Skip to content

L
licenseplates
Commit 0dcaa652 authored by Richard Torenvliet's avatar Richard Torenvliet
Browse files
Options

Merge branch 'master' of github.com:taddeus/licenseplates 

Conflicts:
	docs/report.tex
parents 16018f03 6043646c
Hide whitespace changes
Inline Side-by-side
Showing with 243 additions and 730 deletions
docs/codediagram.png
View replaced file @ 16018f03 View file @ 0dcaa652
docs/codediagram.png

133 KB | W: | H:

docs/codediagram.png

113 KB | W: | H:

docs/codediagram.png
docs/codediagram.png
docs/codediagram.png
docs/codediagram.png
  • 2-up
  • Swipe
  • Onion skin
docs/codediagram.sxd
View file @ 0dcaa652
No preview for this file type
docs/report.tex
View file @ 0dcaa652
......@@ -15,9 +15,9 @@
\maketitle
\section*{Project members}
Gijs van der Voort\\
Raichard Torenvliet\\
Jayke Meijer\\
Gijs van der Voort \\
Richard Torenvliet \\
Jayke Meijer \\
Tadde\"us Kroes\\
Fabi\"en Tesselaar
......@@ -45,38 +45,60 @@ in classifying characters on a license plate.
In short our program must be able to do the following:
\begin{enumerate}
\item Extracting characters using the location points in the xml file.
\item Extract characters using the location points in the xml file.
\item Reduce noise where possible to ensure maximum readability.
\item Transforming a character to a normal form.
\item Creating a local binary pattern histogram vector.
\item Matching the found vector with a learning set.
\item And finally it has to check results with a real data set.
\item Transform a character to a normal form.
\item Create a local binary pattern histogram vector.
\item Recognize the character value of a vector using a classifier.
\item Determine the performance of the classifier with a given test set.
\end{enumerate}
\section{Language of choice}
The actual purpose of this project is to check if LBP is capable of recognizing
license plate characters. We knew the LBP implementation would be pretty
simple. Thus an advantage had to be its speed compared with other license plate
recognition implementations, but the uncertainty of whether we could get some
results made us pick Python. We felt Python would not restrict us as much in
assigning tasks to each member of the group. In addition, when using the
correct modules to handle images, Python can be decent in speed.
license plate characters. Since the LBP algorithm is fairly simple to
implement, it should have a good performance in comparison to other license
plate recognition implementations if implemented in C. However, we decided to
focus on functionality rather than speed. Therefore, we picked Python. We felt
Python would not restrict us as much in assigning tasks to each member of the
group. In addition, when using the correct modules to handle images, Python can
be decent in speed.
\section{Theory}
Now we know what our program has to be capable of, we can start with the
defining what problems we have and how we want to solve these.
defining the problems we have and how we are planning to solve these.
\subsection{Extracting a letter and resizing it}
\subsection{Extracting a character and resizing it}
We need to extract a character from a photo made of a car. We do not have to
find where in this image the characters are, since this is provided in an XML
file with our dataset.
Once we have extracted the points from this XML file, we need to get this
character from the image. For the nature of the Local Binary Pattern algorithm,
we want a margin around the character. However, the points stored in the XML
file are chosen in such a fashion, that the character would be cut out exactly.
Therefore, we choose to take points that are slightly outside of the given
points.
When we have the points we want, we use a perspective transformation to get
an exact image of the character.
The final step is to resize this image in such a fashion, that the stroke
of the character is more or less equal in each image. We do this by setting
the height to a standard size, since each character has the same height on a
license plate. We retain the height-width ratio, so we do not end up with
characters that are different than other examples of the same character,
because the image got stretched, which would of course be a bad thing for
the classification.
Rewrite this section once we have implemented this properly.
\subsection{Transformation}
A simple perspective transformation will be sufficient to transform and resize
the characters to a normalized format. The corner positions of characters in
the dataset are supplied together with the dataset.
the dataset are provided together with the dataset.
\subsection{Reducing noise}
......@@ -92,51 +114,53 @@ part of the license plate remains readable.
\subsection{Local binary patterns}
Once we have separate digits and characters, we intent to use Local Binary
Patterns (Ojala, Pietikäinen \& Harwood, 1994) to determine what character
or digit we are dealing with. Local Binary
Patterns are a way to classify a texture based on the distribution of edge
directions in the image. Since letters on a license plate consist mainly of
straight lines and simple curves, LBP should be suited to identify these.
Patterns (Ojala, Pietikäinen \& Harwood, 1994) to determine what character or
digit we are dealing with. Local Binary Patterns are a way to classify a
texture based on the distribution of edge directions in the image. Since
letters on a license plate consist mainly of straight lines and simple curves,
LBP should be suited to identify these.
\subsubsection{LBP Algorithm}
The LBP algorithm that we implemented can use a variety of neighbourhoods,
including the same square pattern that is introduced by Ojala et al (1994),
and a circular form as presented by Wikipedia.
\begin{itemize}
including the same square pattern that is introduced by Ojala et al (1994), and
a circular form as presented by Wikipedia.
\begin{enumerate}
\item Determine the size of the square where the local patterns are being
registered. For explanation purposes let the square be 3 x 3. \\
\item The grayscale value of the middle pixel is used as threshold. Every
value of the pixel around the middle pixel is evaluated. If it's value is
greater than the threshold it will be become a one else a zero.
\item The grayscale value of the center pixel is used as threshold. Every value
of the pixel around the center pixel is evaluated. If it's value is greater
than the threshold it will be become a one, otherwise it will be a zero.
\begin{figure}[H]
\center
\includegraphics[scale=0.5]{lbp.png}
\caption{LBP 3 x 3 (Pietik\"ainen, Hadid, Zhao \& Ahonen (2011))}
\center
\includegraphics[scale=0.5]{lbp.png}
\caption{LBP 3 x 3 (Pietik\"ainen, Hadid, Zhao \& Ahonen (2011))}
\end{figure}
Notice that the pattern will be come of the form 01001110. This is done when a
the value of the evaluated pixel is greater than the threshold, shift the bit
by the n(with i=i$_{th}$ pixel evaluated, starting with $i=0$).
The pattern will be an 8-bit integer. This is accomplished by shifting the
boolean value of each comparison one to seven places to the left.
This results in a mathematical expression:
This results in the following mathematical expression:
Let I($x_i, y_i$) an Image with grayscale values and $g_n$ the grayscale value
of the pixel $(x_i, y_i)$. Also let $s(g_i, g_c)$ (see below) with $g_c$ =
grayscale value of the center pixel and $g_i$ the grayscale value of the pixel
to be evaluated.
