372 lines
14 KiB
TeX
372 lines
14 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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\usepackage[toc,page,title]{appendix}
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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 using free software \\
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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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a5: 148x210mm
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a6: 105x148xmm
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a7: 74x105mm
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a8: 52x74mm
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Crossing:
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Xmin: 623306
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Ymin: 6109635
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Xmax: 625526
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Ymax: 6111210
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623306 6109635 625526 6111210
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Crossing wxh: 2220, 1575 (m)
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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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Zeimena extents: [606922,6097557,627230,6126362]
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20308 x 28805 (w x h)
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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
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one is using open-source technology to generalize cartographic objects,
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their downscaled counterparts will be incorrectly scale-adjusted. This
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paper explores the available down-scaling implementations, highlights some
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of their deficiencies, and suggests a viable algorithm for an avid GIS
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developer. Once the new algorithm becomes usable from within open-source
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GIS software (e.g. QGIS or PostGIS), small-scale maps created by free
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software will have a chance to be of higher quality.
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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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\newpage
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\section{Introduction}
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\label{sec:introduction}
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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 articles, prototype code has been written for
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most of the algorithms. However, none of them seem to be available for use
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except for the two "classical" ones -- {\DP} and {\VW}.
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\cite{wang1998line} is an algorithm specifically created for cartographic
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generalization and available for general use, though it is only currently
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available in a commercial product. This poses a problem for map creation in
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open source software: there is not a similar high-quality simplification
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algorithm to create down-scaled maps, so any cartographic work, which uses line
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generalization as part of its processing, will be of sub-par quality.
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We believe that availability of high-quality open-source tools is an important
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foundation for future cartographic experimentation and development, thus it
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it benefits the cartographic society as a whole.
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This paper will be reviewing and comparing two widely available algorithms that
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are often used for line generalization:
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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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Review of the available algorithms will be followed by desiderata for a
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possible open-source addition. In the end, we will issue a recommendation,
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which algorithm can be picked up and implemented by an avid GIS developer.
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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 as inputs to the generalization
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algorithms, because the river exhibits both both straight and curved shape, is
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a combination of two curly rivers, and author's familiarity with the location.
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Since the map area is large (approx. 20km by 28km, scale $1:300 000$), we will
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also review a subset of the area of approx 2200m by 1575m. The zoomed-in
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version will help explain some of the deficiencies in the reviewed algorithms.
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\begin{figure}[h]
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\centering
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\includegraphics[width=67.5mm]{zeimena}
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\caption{Lakaja and Žeimena, with marked river crossing area, $1:300 000$}
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\label{fig:zeimena}
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\end{figure}
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\begin{figure}[h]
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\centering
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\includegraphics[width=74mm]{crossing}
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\caption{River crossing area zoomed in, $1:30 000$}
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\label{fig:crossing}
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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:comparison-zeimena} on
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page~\pageref{tab:comparison-zeimena}, both simplication algorithms convert
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bends to chopped lines. This is especially visible in tolerances 256 and 512.
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In a more robust simplification algorithm, the larger tolerance, the larger the
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bends on the original map should be 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{2.1cm} | X | X | }
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Tolerance DP/VW &
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Douglas \& Peucker &
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Visvalingam-Whyatt \tabularnewline \hline
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128/16384 &
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\includegraphics[width=\linewidth]{zeimena-douglas-128} &
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\includegraphics[width=\linewidth]{zeimena-visvalingam-128} \tabularnewline \hline
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256/65536 &
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\includegraphics[width=.5\linewidth]{zeimena-douglas-256} &
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\includegraphics[width=.5\linewidth]{zeimena-visvalingam-256} \tabularnewline \hline
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512/262144 &
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\includegraphics[width=.25\linewidth]{zeimena-douglas-512} &
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\includegraphics[width=.25\linewidth]{zeimena-visvalingam-512} \tabularnewline \hline
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1024/1048576 &
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\includegraphics[width=.125\linewidth]{zeimena-douglas-1024} &
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\includegraphics[width=.125\linewidth]{zeimena-visvalingam-1024} \tabularnewline \hline
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2048/4194304 &
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\includegraphics[width=.0625\linewidth]{zeimena-douglas-2048} &
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\includegraphics[width=.0625\linewidth]{zeimena-visvalingam-2048} \tabularnewline \hline
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4096/16777216 &
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\includegraphics[width=.0625\linewidth]{zeimena-douglas-4096} &
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\includegraphics[width=.0625\linewidth]{zeimena-visvalingam-4096} \tabularnewline \hline
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\end{tabularx}
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\caption{{\DP} and {\VW} on Žeimena}
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\label{tab:comparison-zeimena}
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\end{figure}
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Let's zoom in to the river crossing area for some of the algorithms; see
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table~\ref{tab:comparison-crossing} on page~\pageref{tab:comparison-crossing}.
