Optimization-Based Construction of Quadrilateral Table Cartograms

A quadrilateral table cartogram is a rectangle-shaped figure that visualizes table-form data; quadrilateral cells in a table cartogram are transformed to express the magnitude of positive weights by their areas, while maintaining the adjacency of cells in the original table. However, the previous construction method is difficult to implement because it consists of multiple operations that do not have a unique solution and require complex settings to obtain the desired outputs. In this article, we propose a new construction for quadrilateral table cartograms by recasting the construction as an optimization problem. The proposed method is formulated as a simple minimization problem to achieve mathematical clarity. It can generate quadrilateral table cartograms with smaller deformation of rows and columns, thereby aiding readers to recognize the correspondence between table cartograms and original tables. In addition, we also propose a means of sorting rows and/or columns prior to the construction of table cartograms to reduce excess shape deformation. Applications of the proposed method confirm its capability to output table cartograms that clearly visualize the characteristics of datasets

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

Implementing an Agro-Environmental Information System (AEIS) Based on GIS, Remote Sensing, and Modelling -- A case study for rice in the Sanjiang Plain, NE-China

Information on agro-ecosystems is crucial for understanding the agricultural production and its impacts on the environment, especially over large agricultural areas. The Sanjiang Plain (SJP), covering an area of 108 829 km², is a critical food base located in NE-China. Rice, soya bean and maize are the major crops in the SJP which are sold as commercial grain throughout China. The aim of this study is to set up an Agro-Environmental Information System (AEIS) for the SJP by employing the technologies of geographic information systems (GIS), remote sensing (RS), and agro-ecosystem modelling. As the starting step, data carrying interdisciplinary information from multiple sources are organized and processed. For an AEIS, geospatial data have to be acquired, organized, operated, and even regenerated with good positioning conditions. Georeferencing of the multi-source data is mandatory. In this thesis, high spatial accuracy TerraSAR-X imagery was used as a reference for georeferencing raster satellite data and vector GIS topographic data. For the second step, the georeferenced multi-source data with high spatial accuracy were integrated and categorized using a knowledge-based classifier. Rice was analysed as an example crop. A rice area map was delineated based on a time series of three high resolution FORMOSAT-2 (FS-2) images and field observed GIS topographic data. Information on rice characteristics (i.e., biomass, leaf area index, plant nitrogen concentration and plant nitrogen uptake) was derived from the multi-temporal FS-2 images. Spatial variability of rice growing status on a within-field level was well detected. As the core part of the AEIS, an agro-ecosystem modelling was then applied and subsequently crops and the environmental factors (e.g., climate, soil, field management) are linked together through a series of biochemical functions inherent in the modelling. Consequently, the interactions between agriculture and the environment are better interpreted. In the AEIS for the SJP, the site-specific mode of the DeNitrification-DeComposition (DNDC) model was adapted on regional scales by a technical improvement for the source code. By running for each pixel of the model input raster files, the regional model assimilates raster data as model inputs automatically. In this study, detailed soil data, as well as the accurate field management data in terms of crop cultivation area (i.e. rice) were used as model inputs to drive the regional model. Based on the scenario optimized from field observation, rice yields over the Qixing Farm were estimated and the spatial variability was well detected. For comparison, rice yields were derived from multi-temporal FS-2 images and the spatial patterns were analysed. As representative environmental effects, greenhouse gas of nitrous oxide (N2O) and carbon dioxide (CO2) emitted from the paddy rice fields were estimated by the regional model. This research demonstrated that the AEIS is effective in providing information about (i) agriculture on the region, (ii) the impacts of agricultural practices on the environment, and (iii) simulation scenarios for sustainable strategies, especially for the regional areas (e.g. the SJP) that is lacking of geospatial data