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Motiejus Jakštys
2020-05-27 14:41:47 +03:00
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II/Referatas/mj-referatas.tex
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@@ -164,7 +164,7 @@ Since the map area is large (approx. 20km by 28km, scale $1:300 000$), we will
also review a subset of the area of approx 2200m by 1575m. The zoomed-in
version will help explain some of the deficiencies in the reviewed algorithms.
\begin{figure}[h]
\begin{figure}[H]
\centering
\includegraphics[width=67.5mm]{zeimena}
\caption{Lakaja and Žeimena, with marked river crossing area, $1:300 000$}
@@ -200,7 +200,7 @@ bends to chopped lines. This is especially visible in tolerances 256 and 512.
In a more robust simplification algorithm, the larger tolerance, the larger the
bends on the original map should be retained.
\begin{figure}[h]
\begin{figure}[H]
\renewcommand{\tabularxcolumn}[1]{>{\center\small}m{#1}}
\begin{tabularx}{\textwidth}{ p{2.1cm} | X | X | }
Tolerance DP/VW &
@@ -235,13 +235,9 @@ bends on the original map should be retained.
\label{tab:comparison-zeimena}
\end{figure}
Let's zoom in to the river crossing area for some of the algorithms; see
table~\ref{tab:comparison-crossing} on page~\pageref{tab:comparison-crossing}.
Both {\VW} and {\DP} simplify "blunt" bends (a "blunt" bent looks like a cutout
from a large circle, see figure~\ref{fig:blunt-bent} on
page~\pageref{fig:blunt-bent}). This is not ideal, because large blunt bents
should be retained.
To ease the discussion on shapes in the resulting output, it is useful to
define what a "blunt bend" is: it is a river bent that looks like a cutout from
a large circle, ilustrated in figure~\ref{fig:blunt-bent}.
\begin{figure}[h]
\centering
@@ -254,6 +250,11 @@ should be retained.
\label{fig:blunt-bent}
\end{figure}
Once zoomed in to the river crossing area with {\DP} and {\VW} applied, it becomes apparent that both large
blunts are normalized to single lines, the shape becomes jagged and unpleasant
for the eye. See table~\ref{tab:comparison-crossing} on
page~\pageref{tab:comparison-crossing}.
\begin{figure}[h]
\renewcommand{\tabularxcolumn}[1]{>{\center\small}m{#1}}
\begin{tabularx}{\textwidth}{ p{2.1cm} | X | X | }
@@ -278,21 +279,20 @@ should be retained.
\label{tab:comparison-crossing}
\end{figure}
To sum up, both {\VW} and {\DP} simplify the lines, but their cartographic
output poorly represents lines and bends. Where to look for better output?
There is another issue on the wishlist beyond jaggyness and loss of large bents
-- combining close bends to larger ones.
\subsection{Combining bends}
Consecutive small bends should be combined into larger bends, and that is one
of the least developed aspects of automatic line generalization, according to
\cite{miuller1995generalization}. {\WM} encoded this process to an algorithm.
Imagine there are two small bends close to each other, similar to
figure~\ref{fig:sinewave} on page~\pageref{fig:sinewave}, and one needs to
figure~\ref{fig:sinewave2} on page~\pageref{fig:sinewave2}, and one needs to
generalize it. The bends are too large to ignore replace them with a straight
line, but too small to retain both and retain their complexity.
According to cartographic generalization rules
(\cite{miuller1995generalization}), consecutive small bends should be combined
into larger bends. {\WM} encoded this process to an algorithm.
\begin{figure}[h]
\centering
\includegraphics[width=52mm]{sinewave2}
@@ -301,39 +301,39 @@ line, but too small to retain both and retain their complexity.
\end{figure}
When one applies {\DP} to figure~\ref{fig:sinewave2}, either both bends remain,
or become a straight line, see table~\ref{tab:comparison-sinewave} on
page~\pageref{tab:comparison-sinewave}.
or become a straight line, see table~\ref{tab:comparison-sinewave2} on
page~\pageref{tab:comparison-sinewave2}.