Let I($x_i, y_i$) be a grayscale Image and $g_n$ the value of the pixel $(x_i,
y_i)$. Also let $s(g_i, g_c)$ (see below) with $g_c$ being the value of the
center pixel and $g_i$ the grayscale value of the pixel to be evaluated.
$$
s(g_i, g_c) = \left\{
\begin{array}{l l}
1 & \quad \text{if $g_i$ $\geq$ $g_c$}\\
0 & \quad \text{if $g_i$ $<$ $g_c$}\\
\end{array} \right.
s(g_i, g_c) = \left \{
\begin{array}{l l}
1 & \quad \text{if $g_i$ $\geq$ $g_c$}\\
0 & \quad \text{if $g_i$ $<$ $g_c$}\\
\end{array} \right.
$$
$$LBP_{n, g_c = (x_c, y_c)} = \sum\limits_{i=0}^{n-1} s(g_i, g_c)^{2i} $$
$$LBP_{n, g_c = (x_c, y_c)} = \sum\limits_{i=0}^{n-1} s(g_i, g_c) \cdot 2^i$$
The outcome of this operations will be a binary pattern.
The outcome of this operations will be a binary pattern. Note that the
mathematical expression has the same effect as the bit shifting operation that
we defined earlier.
\item Given this pattern, the next step is to divide the pattern in cells. The
amount of cells depends on the quality of the result, so trial and error is in
......@@ -145,23 +169,23 @@ order. Starting with dividing the pattern in to cells of size 16.
\item Compute a histogram for each cell.
\begin{figure}[H]
\center
\includegraphics[scale=0.7]{cells.png}
\caption{Divide in cells(Pietik\"ainen et all (2011))}
\center
\includegraphics[scale=0.7]{cells.png}
\caption{Divide in cells(Pietik\"ainen et all (2011))}
\end{figure}
\item Consider every histogram as a vector element and concatenate these. The
result is a feature vector of the image.
\item Feed these vectors to a support vector machine. This will ''learn'' which
vector indicates what vector is which character.
\item Feed these vectors to a support vector machine. The SVM will ``learn''
which vectors to associate with a character.
\end{itemize}
\end{enumerate}
To our knowledge, LBP has yet not been used in this manner before. Therefore,
it will be the first thing to implement, to see if it lives up to the
expectations. When the proof of concept is there, it can be used in a final
program.
expectations. When the proof of concept is there, it can be used in a final,
more efficient program.
Later we will show that taking a histogram over the entire image (basically
working with just one cell) gives us the best results.
......@@ -169,19 +193,19 @@ working with just one cell) gives us the best results.
\subsection{Matching the database}
Given the LBP of a character, a Support Vector Machine can be used to classify
the character to a character in a learning set. The SVM uses a concatenation
of each cell in an image as a feature vector (in the case we check the entire
image no concatenation has to be done of course. The SVM can be trained with a
subset of the given dataset called the ''Learning set''. Once trained, the
entire classifier can be saved as a Pickle object\footnote{See
the character to a character in a learning set. The SVM uses the concatenation
of the histograms of all cells in an image as a feature vector (in the case we
check the entire image no concatenation has to be done of course. The SVM can
be trained with a subset of the given dataset called the ``learning set''. Once
trained, the entire classifier can be saved as a Pickle object\footnote{See
\url{http://docs.python.org/library/pickle.html}} for later usage.
In our case the support vector machine uses a radial gauss kernel function. The
SVM finds a seperating hyperplane with minimum margins.
\section{Implementation}
In this section we will describe our implementations in more detail, explaining
choices we made.
In this section we will describe our implementation in more detail, explaining
the choices we made in the process.
\subsection{Character retrieval}
......@@ -192,7 +216,7 @@ stored in XML files. So, the first step is to read these XML files.
\paragraph*{XML reader}
The XML reader will return a 'license plate' object when given an XML file. The
The XML reader will return a `license plate' object when given an XML file. The
licence plate holds a list of, up to six, NormalizedImage characters and from
which country the plate is from. The reader is currently assuming the XML file
and image name are corresponding, since this was the case for the given
......@@ -239,8 +263,8 @@ any unwanted difference in color from the surrounding pixels.
\paragraph*{Camera noise and small amounts of dirt}
The dirt on the license plate can be of different sizes. We can reduce the
smaller amounts of dirt in the same way as we reduce normal noise, by applying
a Gaussian blur to the image. This is the next step in our program.\\
\\
a Gaussian blur to the image. This is the next step in our program.
The Gaussian filter we use comes from the \texttt{scipy.ndimage} module. We use
this function instead of our own function, because the standard functions are
most likely more optimized then our own implementation, and speed is an
......@@ -249,7 +273,7 @@ important factor in this application.
\paragraph*{Larger amounts of dirt}
Larger amounts of dirt are not going to be resolved by using a Gaussian filter.
We rely on one of the characteristics of the Local Binary Pattern, only looking
at the difference between two pixels, to take care of these problems.\\
at the difference between two pixels, to take care of these problems. \\
Because there will probably always be a difference between the characters and
the dirt, and the fact that the characters are very black, the shape of the
characters will still be conserved in the LBP, even if there is dirt
......@@ -269,8 +293,8 @@ tried the following neighbourhoods:
We name these neighbourhoods respectively (8,3)-, (8,5)- and
(12,5)-neighbourhoods, after the number of points we use and the diameter
of the `circle´ on which these points lay.\\
\\
of the `circle´ on which these points lay.
We chose these neighbourhoods to prevent having to use interpolation, which
would add a computational step, thus making the code execute slower. In the
next section we will describe what the best neighbourhood was.
......@@ -302,22 +326,21 @@ increasing our performance, so we only have one histogram to feed to the SVM.
\subsection{Classification}
For the classification, we use a standard Python Support Vector Machine,
\texttt{libsvm}. This is a often used SVM, and should allow us to simply feed
the data from the LBP and Feature Vector steps into the SVM and receive
results.\\
\\
Using a SVM has two steps. First you have to train the SVM, and then you can
use it to classify data. The training step takes a lot of time, so luckily
\texttt{libsvm} offers us an opportunity to save a trained SVM. This means,
you do not have to train the SVM every time.\\
\\
\texttt{libsvm}. This is an often used SVM, and should allow us to simply feed
data from the LBP and Feature Vector steps into the SVM and receive results.
