and architectonic patterns.

Can a given set system be drawn as an Euler diagram? We present the first method that correctly decides this question for arbitrary set systems if the Euler diagram is required to represent each set with a single connected region. If the answer is yes, our method constructs an Euler diagram. If the answer is no, our method yields an Euler diagram for a simplified version of the set system, where a minimum number of set elements have been removed. Further, we integrate known wellformedness criteria for Euler diagrams as additional optimization objectives into our method. Our focus lies on the computation of a planar graph that is embedded in the plane to serve as the dual graph of the Euler diagram. Since even a basic version of this problem is known to be NP-hard, we choose an approach based on integer linear programming (ILP), which allows us to compute optimal solutions with existing mathematical solvers. For this, we draw upon previous research on computing planar supports of hypergraphs and adapt existing ILP building blocks for contiguity-constrained spatial unit allocation and the maximum planar subgraph problem. To generate Euler diagrams for large set systems, for which the proposed simplification through element removal becomes indispensable, we also present an efficient heuristic. We report on experiments with data from MovieDB and Twitter. Over all examples, including 850 non-trivial instances, our exact optimization method failed only for one set system to find a solution without removing a set element. However, with the removal of only a few set elements, the Euler diagrams can be substantially improved with respect to our wellformedness criteria.

As one of the most well-known forms of active mobility, cycling is an environmentally friendly way to explore a destination, becoming increasingly prevalent worldwide. However, safety is the most severe issue facing cyclists and the essential factor for people who are hesitant to use bikes. In this context, we propose a safety assessment method for cycling routes in urban environments. This work presents how to automatically generate a safe cycling map integrating volunteered geographic information with GIS analysis. We start by extracting the indicators that can possibly contribute to cycling safety from OpenStreetMap. Then, we set up a multivariate linear regression equation to solve the importance of indicators. Afterward, we generate a weighted graph model that represents cycling safety. Taking the City of Bonn, Germany, as an example, we implement our approach for this region. The experiment results show that Bonn is a city for safe cycling, confirming the claim that Bonn is a bike-friendly city. Our findings can also be used to plan the safest route for cycling, thereby enhancing the overall biking experience in Bonn.

Footprints of buildings can provide cues about architectural styles and functional types. Learning such latent thematic information from geometry is relevant for various applications, such as urban planning and map generalization. A common task in this context is to cluster a set of building footprints based on their shape characteristics. In this paper, we present a novel method for this task which is based on concepts of graph similarity. We use a graph similarity measure that combines ideas from the Weisfeiler-Lehman-method and optimal transport theory. For the final clustering, we use spectral clustering. To obtain a meaningful graph representation, we propose two algorithms that transform the medial axis of a building footprint into a skeleton graph. We tested our algorithm on a data set from Boston and performed a small user study, where we also compared the results to an existing feature-based clustering method. The study gives a first hint that the results of our algorithm are in line with human similarity perception. Future work is needed to improve the stability of the proposed similarity measure and to confirm our findings with more extensive experiments.

Building footprints are a prerequisite for many tasks such as urban mapping and planning. Such structures are mostly derived using airborne laser scanning which reveals rather roof structures than the underlying hidden footprint boundary. This paper introduces an approach to extract a 2D building boundary from a 3D point cloud stemming from either terrestrial scanning or via close-range sensing using a mobile platform, e.g. drone. To this end, a pipeline of methods including non-parametric kernel density estimation (KDE) of an underlying probability density function, a solution of the Travelling Salesperson Problem (TSP), outlier elimination and line segmentation are presented to extract the underlying building footprint. KDE turns out to be suitable to automatically determine a horizontal cut in the point cloud. An ordering of the resulting points in this cut using a shortest possible tour based on TSP allows for the application of existing line segmentation algorithms, otherwise dedicated to indoor segmentation. Outliers in the resulting segments are removed using Density-Based Spatial Clustering of Applications with Noise (DBSCAN). The segments are then generalized leading to the final footprint geometry. We applied our approach on real-world examples and achieved an IoU between 0.930 and 0.998 assessed by ground truth footprints from both authoritative and volunteered geographic information (VGI) data.

Visualizing sets of elements and their relations is an important research area in information visualization. In this paper, we present MosaicSets: a novel approach to create Euler-like diagrams from non-spatial set systems such that each element occupies one cell of a regular hexagonal or square grid. The main challenge is to find an assignment of the elements to the grid cells such that each set constitutes a contiguous region. As use case, we consider the research groups of a university faculty as elements, and the departments and joint research projects as sets. We aim at finding a suitable mapping between the research groups and the grid cells such that the department structure forms a base map layout. Our objectives are to optimize both the compactness of the entirety of all cells and of each set by itself. We show that computing the mapping is NP-hard. However, using integer linear programming we can solve real-world instances optimally within a few seconds. Moreover, we propose a relaxation of the contiguity requirement to visualize otherwise non-embeddable set systems. We present and discuss different rendering styles for the set overlays. Based on a case study with real-world data, our evaluation comprises quantitative measures as well as expert interviews.

