related work
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Motiejus Jakštys
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@ -5,15 +5,15 @@ CROSSING_TOLERANCES = 64 128 256
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SINEWAVE_SIZE = 120x48
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#CROSSING=622916 6119267 626066 6121487
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GEN1 = $(addsuffix .pdf, \
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$(addprefix sinewave-douglas-,$(SINEWAVE_TOLERANCES)) \
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$(addprefix sinewave-visvalingam-,$(SINEWAVE_TOLERANCES)) \
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$(addprefix sinewave2-douglas-,$(SINEWAVE_TOLERANCES)) \
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$(addprefix sinewave2-visvalingam-,$(SINEWAVE_TOLERANCES)) \
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$(addprefix zeimena-douglas-,$(ZEIMENA_TOLERANCES)) \
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$(addprefix zeimena-visvalingam-,$(ZEIMENA_TOLERANCES)))
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GEN2 = $(addsuffix .pdf, \
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$(addprefix overlaid-zeimena-douglas-,$(CROSSING_TOLERANCES)) \
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$(addprefix overlaid-zeimena-visvalingam-,$(CROSSING_TOLERANCES)) \
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$(addprefix overlaid-sinewave-douglas-,$(SINEWAVE_TOLERANCES)) \
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$(addprefix overlaid-sinewave-visvalingam-,$(SINEWAVE_TOLERANCES)))
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$(addprefix overlaid-sinewave2-douglas-,$(SINEWAVE_TOLERANCES)) \
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$(addprefix overlaid-sinewave2-visvalingam-,$(SINEWAVE_TOLERANCES)))
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mj-referatas.pdf: mj-referatas.tex version.tex bib.bib zeimena.pdf \
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sinewave1.pdf sinewave2.pdf crossing.pdf $(GEN1) $(GEN2)
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@ -35,8 +35,8 @@ $(1): $(2) ./layer2img.py
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./layer2img.py $(3) --group1-infile=$$< --outfile $(1)
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endef
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$(eval $(call algo2img,sinewave,douglas,60x24))
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$(eval $(call algo2img,sinewave,visvalingam,60x24))
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$(eval $(call algo2img,sinewave2,douglas,60x24))
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$(eval $(call algo2img,sinewave2,visvalingam,60x24))
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$(eval $(call algo2img,zeimena,douglas,210x297))
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$(eval $(call algo2img,zeimena,visvalingam,210x297))
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$(eval $(call gpkg2pdf,sinewave1.pdf,sinewave1.gpkg,,--size=$(SINEWAVE_SIZE)))
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@ -45,8 +45,8 @@ $(eval $(call gpkg2pdf,zeimena.pdf,zeimena.gpkg rectangle.gpkg,--size=134x191 --
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$(eval $(call gpkg2pdf,crossing.pdf,zeimena.gpkg,--size=105x74 --clip $(CROSSING)))
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$(eval $(call algo2overlay,zeimena,douglas,--size 148x105 --clip $(CROSSING)))
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$(eval $(call algo2overlay,zeimena,visvalingam,--size 148x105 --clip $(CROSSING)))
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$(eval $(call algo2overlay,sinewave,douglas,--size $(SINEWAVE_SIZE)))
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$(eval $(call algo2overlay,sinewave,visvalingam,--size $(SINEWAVE_SIZE)))
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$(eval $(call algo2overlay,sinewave2,douglas,--size $(SINEWAVE_SIZE)))
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$(eval $(call algo2overlay,sinewave2,visvalingam,--size $(SINEWAVE_SIZE)))
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sinewave%.gpkg: fig2layer.py
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./fig2layer.py -o $@ sine --numwaves=$*
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@ -164,7 +164,7 @@ 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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\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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@ -200,7 +200,7 @@ 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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\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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@ -235,13 +235,9 @@ bends on the original map should be retained.
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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}). This is not ideal, because large blunt bents
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should be retained.
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To ease the discussion on shapes in the resulting output, it is useful to
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define what a "blunt bend" is: it is a river bent that looks like a cutout from
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a large circle, ilustrated in figure~\ref{fig:blunt-bent}.