\begin{figure}[h]
\renewcommand{\tabularxcolumn}[1]{>{\center\small}m{#1}}
\begin{tabularx}{\textwidth}{ p{1.5cm} | X | X | }
Tolerance DP/VW &
Douglas \& Peucker &
Visvalingam-Whyatt \tabularnewline \hline
Tolerance DP/VW &
Douglas \& Peucker &
Visvalingam-Whyatt \tabularnewline \hline
2/4 &
\includegraphics[width=\linewidth]{overlaid-sinewave-douglas-2} &
\includegraphics[width=\linewidth]{overlaid-sinewave-visvalingam-2} \tabularnewline \hline
2/4 &
\includegraphics[width=\linewidth]{overlaid-sinewave2-douglas-2} &
\includegraphics[width=\linewidth]{overlaid-sinewave2-visvalingam-2} \tabularnewline \hline
16/256 &
\includegraphics[width=\linewidth]{overlaid-sinewave-douglas-16} &
\includegraphics[width=\linewidth]{overlaid-sinewave-visvalingam-16} \tabularnewline \hline
16/256 &
\includegraphics[width=\linewidth]{overlaid-sinewave2-douglas-16} &
\includegraphics[width=\linewidth]{overlaid-sinewave2-visvalingam-16} \tabularnewline \hline
32/1024 &
\includegraphics[width=\linewidth]{overlaid-sinewave-douglas-32} &
\includegraphics[width=\linewidth]{overlaid-sinewave-visvalingam-32} \tabularnewline \hline
\includegraphics[width=\linewidth]{overlaid-sinewave2-douglas-32} &
\includegraphics[width=\linewidth]{overlaid-sinewave2-visvalingam-32} \tabularnewline \hline
40/1600 &
\includegraphics[width=\linewidth]{overlaid-sinewave-douglas-40} &
\includegraphics[width=\linewidth]{overlaid-sinewave-visvalingam-40} \tabularnewline \hline
40/1600 &
\includegraphics[width=\linewidth]{overlaid-sinewave2-douglas-40} &
\includegraphics[width=\linewidth]{overlaid-sinewave2-visvalingam-40} \tabularnewline \hline
\end{tabularx}
\caption{{\DP} and {\VW} on example wave}
\label{tab:comparison-sinewave}
\label{tab:comparison-sinewave2}
\end{figure}
Ideally, the double-bend in figure~\ref{fig:sinewave2} should be normalized to a
larger single-bend, similar to figure~\ref{fig:sinewave1} on
Ideally, the double-bend in figure~\ref{fig:sinewave2} should be normalized to
a larger single-bend, similar to figure~\ref{fig:sinewave1} on
page~\pageref{fig:sinewave2}.
\begin{figure}[h]
@@ -343,6 +343,39 @@ page~\pageref{fig:sinewave2}.
\label{fig:sinewave1}
\end{figure}
To recap, both {\VW} and {\DP} simplify the lines, but their cartographic
output, when zoomed in, looks poorly to the human eye. Can a better solution be
found?
\section{Recommendation}
\label{sec:recommendation}
So far, we have reviewed two widely available open-source generalization
algorithms {\DP} and {\VW}, and now can enumerate the shortcomings:
\begin{itemize}
\item Resulting generalized lines look jaggy and, when zoomed in,
unpleasant to the eye.
\item Blunt bends are generalized to straight lines, even though sometimes
they should remain blunt bends (or even exhagerated bends).
\item Consecutive small bends should be normalized into a larger bend.
\end{itemize}
According to \cite{wang1998line}, their algorithm fixes all 3 issues above. The
algorithm is relatively simple to understand for a non-expert cartographer
software developer, and thus should be feasible to implement in a few weeks.
\section{Conclusions}
\label{sec:conclusions}
We have evaluated two readily available line simplification algorithms using a
river sample and a synthetic bend: {\VW} and {\DP}. Once looking at the
examples, it is quite easy to see the most glaring deficiencies when applying
those two for comparing cartographic generalization.
We are suggesting to complement open-source list of
available algorithms with {\WM}, which was created for cartographic
generalization, and should fix the shortcomings identified in this paper.
\section{Related Work and future suggestions}
\label{sec:related_work}
@@ -356,13 +389,6 @@ As noted in parameter~\ref{itm:2} on page~\pageref{itm:2}, it would be useful
to have a formula mapping {\DP} tolerance to {\VW}. That way, visual
comparisons between line simplification algorithms could be more objective.
\section{Conclusions}
\label{sec:conclusions}
We have practically evaluated two readily available line simplification
algorithms with a river sample: {\VW} and {\DP}, and outlined their
deficiencies. We are suggesting to implement {\WM} and compare it to the other
two.
\printbibliography