The State of the Art in Cartograms

Cartograms combine statistical and geographical information in thematic maps, where areas of geographical regions (e.g., countries, states) are scaled in proportion to some statistic (e.g., population, income). Cartograms make it possible to gain insight into patterns and trends in the world around us and have been very popular visualizations for geo-referenced data for over a century. This work surveys cartogram research in visualization, cartography and geometry, covering a broad spectrum of different cartogram types: from the traditional rectangular and table cartograms, to Dorling and diffusion cartograms. A particular focus is the study of the major cartogram dimensions: statistical accuracy, geographical accuracy, and topological accuracy. We review the history of cartograms, describe the algorithms for generating them, and consider task taxonomies. We also review quantitative and qualitative evaluations, and we use these to arrive at design guidelines and research challenges

Density-equalizing maps for simply-connected open surfaces

In this paper, we are concerned with the problem of creating flattening maps of simply-connected open surfaces in $\mathbb{R}^3$. Using a natural principle of density diffusion in physics, we propose an effective algorithm for computing density-equalizing flattening maps with any prescribed density distribution. By varying the initial density distribution, a large variety of mappings with different properties can be achieved. For instance, area-preserving parameterizations of simply-connected open surfaces can be easily computed. Experimental results are presented to demonstrate the effectiveness of our proposed method. Applications to data visualization and surface remeshing are explored

Algorithms for necklace maps

Necklace maps visualize quantitative data associated with regions by placing scaled symbols, usually disks, without overlap on a closed curve (the necklace) surrounding the map regions. Each region is projected onto an interval on the necklace that contains its symbol. In this paper we address the algorithmic question how to maximize symbol sizes while keeping symbols disjoint and inside their intervals. For that we reduce the problem to a one-dimensional problem which we solve efficiently. Solutions to the one-dimensional problem provide a very good approximation for the original necklace map problem. We consider two variants: Fixed-Order, where an order for the symbols on the necklace is given, and Any-Order where any symbol order is possible. The Fixed-Order problem can be solved in O(n log n) time. We show that the Any-Order problem is NP-hard for certain types of intervals and give an exact algorithm for the decision version. This algorithm is fixed-parameter tractable in the thickness K of the input. Our algorithm runs in O(n log n + n2K4K) time which can be improved to O(n log n + nK2K) time using a heuristic. We implemented our algorithm and evaluated it experimentally. Keywords: Necklace maps; scheduling; automated cartograph