Using a SVM has two steps. First, the SVM has to be trained, and then it can be
used to classify data. The training step takes a lot of time, but luckily
\texttt{libsvm} offers us an opportunity to save a trained SVM. This means that
the SVM only has to be changed once.
We have decided to only include a character in the system if the SVM can be
trained with at least 70 examples. This is done automatically, by splitting
the data set in a trainingset and a testset, where the first 70 examples of
a character are added to the trainingset, and all the following examples are
added to the testset. Therefore, if there are not enough examples, all
available examples end up in the trainingset, and non of these characters
end up in the testset, thus they do not decrease our score. However, if this
trained with at least 70 examples. This is done automatically, by splitting the
data set in a learning set and a test set, where the first 70 examples of a
character are added to the learning set, and all the following examples are
added to the test set. Therefore, if there are not enough examples, all
available examples end up in the learning set, and non of these characters end
up in the test set, thus they do not decrease our score. However, if this
character later does get offered to the system, the training is as good as
possible, since it is trained with all available characters.
......@@ -326,15 +349,19 @@ possible, since it is trained with all available characters.
In order to work with the code, we wrote a number of scripts. Each of these
scripts is named here and a description is given on what the script does.
\subsection*{\texttt{find\_svm\_params.py}}
\subsection*{\texttt{create\_characters.py}}
\subsection*{\texttt{create\_classifier.py}}
\subsection*{\texttt{LearningSetGenerator.py}}
\subsection*{\texttt{find\_svm\_params.py}}
\subsection*{\texttt{load\_characters.py}}
\subsection*{\texttt{generate\_learning\_set.py}}
......@@ -345,6 +372,7 @@ scripts is named here and a description is given on what the script does.
\subsection*{\texttt{run\_classifier.py}}
\section{Finding parameters}
Now that we have a functioning system, we need to tune it to work properly for
......@@ -362,8 +390,8 @@ available. These parameters are:\\
$\gamma$ & Parameter for the Radial kernel used in the SVM.\\
$c$ & The soft margin of the SVM. Allows how much training
errors are accepted.\\
\end{tabular}\\
\\
\end{tabular}
For each of these parameters, we will describe how we searched for a good
value, and what value we decided on.
......@@ -371,8 +399,8 @@ value, and what value we decided on.
The first parameter to decide on, is the $\sigma$ used in the Gaussian blur. To
find this parameter, we tested a few values, by trying them and checking the
results. It turned out that the best value was $\sigma = 1.4$.\\
\\
results. It turned out that the best value was $\sigma = 1.4$.
Theoretically, this can be explained as follows. The filter has width of
$6 * \sigma = 6 * 1.4 = 8.4$ pixels. The width of a `stroke' in a character is,
after our resize operations, around 8 pixels. This means, our filter `matches'
......@@ -388,13 +416,13 @@ classification less affected by relative movement of a character compared to
those in the learning set, since the important structure will be more likely to
remain in the same cell. However, if the cell size is too big, there will not
be enough cells to properly describe the different areas of the character, and
the feature vectors will not have enough elements.\\
\\
the feature vectors will not have enough elements.
In order to find this parameter, we used a trial-and-error technique on a few
cell sizes. During this testing, we discovered that a lot better score was
reached when we take the histogram over the entire image, so with a single
cell. Therefore, we decided to work without cells.\\
\\
cell. Therefore, we decided to work without cells.
A reason we can think of why using one cell works best is that the size of a
single character on a license plate in the provided dataset is very small.
That means that when dividing it into cells, these cells become simply too
......@@ -423,17 +451,17 @@ exact each element in the learning set should be taken. A large soft margin
means that an element in the learning set that accidentally has a completely
different feature vector than expected, due to noise for example, is not taken
into account. If the soft margin is very small, then almost all vectors will be
taken into account, unless they differ extreme amounts.\\
taken into account, unless they differ extreme amounts. \\
$\gamma$ is a variable that determines the size of the radial kernel, and as
such determines how steep the difference between two classes can be.\\
\\
such determines how steep the difference between two classes can be.
Since these parameters both influence the SVM, we need to find the best
combination of values. To do this, we perform a so-called grid-search. A
grid-search takes exponentially growing sequences for each parameter, and
checks for each combination of values what the score is. The combination with
the highest score is then used as our parameters, and the entire SVM will be
trained using those parameters.\\
\\
trained using those parameters.
The results of this grid-search are shown in the following table. The values
in the table are rounded percentages, for easy displaying.
......@@ -481,15 +509,15 @@ Of course, it is vital that the recognition of a license plate is correct,
almost correct is not good enough here. Therefore, we have to get the highest
accuracy score we possibly can.\\
\\ According to Wikipedia \cite{wikiplate}
commercial license plate recognition software score about $90\%$ to $94\%$,
under optimal conditions and with modern equipment.\\
\\
accuracy score we possibly can. commercial license plate recognition software
score about $90\%$ to $94\%$, under optimal conditions and with modern equipment.
Our program scores an average of $93\%$. However, this is for a single
character. That means that a full license plate should theoretically
get a score of $0.93^6 = 0.647$, so $64.7\%$. That is not particularly
good compared to the commercial ones. However, our focus was on getting
good scores per character, and $93\%$ seems to be a fairly good result.\\
\\
good scores per character, and $93\%$ seems to be a fairly good result.
Possibilities for improvement of this score would be more extensive
grid-searches, finding more exact values for $c$ and $\gamma$, more tests
for finding $\sigma$ and more experiments on the size and shape of the
......@@ -502,20 +530,20 @@ can be a lot of cars passing a camera in a short time, especially on a highway.
Therefore, we measured how well our program performed in terms of speed. We
measure the time used to classify a license plate, not the training of the
dataset, since that can be done offline, and speed is not a primary necessity
there.\\
\\
there.
The speed of a classification turned out to be reasonably good. We time between
the moment a character has been 'cut out' of the image, so we have a exact
image of a character, to the moment where the SVM tells us what character it
is. This time is on average $65$ ms. That means that this
technique (tested on an AMD Phenom II X4 955 CPU running at 3.2 GHz)
can identify 15 characters per second.\\
\\
can identify 15 characters per second.
This is not spectacular considering the amount of calculating power this CPU
can offer, but it is still fairly reasonable. Of course, this program is
written in Python, and is therefore not nearly as optimized as would be
possible when written in a low-level language.\\
\\
possible when written in a low-level language.
Another performance gain is by using one of the other two neighbourhoods.
