We present a new circular-arc cartogram model in which countries are drawn as polygons with circular arcs instead of straight-line segments. Given a political map and values associated with each country in the map, a cartogram is a distorted map in which the areas of the countries are proportional to the corresponding values. In the circular-arc cartogram model straight-line segments can be replaced by circular arcs in order to modify the areas of the polygons, while the corners of the polygons remain fixed. The countries in circular-arc cartograms have the aesthetically pleasing appearance of clouds or snowflakes, depending on whether their edges are bent outwards or inwards. This makes it easy to determine whether a country has grown or shrunk, just by its overall shape. We show that determining whether a given map and given area-values can be realized as a circular-arc cartogram is an NP-hard problem. Next we describe a heuristic method for constructing circular-arc cartograms, which uses a max-flow computation on the dual graph of the map, along with a computation of the straight skeleton of the underlying polygonal decomposition. Our method is implemented and produces cartograms that, while not yet perfectly accurate, achieve many of the desired areas in our real-world examples.
A popular method by Gastner and Newman @cite_6 projects the original map onto a distorted grid, calculated so that cell areas match the pre-defined values. This method relies on a physical model in which the desired areas are achieved via an iterative diffusion process. Flow moves from one country to another until a balanced distribution is reached, i.e., the density is the same everywhere. The cartograms produced this way are mostly readable and have no cartographic error. However, some countries may be deformed into shapes very different from those in the original map, and the complexity of the polygons can increase significantly.
@cite_6
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High-resolution population density maps are a critical component for global development efforts, including service delivery, resource allocation, and disaster response. Traditional population density efforts are predominantly survey driven, which are laborious, prohibitively expensive, infrequently updated, and inaccurate -- especially in remote areas. Furthermore, these maps are developed on a regional-basis where the methods used vary region to region, hence introducing notable spatio-temporal heterogeneity and bias. The advent of global-scale satellite imagery provides us with an unprecedented opportunity to create inexpensive, accurate, homogeneous, and rapidly updated population maps. To fulfill this vision, we must overcome both infrastructure and methodological obstacles. We propose a convolutional neural network approach that addresses some of the methodological challenges, while employing a publicly available, albeit low resolution, remote sensed product. The method converts satellite images into population density estimates. To explore both the accuracy and generalizability of our approach, we train our neural network on Tanzanian imagery and test the model on Kenyan data. We show that our method is able to generalize to unseen data and we improve upon the current state of the art by 177 percent. In this paper, we are concerned with the problem of creating flattening maps of simply connected open surfaces in @math . Using a natural principle of density diffusion in physics, we propose an effective algorithm for computing density-equalizing maps with any prescribed density distribution. By varying the initial density distribution, a large variety of flattening maps 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. Continuous area cartograms distort planimetric maps to produce a desired set of areas while preserving the topology of the original map. We present a computer algorithm which achieves the result iteratively with high accuracy. The approach uses a model of forces exerted from each polygon centroid, acting on coordinates in inverse proportion to distance. This algorithm can handle more realistic descriptions of polygon boundaries than previous algorithms and manual methods, thus enhancing visual recognition. For crowded scenes, the accuracy of object-based computer vision methods declines when the images are low-resolution and objects have severe occlusions. Taking counting methods for example, almost all the recent state-of-the-art counting methods bypass explicit detection and adopt regression-based methods to directly count the objects of interest. Among regression-based methods, density map estimation, where the number of objects inside a subregion is the integral of the density map over that subregion, is especially promising because it preserves spatial information, which makes it useful for both counting and localization (detection and tracking). With the power of deep convolutional neural networks (CNNs) the counting performance has improved steadily. The goal of this paper is to evaluate density maps generated by density estimation methods on a variety of crowd analysis tasks, including counting, detection, and tracking. Most existing CNN methods produce density maps with resolution that is smaller than the original images, due to the downsample strides in the convolution pooling operations. To produce an original-resolution density map, we also evaluate a classical CNN that uses a sliding window regressor to predict the density for every pixel in the image. We also consider a fully convolutional (FCNN) adaptation, with skip connections from lower convolutional layers to compensate for loss in spatial information during upsampling. In our experiments, we found that the lower-resolution density maps sometimes have better counting performance. In contrast, the original-resolution density maps improved localization tasks, such as detection and tracking, compared to bilinear upsampling the lower-resolution density maps. Finally, we also propose several metrics for measuring the quality of a density map, and relate them to experiment results on counting and localization.