The Visvalingam algorithm: metrics, measures and heuristics

This paper provides the background necessary for a clear understanding of forthcoming papers relating to the Visvalingam algorithm for line generalisation, for example on the testing and usage of its implementations. It distinguishes the algorithm from implementation-specific issues to explain why it is possible to get inconsistent but equally valid output from different implementations. By tracing relevant developments within the now-disbanded Cartographic Information Systems Research Group (CISRG) of the University of Hull, it explains why a) a partial metric-driven implementation was, and still is, sufficient for many projects but not for others; b) why the Effective Area (EA) is a measure derived from a metric; c) why this measure (EA) may serve as a heuristic indicator for in-line feature segmentation and model-based generalisation; and, d) how metrics may be combined to change the order of point elimination. The issues discussed in this paper also apply to the use of other metrics. It is hoped that the background and guidance provided in this paper will enable others to participate in further research based on the algorithm

Bloch's function D for weighted effective areas : impact of tuning parameters

Abstract When Visvalingam’s algorithm was first presented, it was noted that it could be driven with any metric to suit different purposes, types of features and degrees of generalisation. It was illustrated with the concept of the effective area (EA). The intelligent application of metrics with and without weighting requires the prior segmentation of polylines with heterogeneous shapes into geometrically similar sections. Automatic line segmentation remains a research challenge. Meanwhile, different weighting functions have been used with different types of lines as noted in this paper. EA has a tendency to output spiky lines. Attempts have been made to give less weight to acute angles and favour obtuse angles. This yields visually more pleasing lines but has a tendency to chop elongated features, such as streams. Bloch’s function D (which implements the Visvalingam/ weighted area option in recent versions of Mapshaper) was chosen to investigate whether the parameter values could be tuned to improve the output. The tweaking of parameter values can give unexpected and unpredictable results. The results from a systematic approach to tweaking the parameters are presented here. These suggest that the chopping effect may be exacerbated by the use of inappropriate parameter values. By fine tuning Bloch’s function D, it was possible to derive pleasing smaller scale representations of convoluted coastlines with a complex network of creeks using under 5 percent of the original points. Although the output is not identical to manual generalisations of the same coastline, they may be acceptable (at this stage of research) for this type of coastline. Function D is not useful for generalising unsegmented coastlines, such as the 1: 50000 coastline of Humberside

Testing implementations of Visvalingam's algorithm for line generalisation

There are a growing number of open source and commercial implementations of the Visvalingam algorithm for line generalisation. The algorithm provides scope for implementation-specific interpretations, with different outcomes. This is inevitable and sometimes necessary and, they do not necessarily imply that an implementation is flawed. The only restriction is that the output must not be so inconsistent with the intent of the algorithm that it becomes unusable. This paper provides some ideas, data and sample output to help users compare the output from their implementations with those produced by Visvalingam. This may help them ascertain whether some problems they may encounter appear to be specific to their implementation or whether they are a general feature of the algorithm. This paper assesses the utility and limitations of the Mapshaper options for Visvalingam’s algorithm. Similar, but not identical, depictions of coastlines are produced by Visvalingam’s implementation and by Mapshaper. However, the programs produce very dissimilar output for the rectangular Koch island, also known as the quadratic Koch island - Mapshaper’s output is unbalanced for both its Visvalingam and Douglas-Peucker options. This suggests that the problem, which is not immediately obvious, is in some function inherited by both options. Both programs produce near identical output when Mapshaper’s Visvalingam/weighted area option was compared using coastlines. This suggests that the problem arises from Mapshaper’s treatment of equal-valued metrics; this can be changed. Implementers and users may wish to use the data and methods given in this paper to test their own implementations if and when necessary

Geometric data for testing implementations of point reduction algorithms : case study using Mapshaper v 0.2.28 and previous versions