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Both {\VW} and {\DP} simplify "blunt" bends (a "blunt" bent looks like a cutout
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from a large circle, see figure~\ref{fig:blunt-bent} on
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page~\pageref{fig:blunt-bent}.
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\begin{figure}[h]
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\centering
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\begin{tikzpicture}
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\draw (-5,0) -- (-3, 0) ;
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\draw (0,0) arc (60:120:3) ;
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\draw (0,0) -- (2, 0) ;
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\end{tikzpicture}
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\caption{Blunt bent}
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\label{fig:blunt-bent}
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\end{figure}
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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{2.1cm} | X | X | }
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Tolerance DP/VW &
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Douglas \& Peucker &
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Visvalingam-Whyatt \tabularnewline \hline
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64/4096 &
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\includegraphics[width=\linewidth]{overlaid-zeimena-douglas-64} &
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\includegraphics[width=\linewidth]{overlaid-zeimena-visvalingam-64} \tabularnewline \hline
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128/16384 &
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\includegraphics[width=\linewidth]{overlaid-zeimena-douglas-128} &
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\includegraphics[width=\linewidth]{overlaid-zeimena-visvalingam-128} \tabularnewline \hline
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256/65536 &
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\includegraphics[width=\linewidth]{overlaid-zeimena-douglas-256} &
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\includegraphics[width=\linewidth]{overlaid-zeimena-visvalingam-256} \tabularnewline \hline
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\end{tabularx}
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\caption{{\DP} and {\VW} on river crossing area}
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\label{tab:comparison-crossing}
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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{fig:sinewave} on page~\pageref{fig:sinewave}, and one needs to
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generalize it. The bends are too large to ignore replace them with a straight
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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{fig:sinewave}
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\end{figure}
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When one applies {\DP} to figure~\ref{fig:sinewave}, either both bends remain,
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or become a straight line, see table~\ref{tab:comparison-sinewave} on
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page~\pageref{tab:comparison-sinewave}.
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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 DP/VW &
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Douglas \& Peucker &
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Visvalingam-Whyatt \tabularnewline \hline
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2/4 &
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\includegraphics[width=\linewidth]{overlaid-sinewave-douglas-2} &
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\includegraphics[width=\linewidth]{overlaid-sinewave-visvalingam-2} \tabularnewline \hline
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16/256 &
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\includegraphics[width=\linewidth]{overlaid-sinewave-douglas-16} &
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\includegraphics[width=\linewidth]{overlaid-sinewave-visvalingam-16} \tabularnewline \hline
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32/1024 &
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\includegraphics[width=\linewidth]{overlaid-sinewave-douglas-32} &
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\includegraphics[width=\linewidth]{overlaid-sinewave-visvalingam-32} \tabularnewline \hline
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40/1600 &
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\includegraphics[width=\linewidth]{overlaid-sinewave-douglas-40} &
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\includegraphics[width=\linewidth]{overlaid-sinewave-visvalingam-40} \tabularnewline \hline
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\end{tabularx}
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\caption{{\DP} and {\VW} on example wave}
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\label{tab:comparison-sinewave}
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\end{figure}
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Ideally, the double-bend in figure~\ref{fig:sinewave} should be normalized to a
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larger single-bend, similar to figure~ on page~.
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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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\iffalse
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may enable this before publishing
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\begin{appendices}
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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 river in context}
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\end{figure}
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\end{appendices}
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\fi
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\end{document}
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