Since these have 8 points instead of 12 points, this increases performance
drastically, but at the cost of accuracy. With the (8,5)-neighbourhood
......@@ -528,12 +556,12 @@ is not advisable to use.
In the end it turns out that using Local Binary Patterns is a promising
technique for License Plate Recognition. It seems to be relatively indifferent
for the amount of dirt on license plates and different fonts on these plates.\\
\\
for the amount of dirt on license plates and different fonts on these plates.
The performance speed wise is fairly good, when using a fast machine. However,
this is written in Python, which means it is not as efficient as it could be
when using a low-level languages.
\\
We believe that with further experimentation and development, LBP's can
absolutely be used as a good license plate recognition method.
......@@ -549,15 +577,18 @@ were and whether we were able to find a proper solution for them.
We did experience a number of problems with the provided dataset. A number of
these are problems to be expected in a real world problem, but which make
development harder. Others are more elemental problems.\\
development harder. Others are more elemental problems.
The first problem was that the dataset contains a lot of license plates which
are problematic to read, due to excessive amounts of dirt on them. Of course,
this is something you would encounter in the real situation, but it made it
hard for us to see whether there was a coding error or just a bad example.\\
hard for us to see whether there was a coding error or just a bad example.
Another problem was that there were license plates of several countries in
the dataset. Each of these countries has it own font, which also makes it
hard to identify these plates, unless there are a lot of these plates in the
learning set.\\
learning set.
A problem that is more elemental is that some of the characters in the dataset
are not properly classified. This is of course very problematic, both for
training the SVM as for checking the performance. This meant we had to check
......@@ -579,6 +610,7 @@ every team member was up-to-date and could start figuring out which part of the
implementation was most suited to be done by one individually or in a pair.
\subsubsection*{Who did what}
Gijs created the basic classes we could use and helped everyone by keeping
track of what was required to be finished and whom was working on what.
Tadde\"us and Jayke were mostly working on the SVM and all kinds of tests
......@@ -627,7 +659,6 @@ can help in future research to achieve a higher accuracy rate.
\end{figure}
\end{document}
\begin{thebibliography}{9}
\bibitem{lbp1}
Matti Pietik\"ainen, Guoyin Zhao, Abdenour hadid,
......@@ -642,3 +673,14 @@ can help in future research to achieve a higher accuracy rate.
Retrieved from http://en.wikipedia.org/wiki/Automatic\_number\_plate\_recognition
\end{thebibliography}
\appendix
\section{Faulty Classifications}
\begin{figure}[H]
\center
\includegraphics[scale=0.5]{faulty.png}
\caption{Faulty classifications of characters}
\end{figure}
\end{document}
docs/verslag.tex deleted 100644 → 0
View file @ 16018f03
\documentclass[a4paper]{article}
\usepackage{amsmath}
\usepackage{hyperref}
\usepackage{graphicx}
\title{Using local binary patterns to read license plates in photographs}
% Paragraph indentation
\setlength{\parindent}{0pt}
\setlength{\parskip}{1ex plus 0.5ex minus 0.2ex}
\begin{document}
\maketitle
\section*{Project members}
Gijs van der Voort\\
Richard Torenvliet\\
Jayke Meijer\\
Tadde\"us Kroes\\
Fabi\'en Tesselaar
\tableofcontents
\pagebreak
\setcounter{secnumdepth}{1}
\section{Problem description}
License plates are used for uniquely identifying motorized vehicles and are
made to be read by humans from great distances and in all kinds of weather
conditions.
Reading license plates with a computer is much more difficult. Our dataset
contains photographs of license plates from various angles and distances. This
means that not only do we have to implement a method to read the actual
characters, but given the location of the license plate and each individual
character, we must make sure we transform each character to a standard form.
This has to be done or else the local binary patterns will never match!
Determining what character we are looking at will be done by using Local Binary
Patterns. The main goal of our research is finding out how effective LBP's are
in classifying characters on a license plate.
In short our program must be able to do the following:
\begin{enumerate}
\item Use a perspective transformation to obtain an upfront view of license
plate.
\item Reduce noise where possible to ensure maximum readability.
\item Extracting characters using the location points in the xml file.
\item Transforming a character to a normal form.
\item Creating a local binary pattern histogram vector.
\item Matching the found vector with a learning set.
\item And finally it has to check results with a real data set.
\end{enumerate}
\section{Language of choice}
The actual purpose of this project is to check if LBP is capable of recognizing
license plate characters. We knew the LBP implementation would be pretty
simple. Thus an advantage had to be its speed compared with other license plate
recognition implementations, but the uncertainity of whether we could get some
results made us pick Python. We felt Python would not restrict us as much in
assigning tasks to each member of the group. In addition, when using the
correct modules to handle images, Python can be decent in speed.
\section{Implementation}
Now we know what our program has to be capable of, we can start with the
implementations.
\subsection{Transformation}
A simple perspective transformation will be sufficient to transform and resize
the plate to a normalized format. The corner positions of license plates in the
dataset are supplied together with the dataset.
\subsection{Extracting a letter}
NO LONGER VALID!
Because we are already given the locations of the characters, we only need to
transform those locations using the same perspective transformation used to
create a front facing license plate. The next step is to transform the
characters to a normalized manner. The size of the letter W is used as a
standard to normalize the width of all the characters, because W is the widest
character of the alphabet. We plan to also normalize the height of characters,
the best manner for this is still to be determined.
\begin{enumerate}
\item Crop the image in such a way that the character precisely fits the
image.
\item Scale the image to a standard height.
\item Extend the image on either the left or right side to a certain width.
\end{enumerate}
The resulting image will always have the same size, the character contained
will always be of the same height, and the character will alway be positioned
at either the left of right side of the image.
\subsection{Reducing noise}
Small amounts of noise will probably be suppressed by usage of a Gaussian
filter. A real problem occurs in very dirty license plates, where branches and
dirt over a letter could radically change the local binary pattern. A question
we can ask ourselves here, is whether we want to concentrate ourselves on these
exceptional cases. By law, license plates have to be readable. Therefore, we
will first direct our attention at getting a higher score in the 'regular' test
set before addressing these cases. Considered the fact that the LBP algorithm
divides a letter into a lot of cells, there is a good change that a great
number of cells will still match the learning set, and thus still return the
correct character as a best match. Therefore, we expect the algorithm to be
very robust when dealing with noisy images.
