268 lines
9.8 KiB
TeX
268 lines
9.8 KiB
TeX
\documentclass[a4paper]{article}
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\iffalse
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\usepackage[L7x,T1]{fontenc}
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\usepackage[lithuanian]{babel}
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\else
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\usepackage[T1]{fontenc}
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\usepackage[english]{babel}
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\fi
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\usepackage[utf8]{inputenc}
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\usepackage{a4wide}
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\usepackage{csquotes}
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\usepackage[maxbibnames=99,style=authoryear]{biblatex}
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\usepackage[pdfusetitle]{hyperref}
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\usepackage{enumitem}
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\addbibresource{bib.bib}
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\usepackage{caption}
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\usepackage{subcaption}
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\usepackage{gensymb}
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\usepackage{varwidth}
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\usepackage{tabularx}
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\usepackage{float}
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\usepackage{tikz}
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\usetikzlibrary{er,positioning}
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\input{version}
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\newcommand{\DP}{Douglas \& Peucker}
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\newcommand{\VW}{Visvalingam--Whyatt}
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\newcommand{\WM}{Wang--M{\"u}ller}
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\title{
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Cartografic Generalization of Lines \\
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(example of rivers) \\ \vspace{4mm}
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}
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\iffalse
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https://bost.ocks.org/mike/simplify/
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http://bl.ocks.org/msbarry/9152218
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small scale: 1:XXXXXX
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large scale: 1:XXX
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a4: 210x297mm
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a6: 105x148xmm
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a7: 74x105mm
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a8: 52x74mm
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connect rivers first to a single polylines:
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- some algs can preserve connectivity, some not.
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ideal hypothesis: mueller algorithm + topology may fully realize cartographic generalization tasks.
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what scales and what distances?
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= Intro: Aktualumas
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FOSS nėra realizuotas tinkamas kartografinio realizavimo algoritmas (2–3 sakiniai). Kad kartografai turėtų
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įrankį upių generalizavimui.
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Bazė: imame tai, ką dabar turi kartografai įrankių paletėj.
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Imti mažus upės vingius. Paimti mažas atkarpėles ir palyginti su originalia.
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Todėl, kad nėra kilpų.
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\fi
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\author{Motiejus Jakštys}
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\date{
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\vspace{10mm}
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Version: \VCDescribe \\ \vspace{4mm}
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Generated At: \GeneratedAt
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}
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\begin{document}
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\maketitle
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\begin{abstract}
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\label{sec:abstract}
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Current open-source line generalization solutions have their roots in
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mathematics and geometry, thus emit poor cartographic output. Therefore, if one
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is using open-source technology to create a small-scale map, downscaled lines
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(e.g. rivers) will not be professionally scale-adjusted. This paper explores
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line generalization algorithms and suggests one for an avid GIS developer to
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implement. Once it is usable from within open-source GIS software (e.g. QGIS or
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PostGIS), rivers on these small-scale maps will look professionally downscaled.
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\end{abstract}
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\newpage
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\tableofcontents
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\listoffigures
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\section{Introduction}
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\label{sec:introduction}
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Cartographic generalization is one of the key processes of creating small-scale
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maps: how can one approximate object features, without losing its main
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cartographic properties? The problem is universally challenging across many
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geographical entities (\cite{muller1991generalization},
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\cite{mcmaster1992generalization}). This paper focuses on line generalization
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for natural rivers: which algorithm should be picked when down-scaling a river
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map?
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We examine readily available open-source algorithms using a concrete
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cartographical example, and make a suggestion on which algorithm could be
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implemented next.
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\section{What's available}
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Line generalization algorithms are well studied, but expose deficiencies in
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large-scale reduction (\cite{monmonier1986toward}, \cite{mcmaster1993spatial}).
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Most of these techniques are based on mathematical shape representation, rather
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than cartographic characteristics of the line.
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A number of cartographic line generalization algorithms have been researched,
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which claim to better process cartographic objects like lines. These fall into
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two rough categories:
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\begin{itemize}
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\item Cartographic knowledge was encoded to an algorithm (bottom-up
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approach). One among these are \cite{wang1998line}.
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\item Mathematical shape transformation which yields a more
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cartographically suitable down-scaling. E.g. \cite{jiang2003line},
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\cite{dyken2009simultaneous}, \cite{mustafa2006dynamic},
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\cite{nollenburg2008morphing}.
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\end{itemize}
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During research for the mentioned papers, code has been written for all of the
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algorithms above, however, is not to be found in a usable form.
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\cite{wang1998line} is available in a commercial product, but the author of
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this paper does not have means to try it.
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To sum up, this paper will be comparing the following algorithms:
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\begin{itemize}
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\item \cite{douglas1973algorithms} via
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\href{https://postgis.net/docs/ST_Simplify.html}{PostGIS Simplify}.
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\item \cite{visvalingam1993line} via
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\href{https://postgis.net/docs/ST_SimplifyVW.html}{PostGIS SimplifyVW}.
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\end{itemize}
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\section{Visual comparison}
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Lakaja and large part of Žeimena (see figure~\ref{fig:zeimena} on
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page~\pageref{fig:zeimena}) will be used, because the river exhibits both both
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straight and curved shape, is a combination of two curly rivers, and author's
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familiarity with the location.
