Evaluating Cartogram Effectiveness

Cartograms are maps in which areas of geographic regions (countries, states) appear in proportion to some variable of interest (population, income). Cartograms are popular visualizations for geo-referenced data that have been used for over a century and that make it possible to gain insight into patterns and trends in the world around us. Despite the popularity of cartograms and the large number of cartogram types, there are few studies evaluating the effectiveness of cartograms in conveying information. Based on a recent task taxonomy for cartograms, we evaluate four major different types of cartograms: contiguous, non-contiguous, rectangular, and Dorling cartograms. Specifically, we evaluate the effectiveness of these cartograms by quantitative performance analysis, as well as by subjective preferences. We analyze the results of our study in the context of some prevailing assumptions in the literature of cartography and cognitive science. Finally, we make recommendations for the use of different types of cartograms for different tasks and settings

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

The use of cartograms for BGS data and information representation

Cartograms are shown to be superior to both choropleth maps and bar charts, as they are designed to deliver geospatial statistics effectively and efficiently. This report presents the results of research in establishing the potential for the use of area cartograms for science information delivery. The research involved establishing an overview of all the types of cartogram used; noting the types of data used in their creation and identifying similar sources of data that may prove appropriate for use in cartograms. Test examples were created and presented along with an evaluation as to their effectiveness and efficiency in communicating spatially orientated datasets. The work was carried out as part of the Data Representation and Presentation project for the Geospatial Capture and Solutions team. This forms part of a wider research project investigating new ways in which BGS can display science and information more effectively to a broad range of audiences

Computing Fast and Scalable Table Cartograms for Large Tables

Given an m x n table T of positive weights and a rectangle R with an area equal to the sum of the weights, a table cartogram computes a partition of R into m x n convex quadrilateral faces such that each face has the same adjacencies as its corresponding cell in T, and has an area equal to the cell's weight. In this thesis, we explored different table cartogram algorithms for a large table with thousands of cells and investigated the potential applications of large table cartograms. We implemented Evans et al.'s table cartogram algorithm that guarantees zero area error and adapted a diffusion-based cartographic transformation approach, FastFlow, to produce large table cartograms. We introduced a constraint optimization-based table cartogram generation technique, TCarto, leveraging the concept of force-directed layout. We implemented TCarto with column-based and quadtree-based parallelization to compute table cartograms for table with thousands of cells. We presented several potential applications of large table cartograms to create the diagrammatic representations in various real-life scenarios, e.g., for analyzing spatial correlations between geospatial variables, understanding clusters and densities in scatterplots, and creating visual effects in images (i.e., expanding illumination, mosaic art effect). We presented an empirical comparison among these three table cartogram techniques with two different real-life datasets: a meteorological weather dataset and a US State-to-State migration flow dataset. FastFlow and TCarto both performed well on the weather data table. However, for US State-to-State migration flow data, where the table contained many local optima with high value differences among adjacent cells, FastFlow generated concave quadrilateral faces. We also investigated some potential relationships among different measurement metrics such as cartographic error (accuracy), the average aspect ratio (the readability of the visualization), computational speed, and the grid size of the table. Furthermore, we augmented our proposed TCarto with angle constraint to enhance the readability of the visualization, conceding some cartographic error, and also inspected the potential relationship of the restricted angles with the accuracy and the readability of the visualization. In the output of the angle constrained TCarto algorithm on US State-to-State migration dataset, it was difficult to identify the rows and columns for a cell upto 20 degree angle constraint, but appeared to be identifiable for more than 40 degree angle constraint

Alternate distance metrics in spatial statistics: radial adjustment of vectors in Euclidean networks

The propensity of utilizing Euclidean distance metrics when calculating spatial statistics generally ignores the underlying connectivity between the features under analysis. A procedure is developed to compensate for the distance discrepancies inherent in spatial statistics algorithms by temporarily transforming the model features into an alternate distance metric space that more realistically represents the functional connectivity distance between spatial elements. -- Comparative statistical analysis results between the adjusted and un-adjusted spatial arrangements suggest that statistical measures that are strictly distance based can display dramatic differences in the magnitude of these results. Global autocorrelation measures display much less variation while local autocorrelation measures can result in regions of expanded spatial clustering

Dynamic visualization of geographic networks using surface deformations /

Visualization techniques for geographic data show vast variations which are well-developed over centuries. While most of the known techniques are sound for low dimensional data sets, few techniques exist for visualization of high dimensional data within the geographic framework. This thesis investigates visualization of temporal. high dimensional network data within the geographic context. The resulting visualization system employs network visualization techniques in conjunction with cartographic visualization methods for providing a qualitative feel for the data, while conventional methods are employed for detailed examination. In turn, the visualization facilitates comprehension of non-spatial variables with respect to the geographic context

Interactive visualization for missing values, time series, and areal data

Visualization is widely used to explore data, examine variation, reveal trends, and diagnose models. Furthermore, interactive plots can re-focus the view to features of interest, drill down into a fine resolution, query or lookup elements, look at data from various directions, and connect plots with model analysis. However, for specific data types and specific exploratory purposes, the general interactions like brushing, panning, zooming, and querying can be insufficient. The lack of a grammar for interactive graphics makes differences between the user interactions on data and on the view of data difficult to delineate. This thesis partially addresses these issues and fills gaps in methodology from three application areas: missing values, temporal/longitudinal data, and areal data. Interactive graphics plays different roles in three areas. In missing data analysis, many imputation methods have been developed but little has been done for exploring the missing value structure to determine the missingness pattern, or to evaluate the imputations. This research addresses this gap, focusing on an interactive tool to explore missings, check the missingness assumptions, and compare imputation methods. For temporal and longitudinal data, using static plots is inadequate for exploring the trends, seasonality or unusual individuals, especially when the data set is large. This research develops special interactions and discusses the elements and pipeline in the interactivity construction. It is implemented in the R package, cranvastime, with details on how to use for a number of datasets. For the areal data, cartograms are widely used but there is no universally good algorithm for cartogram construction or evaluation. This research proposes an evaluation criterion and utilizes an interactive interface to optimize the visualization between the original shape-reserved map and area-reserved cartogram

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