\subsection{Local binary patterns}
Once we have separate digits and characters, we intent to use Local Binary
Patterns (Ojala, Pietikäinen \& Harwood, 1994) to determine what character
or digit we are dealing with. Local Binary
Patterns are a way to classify a texture based on the distribution of edge
directions in the image. Since letters on a license plate consist mainly of
straight lines and simple curves, LBP should be suited to identify these.
\subsubsection{LBP Algorithm}
The LBP algorithm that we implemented is a square variant of LBP, the same
that is introduced by Ojala et al (1994). Wikipedia presents a different
form where the pattern is circular, this form is convenient because with
interpolation you can choose the size of the circle \textbf{and} how many
neighbours the circle has.
In the literature there are lots of examples where LBP is used for surface
recognition, facial recognition, human face emotion recoqnition (Pietik\"ainen, Hadid, Zhao \& Ahonen (2011))
\begin{itemize}
\item Determine the size of the square where the local patterns are being
registered. For explanation purposes let the square be 3 x 3. \\
\item The grayscale value of the middle pixel is used a threshold. Every value
of the pixel around the middle pixel is evaluated. If it's value is greater
than the threshold it will be become a one else a zero.
\begin{figure}[h!]
\center
\includegraphics[scale=0.5]{lbp.png}
\caption{LBP 3 x 3 (Pietik\"ainen et all (2011))}
\end{figure}
Notice that the pattern will be come of the form 01001110. This is done when a
the value of the evaluated pixel is greater than the threshold, shift the bit
by the n(with i=i$_{th}$ pixel evaluated, starting with $i=0$).
This results in a mathematical expression:
Let I($x_i, y_i$) an Image with grayscale values and $g_n$ the grayscale value
of the pixel $(x_i, y_i)$. Also let $s(g_i, g_c)$ (see below) with $g_c$ = grayscale value
of the center pixel and $g_i$ the grayscale value of the pixel to be evaluated.
$$
s(g_i, g_c) = \left\{
\begin{array}{l l}
1 & \quad \text{if $g_i$ $\geq$ $g_c$}\\
0 & \quad \text{if $g_i$ $<$ $g_c$}\\
\end{array} \right.
$$
$$LBP_{n, g_c = (x_c, y_c)} = \sum\limits_{i=0}^{n-1} s(g_i, g_c)^{2i} $$
The outcome of this operations will be a binary pattern.
\item Given this pattern, the next step is to divide the pattern in cells. The
amount of cells depends on the quality of the result, so trial and error is in
order. Starting with dividing the pattern in to cells of size 16.
\item Compute a histogram for each cell.
\begin{figure}[h!]
\center
\includegraphics[scale=0.7]{cells.png}
\caption{Divide in cells(Pietik\"ainen et al. (2011))}
\end{figure}
\item Consider every histogram as a vector element and concatenate these. The
result is a feature vector of the image.
\item Feed these vectors to a support vector machine. This will ''learn'' which
vector indicates what vector is which character.
\end{itemize}
To our knowledge, LBP has yet not been used in this manner before. Therefore,
it will be the first thing to implement, to see if it lives up to the
expectations. When the proof of concept is there, it can be used in the final
program.
Important to note is that due to the normalization of characters before
applying LBP. Therefore, no further normalization is needed on the histograms.
Given the LBP of a character, a Support Vector Machine can be used to classify
the character to a character in a learning set.
\subsection{Matching the database}
Given the LBP of a character, a Support Vector Machine can be used to classify
the character to a character in a learning set. The SVM uses the collection of
histograms of an image as a feature vector. The SVM can be trained with a
subsection of the given dataset called the ''Learning set''. Once trained, the
entire classifier can be saved as a Pickle object\footnote{See
\url{http://docs.python.org/library/pickle.html}} for later usage.
In our case a support vector machine uses a radial gauss kernel. The SVM finds
a seperating hyperplane with minimum margins.
\section{Implementation}
In this section we will describe our implementations in more detail, explaining
choices we made.
\subsection{Licenseplate retrieval}
In order to retrieve the license plate from the entire image, we need to
perform a perspective transformation. However, to do this, we need to know the
coordinates of the four corners of the licenseplate. For our dataset, this is
stored in XML files. So, the first step is to read these XML files.
\paragraph*{XML reader}
The XML reader will return a 'license plate' object when given an XML file. The
licence plate holds a list of, up to six, NormalizedImage characters and from
which country the plate is from. The reader is currently assuming the XML file
and image name are corresponding. Since this was the case for the given
dataset. This can easily be adjusted if required.
To parse the XML file, the minidom module is used. So the XML file can be
treated as a tree, where one can search for certain nodes. In each XML
file it is possible that multiple versions exist, so the first thing the reader
will do is retrieve the current and most up-to-date version of the plate. The
reader will only get results from this version.
Now we are only interested in the individual characters so we can skip the
location of the entire license plate. Each character has
a single character value, indicating what someone thought what the letter or
digit was and four coordinates to create a bounding box. To make things not to
complicated a Character class and Point class are used. They
act pretty much as associative lists, but it gives extra freedom on using the
data. If less then four points have been set the character will not be saved.
When four points have been gathered the data from the actual image is being
requested. For each corner a small margin is added (around 3 pixels) so that no
features will be lost and minimum amounts of new features will be introduced by
noise in the margin.
In the next section you can read more about the perspective transformation that
is being done. After the transformation the character can be saved: Converted
to grayscale, but nothing further. This was used to create a learning set. If
it doesn't need to be saved as an actual image it will be converted to a
NormalizedImage. When these actions have been completed for each character the
license plate is usable in the rest of the code.
\paragraph*{Perspective transformation}
Once we retrieved the cornerpoints of the license plate, we feed those to a
module that extracts the (warped) license plate from the original image, and
creates a new image where the license plate is cut out, and is transformed to a
rectangle.
\subsection{Noise reduction}
The image contains a lot of noise, both from camera errors due to dark noise
etc., as from dirt on the license plate. In this case, noise therefore means
any unwanted difference in color from the surrounding pixels.
\paragraph*{Camera noise and small amounts of dirt}
The dirt on the license plate can be of different sizes. We can reduce the
smaller amounts of dirt in the same way as we reduce normal noise, by applying
a Gaussian blur to the image. This is the next step in our program.\\
\\
The Gaussian filter we use comes from the \texttt{scipy.ndimage} module. We use
this function instead of our own function, because the standard functions are
most likely more optimized then our own implementation, and speed is an
important factor in this application.