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\begin{figure}[H]
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\centering
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\includegraphics[width=148mm]{zeimena-pretty}
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\caption{Lakaja and Žeimena}
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\label{fig:zeimena}
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\end{figure}
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To visually evaluate the Žeimena sample, examples for {\DP} and {\VW}
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were created using the following parameters:
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\begin{enumerate}[label=(\Roman*)]
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\item {\DP} tolerance: $tolerance := 125 * 2^n, n = 0,1,...,5$.
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\item {\VW} tolerance: $vwtolerance = tolerance ^ 2$\label{itm:2}.
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\end{enumerate}
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Parameter~\ref{itm:2} requires explanation. Tolerance for {\DP} is specified in
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linear units, in this case, meters. Tolerance for {\VW} is specified in area
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units $m^2$. As author was not able to locate formal comparisons between the
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two (i.e. how to calculate one tolerance value from the other, so the results
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are comparable?), {\DP} tolerance was arbitrarily squared and fed to {\VW}. To
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author's eye, this provides comparable and reasonable results, though could be
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researched.
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As can be observed in table~\ref{tab:dp-vs-vw} on page~\pageref{tab:dp-vs-vw},
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both simplication algorithms convert bends to chopped lines. This is especially
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visible in tolerances 250 and 500. In a more robust simplification algorithm,
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the larger tolerance, the larger the bends on the original map should be
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retained.
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\begin{figure}[H]
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\renewcommand{\tabularxcolumn}[1]{>{\center\small}m{#1}}
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\begin{tabularx}{\textwidth}{ p{1.5cm} | X | X | }
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Tolerance &
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Douglas \& Peucker &
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Visvalingam-Whyatt \tabularnewline \hline
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125 &
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\includegraphics[width=\linewidth]{zeimena-douglas-125} &
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\includegraphics[width=\linewidth]{zeimena-visvalingam-125} \tabularnewline \hline
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250 &
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\includegraphics[width=.5\linewidth]{zeimena-douglas-250} &
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\includegraphics[width=.5\linewidth]{zeimena-visvalingam-250} \tabularnewline \hline
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500 &
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\includegraphics[width=.25\linewidth]{zeimena-douglas-500} &
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\includegraphics[width=.25\linewidth]{zeimena-visvalingam-500} \tabularnewline \hline
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1000 &
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\includegraphics[width=.125\linewidth]{zeimena-douglas-1000} &
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\includegraphics[width=.125\linewidth]{zeimena-visvalingam-1000} \tabularnewline \hline
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2000 &
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\includegraphics[width=.0625\linewidth]{zeimena-douglas-2000} &
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\includegraphics[width=.0625\linewidth]{zeimena-visvalingam-2000} \tabularnewline \hline
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4000 &
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\includegraphics[width=.0625\linewidth]{zeimena-douglas-4000} &
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\includegraphics[width=.0625\linewidth]{zeimena-visvalingam-4000} \tabularnewline \hline
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\end{tabularx}
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\caption{{\DP} and {\VW} side-by-side visual comparison}
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\label{tab:dp-vs-vw}
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\end{figure}
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To sum up, both {\VW} and {\DP} simplify the lines, but their cartographic
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output poorly represents lines and bends. Where to look for better output?
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\subsection{Combining bends}
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Consecutive small bends should be combined into larger bends, and that is one
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of the least developed aspects of automatic line generalization, according to
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\cite{miuller1995generalization}. {\WM} encoded this process to an algorithm.
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Imagine there are two small bends close to each other, similar to
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figure~\ref{pic:sinewave} on page~\pageref{pic:sinewave}, and one needs
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to generalize it. The bends are too large to ignore replace them with a
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straight line, but too small to retain both and retain their complexity.
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\begin{figure}[h]
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\centering
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\includegraphics[width=52mm]{sinewave}
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\caption{Example river bend that should be generalized}
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\label{pic:sinewave}
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\end{figure}
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When one applies {\DP} to figure~\ref{pic:sinewave}, either both bends remain,
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or become a straight line.
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\begin{figure}[h]
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\centering
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\includegraphics[width=52mm]{sinewave-douglas-5}
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\caption{Example bend, generalized}
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\label{pic:sinewave-douglas-5}
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\end{figure}
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\section{Related Work and future suggestions}
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\label{sec:related_work}
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\cite{stanislawski2012automated} studied different types of metric assessments,
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such as Hausdorff distance, segment length, vector shift, surface displacement,
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and tortuosity for the generalization of linear geographic elements. This
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research can provide references to the appropriate settings of the line
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generalization parameters for the maps at various scales.
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As noted in parameter~\ref{itm:2} on page~\pageref{itm:2}, it would be useful
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to have a formula mapping {\DP} tolerance to {\VW}. That way, visual
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comparisons between line simplification algorithms could be more objective.
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\section{Conclusions}
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\label{sec:conclusions}
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We have practically evaluated two readily available line simplification
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algorithms with a river sample: {\VW} and {\DP}, and outlined their
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deficiencies. We are suggesting to implement {\WM} and compare it to the other
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two.
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\printbibliography
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\end{document}
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