The physical arrangement of soil compounds in microaggregates is important in many ways, e.g. by controlling soil stability and C sequestration. However, little is known about the spatial arrangement of organic and inorganic compounds in soil microaggregates, due to the lack of in-situ analyses in undisturbed material. Here we hypothesize that microaggregates are spatially organized, resulting in deterministic, predictable spatial patterns of different organic matter and mineral phases and that this organization depends on the abundance of specific phases such as on clay mineral content. We separated the water stable, occluded large and small microaggregate fractions from Ap horizons of a sequence of sandy to loamy Luvisols (19 to 35% clay, Scheyern, Germany) and subjected in total 60 individual aggregates to elemental mapping by electron probe micro analysis (EPMA), which recorded C, N, P, Al, Fe, Ca, K, Cl, and Si contents at µm scale resolution. Spatial arrangements of soil organic matter and soil minerals were extracted using cluster analyses. We found a pronounced heterogeneity in aggregate structure and composition, which was not reproducible and largely independent from clay content in soil. However, neighborhood analyses revealed close spatial correlations between organic matter debris (C:N app. 100:10) and microbial organic matter (C:N app. 10:1) indicating a spatial relationship between source and consumer. There was no systematic relationship between soil minerals and organic matter, suggesting that well-established macroscale correlations between contents of pedogenic oxides and clay minerals with soil organic matter storage do not apply to soil microaggregates.

We present a new method for the task of detecting groups of polygons in a given geographic data set and computing a representative polygon for each group. This task is relevant in map generalization where the aim is to derive a less detailed map from a given map. Following a classical approach, we define the output polygons by merging the input polygons with a set of triangles that we select from a constrained Delaunay triangulation of the input polygons’ exterior. The innovation of our method is to compute the selection of triangles by solving a bicriteria optimization problem. While on the one hand we aim at minimizing the total area of the outputs polygons, we aim on the other hand at minimizing their total perimeter. We combine these two objectives in a weighted sum and study two computational problems that naturally arise. In the first problem, the parameter that balances the two objectives is fixed and the aim is to compute a single optimal solution. In the second problem, the aim is to compute a set containing an optimal solution for every possible value of the parameter. We present efficient algorithms for these problems based on computing a minimum cut in an appropriately defined graph. Moreover, we show how the result set of the second problem can be approximated with few solutions. In an experimental evaluation, we finally show that the method is able to derive settlement areas from building footprints that are similar to reference solutions. 2012 ACM Subject Classification Information systems → Geographic information systems; Theory of computation → Computational geometry

The automatic generation of travel‐time maps is a prerequisite for many fields of application such as tourist assistance and spatial decision support systems, for example to analyze the accessibility of health and social facilities. The task is to determine outlines of zones that are reachable from a user’s location in a given amount of time. In this work we focus on travel‐time maps with a formally guaranteed SEPARATION PROPERTY in the sense that a zone exactly contains the part of the road network that is reachable within a pre‐defined time from a given starting point and start time. In contrast to other automated methods that create travel‐time maps, our approach generates schematized travel‐time maps that reduce the visual complexity by representing each zone by an octilinear polygon, that is, the edges of the polygons use only eight pre‐defined orientations. We aim for octilinear polygons with a small number of bends to further optimize the legibility of the map. The reachable parts of the road network are determined by the integration of timetable information for different modes of public transportation, for example buses, trains or ferries, and pedestrian walkways based on a multimodal time‐expanded network. Moreover, the travel‐time maps generated visualize multiple travel times using a map overlay of different time zones and taking natural barriers such as rivers into account. In experiments on real‐world data we compare our schematic visualizations to travel‐time maps created with other visualization techniques with respect to simple but robust quality measures such as the number of bends and the perimeter of the zones.

Knowing the distance to nearby objects is crucial for autonomous cars to navigate safely in everyday traffic. In this paper, we investigate monocular depth estimation, which advanced substantially within the last years and is providing increasingly more accurate results while only requiring a single camera image as input. In line with recent work, we use an encoder-decoder structure with so-called packing layers to estimate depth values in a self-supervised fashion. We propose integrating a joint pre-training of semantic segmentation plus depth estimation on a dataset providing semantic labels. By using a separate semantic decoder that is only needed for pre-training, we can keep the network comparatively small. Our extensive experimental evaluation shows that the addition of such pre-training improves the depth estimation performance substantially. Finally, we show that we achieve competitive performance on the KITTI dataset despite using a much smaller and more efficient network.

In the last decades, there has been an increasing interest in animal protection and welfare issues. Heart rate variability (HRV) measurement with portable heart rate monitors on cows has established itself as a suitable method for assessing physiological states. However, more forward-looking technologies, already successfully applied to evaluate HRV data, are pushing the market. This study examines the validity and usability of collecting HRV data by exchanging the Polar watch V800 as a receiving unit of the data compared to a custom smartphone application on cows. Therefore, both receivers tap one signal sent by the Polar H7 transmitter simultaneously. Furthermore, there is a lack of suitable methods for the preparation and calculation of HRV parameters, especially for livestock. A method is presented for calculating more robust time domain HRV parameters via median formation. The comparisons of the respective simultaneous recordings were conducted after artifact correction for time domain HRV parameters. High correlations (r = 0.82–0.98) for cows as well as for control data set in human being (r = 0.98–0.99) were found. The utilization of smart devices and the robust method to determine time domain HRV parameters may be suitable to generate valid HRV data on cows in field-based settings.