\paragraph*{Larger amounts of dirt}
Larger amounts of dirt are not going to be resolved by using a Gaussian filter.
We rely on one of the characteristics of the Local Binary Pattern, only looking
at the difference between two pixels, to take care of these problems.\\
Because there will probably always be a difference between the characters and
the dirt, and the fact that the characters are very black, the shape of the
characters will still be conserved in the LBP, even if there is dirt
surrounding the character.
\subsection{Character retrieval}
The retrieval of the character is done the same as the retrieval of the license
plate, by using a perspective transformation. The location of the characters on
the license plate is also available in de XML file, so this is parsed from that
as well.
\subsection{Creating Local Binary Patterns and feature vector}
Every pixel is a center pixel and it is also a value to evaluate, but not at the
same time. Every pixel is evaluated as shown in the section about the LBP algorithm,
in a square.
The 8 neighbours around that pixel are evaluated. This area can be bigger but this
form is the generic form of LBP, no interpolation is needed because the pixels adressed
as neighbours are indeed pixels.
Take an example where the
full square can be evaluated, there are cases where the neighbours are out of
bounds. The first to be checked is the pixel in the left
bottom corner in the square 3 x 3, with coordinate $(x - 1, y - 1)$ with $g_c$
as center pixel on location $(x, y)$. If the grayscale value of the
neighbour in the left bottom corner is greater than the grayscale
value of the center pixel than return true. Bitshift the first bit with 7. The
outcome is now 1000000. The second neighbour will be bitshifted with 6, and so
on. Until we are at 0. The result is a binary pattern of the local point just
evaluated.
Now only the edge pixels are a problem, but a simpel check if the location of
the neighbour is still in the image can resolve this. We simply return false if
it is.
\paragraph*{Histogram and Feature Vector}
After all the Local Binary Patterns are created for every pixel. This pattern
is divided in to cells. The feature vector is the vector of concatenated
histograms. These histograms are created for cells. These cells are created by
dividing the \textbf{pattern} in to cells and create a histogram of that. So multiple
cells are related to one histogram. All the histograms are concatenated and
feeded to the SVM that will be discussed in the next section, Classification.
\subsection{Classification}
\section{Finding parameters}
Now that we have a functioning system, we need to tune it to work properly for
license plates. This means we need to find the parameters. Throughout the
program we have a number of parameters for which no standard choice is
available. These parameters are:\\
\\
\begin{tabular}{l|l}
Parameter & Description\\
\hline
$\sigma$ & The size of the Gaussian blur.\\
\emph{cell size} & The size of a cell for which a histogram of LBPs will
be generated.\\
$\gamma$ & Parameter for the Radial kernel used in the SVM.\\
$c$ & The soft margin of the SVM. Allows how much training
errors are accepted.
\end{tabular}\\
\\
For each of these parameters, we will describe how we searched for a good
value, and what value we decided on.
\subsection{Parameter $\sigma$}
The first parameter to decide on, is the $\sigma$ used in the Gaussian blur. To
find this parameter, we tested a few values, by checking visually what value
removed most noise out of the image, while keeping the edges sharp enough to
work with. By checking in the neighbourhood of the value that performed best,
we where able to 'zoom in' on what we thought was the best value. It turned out
that this was $\sigma = ?$.
\subsection{Parameter \emph{cell size}}
The cell size of the Local Binary Patterns determines over what region a
histogram is made. The trade-off here is that a bigger cell size makes the
classification less affected by relative movement of a character compared to
those in the learning set, since the important structure will be more likely to
remain in the same cell. However, if the cell size is too big, there will not
be enough cells to properly describe the different areas of the character, and
the feature vectors will not have enough elements.\\
\\
In order to find this parameter, we used a trial-and-error technique on a few
basic cell sizes, being ?, 16, ?. We found that the best result was reached by
using ??.
\subsection{Parameters $\gamma$ \& $c$}
The parameters $\gamma$ and $c$ are used for the SVM. $c$ is a standard
parameter for each type of SVM, called the 'soft margin'. This indicates how
exact each element in the learning set should be taken. A large soft margin
means that an element in the learning set that accidentally has a completely
different feature vector than expected, due to noise for example, is not taken
into account. If the soft margin is very small, then almost all vectors will be
taken into account, unless they differ extreme amounts.\\
$\gamma$ is a variable that determines the size of the radial kernel, and as
such blablabla.\\
\\
Since these parameters both influence the SVM, we need to find the best
combination of values. To do this, we perform a so-called grid-search. A
grid-search takes exponentially growing sequences for each parameter, and
checks for each combination of values what the score is. The combination with
the highest score is then used as our parameters, and the entire SVM will be
trained using those parameters.\\
\\
We found that the best values for these parameters are $c=?$ and $\gamma =?$.
\section{Results}
The goal was to find out two things with this research: The speed of the
classification and the accuracy. In this section we will show our findings.
\subsection{Speed}
Recognizing license plates is something that has to be done fast, since there
can be a lot of cars passing a camera in a short time, especially on a highway.
Therefore, we measured how well our program performed in terms of speed. We
measure the time used to classify a license plate, not the training of the
dataset, since that can be done offline, and speed is not a primary necessity
there.\\
\\
The speed of a classification turned out to be blablabla.
\subsection{Accuracy}
Of course, it is vital that the recognition of a license plate is correct,
almost correct is not good enough here. Therefore, we have to get the highest
accuracy score we possibly can.\\
\\ According to Wikipedia
\footnote{
\url{http://en.wikipedia.org/wiki/Automatic_number_plate_recognition}},
commercial license plate recognition software score about $90\%$ to $94\%$,
under optimal conditions and with modern equipment. Our program scores an
average of blablabla.
\section{Difficulties}
During the implementation and testing of the program, we did encounter a
number of difficulties. In this section we will state what these difficulties
were and whether we were able to find a proper solution for them.
\subsection*{Dataset}
We did experience a number of problems with the provided dataset. A number of
these are problems to be expected in a real world problem, but which make
development harder. Others are more elemental problems.\\
The first problem was that the dataset contains a lot of license plates which
are problematic to read, due to excessive amounts of dirt on them. Of course,
this is something you would encounter in the real situation, but it made it
hard for us to see whether there was a coding error or just a bad example.\\
Another problem was that there were license plates of several countries in
the dataset. Each of these countries has it own font, which also makes it
hard to identify these plates, unless there are a lot of these plates in the
learning set.\\
A problem that is more elemental is that some of the characters in the dataset
are not properly classified. This is of course very problematic, both for
training the SVM as for checking the performance. This meant we had to check
each character whether its description was correct.