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\begin{figure}[h]
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\centering
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@ -254,6 +250,11 @@ should be retained.
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\label{fig:blunt-bent}
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\end{figure}
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Once zoomed in to the river crossing area with {\DP} and {\VW} applied, it becomes apparent that both large
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blunts are normalized to single lines, the shape becomes jagged and unpleasant
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for the eye. See table~\ref{tab:comparison-crossing} on
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page~\pageref{tab:comparison-crossing}.
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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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@ -278,21 +279,20 @@ should be retained.
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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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There is another issue on the wishlist beyond jaggyness and loss of large bents
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-- combining close bends to larger ones.
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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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figure~\ref{fig:sinewave2} on page~\pageref{fig:sinewave2}, 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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According to cartographic generalization rules
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(\cite{miuller1995generalization}), consecutive small bends should be combined
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into larger bends. {\WM} encoded this process to an algorithm.
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\begin{figure}[h]
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\centering
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\includegraphics[width=52mm]{sinewave2}
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@ -301,39 +301,39 @@ line, but too small to retain both and retain their complexity.
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\end{figure}
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When one applies {\DP} to figure~\ref{fig:sinewave2}, 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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or become a straight line, see table~\ref{tab:comparison-sinewave2} on
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page~\pageref{tab:comparison-sinewave2}.
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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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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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2/4 &
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\includegraphics[width=\linewidth]{overlaid-sinewave2-douglas-2} &
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\includegraphics[width=\linewidth]{overlaid-sinewave2-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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16/256 &
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\includegraphics[width=\linewidth]{overlaid-sinewave2-douglas-16} &
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\includegraphics[width=\linewidth]{overlaid-sinewave2-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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\includegraphics[width=\linewidth]{overlaid-sinewave2-douglas-32} &
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\includegraphics[width=\linewidth]{overlaid-sinewave2-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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40/1600 &
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\includegraphics[width=\linewidth]{overlaid-sinewave2-douglas-40} &
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\includegraphics[width=\linewidth]{overlaid-sinewave2-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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\label{tab:comparison-sinewave2}
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\end{figure}
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Ideally, the double-bend in figure~\ref{fig:sinewave2} should be normalized to a
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larger single-bend, similar to figure~\ref{fig:sinewave1} on
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Ideally, the double-bend in figure~\ref{fig:sinewave2} should be normalized to
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a larger single-bend, similar to figure~\ref{fig:sinewave1} on
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page~\pageref{fig:sinewave2}.
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\begin{figure}[h]
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@ -343,6 +343,39 @@ page~\pageref{fig:sinewave2}.
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\label{fig:sinewave1}
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\end{figure}
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To recap, both {\VW} and {\DP} simplify the lines, but their cartographic
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output, when zoomed in, looks poorly to the human eye. Can a better solution be
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found?
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\section{Recommendation}
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\label{sec:recommendation}
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So far, we have reviewed two widely available open-source generalization
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algorithms {\DP} and {\VW}, and now can enumerate the shortcomings:
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\begin{itemize}
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\item Resulting generalized lines look jaggy and, when zoomed in,
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unpleasant to the eye.
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\item Blunt bends are generalized to straight lines, even though sometimes
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they should remain blunt bends (or even exhagerated bends).
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\item Consecutive small bends should be normalized into a larger bend.
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\end{itemize}
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According to \cite{wang1998line}, their algorithm fixes all 3 issues above. The
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algorithm is relatively simple to understand for a non-expert cartographer
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software developer, and thus should be feasible to implement in a few weeks.
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\section{Conclusions}
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\label{sec:conclusions}
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We have evaluated two readily available line simplification algorithms using a
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river sample and a synthetic bend: {\VW} and {\DP}. Once looking at the
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examples, it is quite easy to see the most glaring deficiencies when applying
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those two for comparing cartographic generalization.
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We are suggesting to complement open-source list of
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available algorithms with {\WM}, which was created for cartographic
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generalization, and should fix the shortcomings identified in this paper.
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\section{Related Work and future suggestions}
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\label{sec:related_work}
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@ -356,13 +389,6 @@ 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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