There are several open source and commercial implementations of the Visvalingam algorithm for line generalisation. The algorithm provides scope for implementation-specific interpretations, with different outcomes. This is inevitable and sometimes necessary and, they do not imply that an implementation is flawed. The only restriction is that the output must not be so inconsistent with the intent of the algorithm that it becomes inappropriate. The aim of this paper is to place the algorithm within the literature, and demonstrate the value of the teragon-test for evaluating the appropriateness of implementations; Mapshaper v 0.2.28 and earlier versions are used for illustrative purposes. Data pertaining to natural features, such as coastlines, are insufficient for establishing whether deviations in output are significant. The teragon-test produced an unexpected loss of symmetry from both the Visvalingam and Douglas-Peucker options, making the tested versions unsuitable for some applications outside of cartography. This paper describes the causes, and discusses their implications. Mapshaper 0.3.17 passes the teragon test. Other developers and users should check their implementations using contrived geometric data, such as the teragon data provided in this paper, especially when the source code is not available. The teragon-test is also useful for evaluating other point reduction algorithms

Sources of variability in cartographers' deconstruction of fractals : paper presented at the 18 November 1998 meeting of the British Cartographic Society's Design Group at the University of Glasgow

CISRG discussion paper ; 1

Testing implementations of Visvalingam's algorithm for line generalisation

There are a growing number of open source and commercial implementations of the Visvalingam algorithm for line generalisation. The algorithm provides scope for implementation-specific interpretations, with different outcomes. This is inevitable and sometimes necessary and, they do not necessarily imply that an implementation is flawed. The only restriction is that the output must not be so inconsistent with the intent of the algorithm that it becomes unusable. This paper provides some ideas, data and sample output to help users compare the output from their implementations with those produced by Visvalingam. This may help them ascertain whether some problems they may encounter appear to be specific to their implementation or whether they are a general feature of the algorithm. This paper assesses the utility and limitations of the Mapshaper options for Visvalingam’s algorithm. Similar, but not identical, depictions of coastlines are produced by Visvalingam’s implementation and by Mapshaper. However, the programs produce very dissimilar output for the rectangular Koch island, also known as the quadratic Koch island - Mapshaper’s output is unbalanced for both its Visvalingam and Douglas-Peucker options. This suggests that the problem, which is not immediately obvious, is in some function inherited by both options. Both programs produce near identical output when Mapshaper’s Visvalingam/weighted area option was compared using coastlines. This suggests that the problem arises from Mapshaper’s treatment of equal-valued metrics; this can be changed. Implementers and users may wish to use the data and methods given in this paper to test their own implementations if and when necessary

Mapping Shape to Visuomotor Mapping: Learning and Generalisation of Sensorimotor Behaviour Based on Contextual Information

Humans can learn and store multiple visuomotor mappings (dual-adaptation) when feedback for each is provided alternately. Moreover, learned context cues associated with each mapping can be used to switch between the stored mappings. However, little is known about the associative learning between cue and required visuomotor mapping, and how learning generalises to novel but similar conditions. To investigate these questions, participants performed a rapid target-pointing task while we manipulated the offset between visual feedback and movement end-points. The visual feedback was presented with horizontal offsets of different amounts, dependent on the targets shape. Participants thus needed to use different visuomotor mappings between target location and required motor response depending on the target shape in order to ?hit? it. The target shapes were taken from a continuous set of shapes, morphed between spiky and circular shapes. After training we tested participants performance, without feedback, on different target shapes that had not been learned previously. We compared two hypotheses. First, we hypothesised that participants could (explicitly) extract the linear relationship between target shape and visuomotor mapping and generalise accordingly. Second, using previous findings of visuomotor learning, we developed a (implicit) Bayesian learning model that predicts generalisation that is more consistent with categorisation (i.e. use one mapping or the other). The experimental results show that, although learning the associations requires explicit awareness of the cues? role, participants apply the mapping corresponding to the trained shape that is most similar to the current one, consistent with the Bayesian learning model. Furthermore, the Bayesian learning model predicts that learning should slow down with increased numbers of training pairs, which was confirmed by the present results. In short, we found a good correspondence between the Bayesian learning model and the empirical results indicating that this model poses a possible mechanism for simultaneously learning multiple visuomotor mappings