\subsection*{SVM}
We also had trouble with the SVM for Python. The standard Python SVM, libsvm,
had a poor documentation. There was no explanation what so ever on which
parameter had to be what. This made it a lot harder for us to see what went
wrong in the program.
\section{Workload distribution}
The first two weeks were team based. Basically the LBP algorithm could be
implemented in the first hour, while some talked and someone did the typing.
Some additional 'basics' where created in similar fashion. This ensured that
every team member was up-to-date and could start figuring out which part of the
implementation was most suited to be done by one individually or in a pair.
\subsection{Who did what}
Gijs created the basic classes we could use and helped the rest everyone by
keeping track of what required to be finished and whom was working on what.
Tadde\"us and Jayke were mostly working on the SVM and all kinds of tests
whether the histograms were matching and alike. Fabi\"en created the functions
to read and parse the given xml files with information about the license
plates. Upon completion all kinds of learning and data sets could be created.
%Richard je moet even toevoegen wat je hebt gedaan :P:P
%maar miss is dit hele ding wel overbodig Ik dacht dat Rein het zei tijdens
%gesprek van ik wil weten hoe het ging enzo.
\subsection{How it went}
Sometimes one cannot hear the alarm bell and wake up properly. This however was
not a big problem as no one was affraid of staying at Science Park a bit longer
to help out. Further communication usually went through e-mails and replies
were instantaneous! A crew to remember.
\section{Conclusion}
Awesome
\begin{thebibliography}{9}
\bibitem{lbp1}
Matti Pietik\"ainen, Guoyin Zhao, Abdenour hadid,
Timo Ahonen.
\emph{Computational Imaging and Vision}.
Springer-Verlag, London,
1nd Edition,
2011.
\end{thebibliography}
\end{document}
src/Character.py
View file @ 0dcaa652
......@@ -8,6 +8,8 @@ class Character:
self.filename = filename
def get_single_cell_feature_vector(self, neighbours=5):
"""Get the histogram of Local Binary Patterns over this entire
image."""
if hasattr(self, 'feature'):
return
......@@ -15,6 +17,7 @@ class Character:
self.feature = pattern.single_cell_features_vector()
def get_feature_vector(self, cell_size=None):
"""Get the concatenated histograms of Local Binary Patterns. """
pattern = LBP(self.image) if cell_size == None \
else LBP(self.image, cell_size)
......
src/Classifier.py
View file @ 0dcaa652
from svmutil import svm_train, svm_problem, svm_parameter, svm_predict, \
svm_save_model, svm_load_model, RBF
class Classifier:
def __init__(self, c=None, gamma=None, filename=None, neighbours=3, \
verbose=0):
self.neighbours = neighbours
if filename:
# If a filename is given, load a model from the given filename
self.model = svm_load_model(filename)
......@@ -19,6 +16,7 @@ class Classifier:
self.param.gamma = gamma # Parameter for radial kernel
self.model = None
self.neighbours = neighbours
self.verbose = verbose
def save(self, filename):
......
src/GrayscaleImage.py
View file @ 0dcaa652
......@@ -22,20 +22,6 @@ class GrayscaleImage:
for x in xrange(self.data.shape[1]):
yield y, x, self.data[y, x]
#self.__i_x = -1
#self.__i_y = 0
#return self
#def next(self):
# self.__i_x += 1
# if self.__i_x == self.width:
# self.__i_x = 0
# self.__i_y += 1
# if self.__i_y == self.height:
# raise StopIteration
# return self.__i_y, self.__i_x, self[self.__i_y, self.__i_x]
def __getitem__(self, position):
return self.data[position]
......
src/Histogram.py
View file @ 0dcaa652
......@@ -6,13 +6,9 @@ class Histogram:
self.max = max
def add(self, number):
#bin_index = self.get_bin_index(number)
#self.bins[bin_index] += 1
self.bins[number] += 1
def remove(self, number):
#bin_index = self.get_bin_index(number)
#self.bins[bin_index] -= 1
self.bins[number] -= 1
def get_bin_index(self, number):
......
src/NormalizedCharacterImage.py
View file @ 0dcaa652
......@@ -13,14 +13,16 @@ class NormalizedCharacterImage(GrayscaleImage):
self.blur = blur
self.gaussian_filter()
self.increase_contrast()
#self.increase_contrast()
self.height = height
self.resize()
def increase_contrast(self):
self.data -= self.data.min()
self.data = self.data.astype(float) / self.data.max()
# def increase_contrast(self):
# """Increase the contrast by performing a grayscale mapping from the
# current maximum and minimum to a range between 0 and 1."""
# self.data -= self.data.min()
# self.data = self.data.astype(float) / self.data.max()
def gaussian_filter(self):
GaussianFilter(self.blur).filter(self)
......
src/create_characters.py
View file @ 0dcaa652
......@@ -80,6 +80,7 @@ def load_test_set(neighbours, blur_scale, verbose=0):
def generate_sets(neighbours, blur_scale, verbose=0):
"""Split the entire dataset into a trainingset and a testset."""
suffix = '_%s_%s' % (blur_scale, neighbours)
learning_set_file = 'learning_set%s.dat' % suffix
test_set_file = 'test_set%s.dat' % suffix
......
src/create_classifier.py
View file @ 0dcaa652
......@@ -12,8 +12,8 @@ def load_classifier(neighbours, blur_scale, c=None, gamma=None, verbose=0):
if verbose:
print 'Loading classifier...'
classifier = Classifier(filename=classifier_file, verbose=verbose)
classifier.neighbours = neighbours
classifier = Classifier(filename=classifier_file, \
neighbours=neighbours, verbose=verbose)
elif c != None and gamma != None:
if verbose:
print 'Training new classifier...'