전근대 토지대장과 지적도의 대화형 분석을 위한 시각화 설계

학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2016. 2. 서진욱.We propose an interactive visualization design tool, called JigsawMap, for analyzing and mapping historical textual cadasters. A cadaster is an official register that records land properties (e.g., location, ownership, value and size) for land valuation and taxation. Such mapping of old and new cadasters can help historians understand the social and economic background of changes in land uses or ownership. JigsawMap can effectively connect the past land survey results to modern cadastral maps. In order to accomplish the connection process, three steps are performed: (1) segmentation of cadastral map, (2) visualization of textual cadastre, (3) and mapping interaction. We conducted usability studies and long term case studies to evaluate JigsawMap, and received positive responses. We summarize the evaluation results and present design guidelines for participatory design projects with historians. Followed by our study on JigsawMap, we further investigated on each components of our tool for more scalable map connection. First, we designed a hybrid algorithm to semi-automatically segment land pieces on cadastral map. The original JigsawMap provides interface for user to segment land pieces and the experiment result shows that segmentation algorithm accurately extracts the regions. Next, we reconsidered the visual encoding and simplified it to make textual cadastre more scalable. Since the former visual encoding relies on traditional map legend, the visual encoding can be selected based on user expert level. Finally, we redesigned layout algorithm to generate a better initial layout. We used evolution algorithm to articulate ambiguity problem of textual cadastre and the result less suffered from overlapping problem. Overall, our visualization design tool will provide an accurate segmentation result, give the user an option to select visual encoding that suits on their expert level, and generate more readable initial layout which gives an overview of cadastre layout.Chapter 1 Introduction 1 1.1 Background & Motivation 1 1.2 Main Contribution 7 1.3 Organization of the Dissertation 8 Chapter 2 Related Work 11 2.1 Map Data Visualization 11 2.2 Graph Layout Algorithms 13 2.3 Collaborative Map Editing Service 14 2.4 Map Image Segmentation 15 2.5 Premodern Cadastral Maps 17 2.6 Assessing Measures for Cartogram 18 Chapter 3 Visualizing and Mapping Premodern Textual Cadasters to Cadastral Maps 20 3.1 Textual Cadastre 21 3.2 Cadastral Maps 24 3.3 Paper-based Mapping Process and Obstacles 24 3.4 Task Flow in JigsawMap 26 3.5 Design Rationale 32 3.6 Evaluation 34 3.7 Discussion 40 3.8 Design Guidelines When Working with Historians 42 Chapter 4 Accurate Segmentation of Land Regions in Historical Cadastral Maps 44 4.1 Segmentation Pipeline 45 4.2 Preprocessing 46 4.3 Removal of Grid Line 48 4.4 Removal of Characters 52 4.5 Reconstruction of Land Boundaries 53 4.6 Generation of Polygons 55 4.7 Experimental Result 56 4.8 Discussion 59 Chapter 5 Approximating Rectangular Cartogram from Premodern Textual Cadastre 62 5.1 Challenges of the Textual Cadastre Layout 62 5.2 Quality Measures for Assessing Rectangular Cartogram 64 5.3 Quality Measures for Assessing Textual Cadastre 65 5.4 Graph Layout Algorithm 66 5.5 Results 72 5.6 Discussion 73 Chapter 6 Design of Scalable Node Representation for a Large Textual Cadastre 78 6.1 Motivation 78 6.2 Visual Encoding in JigsawMa 80 6.3 Challenges of Current Visual Encoding 81 6.4 Compact Visual Encoding 83 6.5 Results 84 6.6 Discussion 86 Chapter 7 Conclusion 88 Bibliography 90 Abstract in Korean 101Docto

Trends and concerns in digital cartography

CISRG discussion paper ;

Visualizing Set Relations and Cardinalities Using Venn and Euler Diagrams

In medicine, genetics, criminology and various other areas, Venn and Euler diagrams are used to visualize data set relations and their cardinalities. The data sets are represented by closed curves and the data set relationships are depicted by the overlaps between these curves. Both the sets and their intersections are easily visible as the closed curves are preattentively processed and form common regions that have a strong perceptual grouping effect. Besides set relations such as intersection, containment and disjointness, the cardinality of the sets and their intersections can also be depicted in the same diagram (referred to as area-proportional) through the size of the curves and their overlaps. Size is a preattentive feature and so similarities, differences and trends are easily identified. Thus, such diagrams facilitate data analysis and reasoning about the sets. However, drawing these diagrams manually is difficult, often impossible, and current automatic drawing methods do not always produce appropriate diagrams. This dissertation presents novel automatic drawing methods for different types of Euler diagrams and a user study of how such diagrams can help probabilistic judgement. The main drawing algorithms are: eulerForce, which uses a force-directed approach to lay out Euler diagrams; eulerAPE, which draws area-proportional Venn diagrams with ellipses. The user study evaluated the effectiveness of area- proportional Euler diagrams, glyph representations, Euler diagrams with glyphs and text+visualization formats for Bayesian reasoning, and a method eulerGlyphs was devised to automatically and accurately draw the assessed visualizations for any Bayesian problem. Additionally, analytic algorithms that instantaneously compute the overlapping areas of three general intersecting ellipses are provided, together with an evaluation of the effectiveness of ellipses in drawing accurate area-proportional Venn diagrams for 3-set data and the characteristics of the data that can be depicted accurately with ellipses