......
src/xml_helper_functions.py
View file @ 0dcaa652
from os import mkdir
from os.path import exists
from pylab import array, zeros, inv, dot, svd, floor
from pylab import imsave, array, zeros, inv, dot, norm, svd, floor
from xml.dom.minidom import parse
from Point import Point
from Character import Character
from GrayscaleImage import GrayscaleImage
from NormalizedCharacterImage import NormalizedCharacterImage
from LicensePlate import LicensePlate
# sets the entire license plate of an image
def retrieve_data(image, corners):
x0, y0 = corners[0].to_tuple()
x1, y1 = corners[1].to_tuple()
x2, y2 = corners[2].to_tuple()
x3, y3 = corners[3].to_tuple()
# Gets the character data from a picture with a license plate
def retrieve_data(plate, corners):
x0,y0, x1,y1, x2,y2, x3,y3 = corners
M = int(1.2 * (max(x0, x1, x2, x3) - min(x0, x1, x2, x3)))
M = max(x0, x1, x2, x3) - min(x0, x1, x2, x3)
N = max(y0, y1, y2, y3) - min(y0, y1, y2, y3)
matrix = array([
......@@ -29,7 +25,7 @@ def retrieve_data(image, corners):
[ 0, 0, 0, x3, y3, 1, -N * x3, -N * y3, -N]
])
P = inv(get_transformation_matrix(matrix))
P = get_transformation_matrix(matrix)
data = array([zeros(M, float)] * N)
for i in range(M):
......@@ -38,7 +34,7 @@ def retrieve_data(image, corners):
or_coor_h = (or_coor[1][0] / or_coor[2][0],
or_coor[0][0] / or_coor[2][0])
data[j][i] = pV(image, or_coor_h[0], or_coor_h[1])
data[j][i] = pV(plate, or_coor_h[0], or_coor_h[1])
return data
......@@ -50,108 +46,92 @@ def get_transformation_matrix(matrix):
U, D, V = svd(matrix)
p = V[8][:]
return array([
[ p[0], p[1], p[2] ],
[ p[3], p[4], p[5] ],
[ p[6], p[7], p[8] ]
])
return inv(array([[p[0],p[1],p[2]], [p[3],p[4],p[5]], [p[6],p[7],p[8]]]))
def pV(image, x, y):
#Get the value of a point (interpolated x, y) in the given image
if image.in_bounds(x, y):
x_low = floor(x)
x_high = floor(x + 1)
y_low = floor(y)
y_high = floor(y + 1)
x_y = (x_high - x_low) * (y_high - y_low)
if not image.in_bounds(x, y):
return 0
a = x_high - x
b = y_high - y
c = x - x_low
d = y - y_low
x_low, x_high = floor(x), floor(x+1)
y_low, y_high = floor(y), floor(y+1)
x_y = (x_high - x_low) * (y_high - y_low)
return image[x_low, y_low] / x_y * a * b \
+ image[x_high, y_low] / x_y * c * b \
+ image[x_low , y_high] / x_y * a * d \
+ image[x_high, y_high] / x_y * c * d
a = x_high - x
b = y_high - y
c = x - x_low
d = y - y_low
return 0
return image[x_low, y_low] / x_y * a * b \
+ image[x_high, y_low] / x_y * c * b \
+ image[x_low , y_high] / x_y * a * d \
+ image[x_high, y_high] / x_y * c * d
def xml_to_LicensePlate(filename, save_character=None):
image = GrayscaleImage('../images/Images/%s.jpg' % filename)
dom = parse('../images/Infos/%s.info' % filename)
result_characters = []
version = dom.getElementsByTagName("current-version")[0].firstChild.data
info = dom.getElementsByTagName("info")
plate = GrayscaleImage('../images/Images/%s.jpg' % filename)
dom = parse('../images/Infos/%s.info' % filename)
country = ''
result = []
version = get_node(dom, "current-version")
infos = by_tag(dom, "info")
for i in info:
if version == i.getElementsByTagName("version")[0].firstChild.data:
for info in infos:
if not version == get_node(info, "version"):
continue
country = i.getElementsByTagName("identification-letters")[0].firstChild.data
temp = i.getElementsByTagName("characters")
country = get_node(info, "identification-letters")
temp = by_tag(info, "characters")
if len(temp):
characters = temp[0].childNodes
else:
characters = []
break
if not temp: # no characters where found in the file
break
for i, character in enumerate(characters):
if character.nodeName == "character":
value = character.getElementsByTagName("char")[0].firstChild.data
corners = get_corners(character)
characters = temp[0].childNodes
if not len(corners) == 4:
break
for i, char in enumerate(characters):
if not char.nodeName == "character":
continue
character_data = retrieve_data(image, corners)
character_image = NormalizedCharacterImage(data=character_data)
value = get_node(char, "char")
corners = get_corners(char)
result_characters.append(Character(value, corners, character_image, filename))
if not len(corners) == 8:
break
if save_character:
single_character = GrayscaleImage(data=character_data)
data = retrieve_data(plate, corners)
image = NormalizedCharacterImage(data=data)
result.append(Character(value, corners, image, filename))
if save_character:
character_image = GrayscaleImage(data=data)
path = "../images/LearningSet/%s" % value
image_path = "%s/%d_%s.jpg" % (path, i, filename.split('/')[-1])
path = "../images/LearningSet/%s" % value
image_path = "%s/%d_%s.jpg" % (path, i, filename.split('/')[-1])
if not exists(path):
mkdir(path)
if not exists(path):
mkdir(path)
if not exists(image_path):
character_image.save(image_path)
if not exists(image_path):
single_character.save(image_path)
return LicensePlate(country, result)
return LicensePlate(country, result_characters)
def get_corners(dom):
nodes = dom.getElementsByTagName("point")
corners = []
def get_node(node, tag):
return by_tag(node, tag)[0].firstChild.data
margin_y = 3
margin_x = 2
def by_tag(node, tag):
return node.getElementsByTagName(tag)
corners.append(
Point(get_coord(nodes[0], "x") - margin_x,
get_coord(nodes[0], "y") - margin_y)
)
def get_attr(node, attr):
return int(node.getAttribute(attr))
corners.append(
Point(get_coord(nodes[1], "x") + margin_x,
get_coord(nodes[1], "y") - margin_y)
)
corners.append(
Point(get_coord(nodes[2], "x") + margin_x,
get_coord(nodes[2], "y") + margin_y)
)
corners.append(
Point(get_coord(nodes[3], "x") - margin_x,
get_coord(nodes[3], "y") + margin_y)
)
def get_corners(dom):
p = by_tag(dom, "point")
return corners
# Extra padding
y = 3
x = 2
def get_coord(node, attribute):
return int(node.getAttribute(attribute))
# return 8 values (x0,y0, .., x3,y3)
return get_attr(p[0], "x") - x, get_attr(p[0], "y") - y,\
get_attr(p[1], "x") + x, get_attr(p[1], "y") - y,\
get_attr(p[2], "x") + x, get_attr(p[2], "y") + y,\
get_attr(p[3], "x") - x, get_attr(p[3], "y") + y
\ No newline at end of file
Markdown is supported
0% or
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment