Disclaimer: The scripts and libraries uploaded in this project are intended to be a suite of tools for the extraction, manipulation and analysis of network data (graphs) from images. The scripts uploaded here are part of a methods paper detailing the algorithms used which is soon to be published. The original images used as examples in the paper can be found in the /data/originals directory. The images represent a range of different use-cases for NET both from different research projects as well as with regards to the size of the networks they contain. They are ready to be processed without any further modifications.

#Introduction and Overview The ultimate goal of the NET framework is to make images of networks processable by computers. Therefore we want to have a pixel based image as input, as output we want a representation of the network visible in the image that retains as much information about the original network as possible. NET achives this by first segmenting the image and then vectorizing the network and then extracting information. The information we extract is

• First and foremost the graph of the network. We find the crossings (nodes) and connections between crossings (edges) and therefore extract information about the neighborhood relations, the topology of the network.
• We also extract the coordinates of all nodes which enables us to embed them into space. We therefore extract information about the geometry of the network.
• Last but not least we track the radii of the edges in the extraction process. Therefore every edge has a radius which can be identified with its conductivity.

In the following we will first provide detailed instructions on how to install NET on several platforms. Then we describe the functionality and options of each of the four scripts that make up the NET framework.

Setting up the NET framework

The NET framework is a set of python scripts that make use of the python module net_helpers.py and the cythonized library C_net_functions.so. For NET to work you will need three things

1. a working installation of python 2.7 and pip
2. the third party libraries utilized within NET
3. a version of the C_net_functions.pyx file compiled for your platform

List of libraries NET depends on:

• scipy: general scientific computing
• numpy: general scientific computing
• matplotlib: visualization
• cython: for translating python into C and compiling it
• networkx: to handle networks
• scikit-image: for image processing
• opencv: for image processing
• pillow: for image I/O
• shapely: for some geometry operations
• meshpy: for the triangulation

In the following we detail how to get these three things on Linux, Windows and Mac platforms.

Linux

1. Python 2.7 should be installed by default, if it is not, your package manager most likely will provide it. You can get pip by running

   wget https://bootstrap.pypa.io/ez_setup.py -O - | sudo python
   

   (More detailed instructions on how to get pip can be found here).

2. For numpy (and some other libraries) you will need the python-dev package, get it by running

   sudo apt-get install python-dev 
   

   Now you have pip, it should be easy to install most of the other libraries. For example to install networkx, simply run

   pip install networkx
   

   Repeat this process with scipy, matplotlib, cython, scikit-image, pillow, meshpy and shapely. To install opencv, follow the instructions detailed here or scroll to the bottom of the installation instructions for some notes on how to install openCV.

3. To compile your own C_net_functions.so file, navigate to the /net directory and run

   python setup_C_net_functions.py build_ext --inplace
   

   This should create two files called C_net_functions.so and C_net_functions.c, the first you need, the latter you can safely delete.

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Windows

True Windows

1. Download the latest python 2.7 release here and install it. To get pip, if you are on windows 8 or later, start Powershell and run

   (Invoke-WebRequest https://bootstrap.pypa.io/ez_setup.py).Content | python -
   

   If you have an earlier windows version, download ez_setup.py here, navigate to the directory you saved the file in and run

   python ez_setup.py
   

   (More detailed instructions on how to get pip can be found here).

2. Thankfully, Christoph Gohlke maintains a site with a wide collection of python packages for windows. Go to his web page and download the .whl files for scipy, numpy, matplotlib, cython, networkx, scikit-image, opencv, pillow, meshpy and shapely that fit your platform. Install the packages by navigating to the directory you saved them in and run

   pip install SomePackage.whl
   

   for all the packages you downloaded.

3. Navigate to the folder /NET and run

   python setup_C_net_functions.py build_ext --inplace
   

   A file named C_net_functions.pyc should have bean created in the \NET directory Compilation might be abortet with the message "error: Unable to find vcvarsall.bat" There is a relatively easy fix for that (based on this stack overflow post): Install Visual studio 2013 and set the environment variable by running

   SET VS90COMNTOOLS=%VS120COMNTOOLS% 
   

   Rerun

   python setup_c_net_functions.py build_ext --inplace
   

   If it still does not work, you can try the VM-Version described below.

Linux-VM in Windows

(Thanks to Benedikt Best for describing this solution!)

1. Get VMWare Player (licence free for non-commercial use) and install it.

2. Download and install Ubuntu. Make sure your Ubuntu-VM has at least 4GB of RAM, else working with larger images/networks might cause swapping to hard drive and freezing of the computer.

3. Proceed like described in the instructions for the Linux installation above.

Note: for a freshly installed linux, other dependecies might need to be resolved for the third party libraries to run, for example libgeos-dev and libpng3. In general if a dependency is missing for a library, the error occurring when trying to install said library will give you a hint of what is missing and you can simply get the dependency by running

pip install somedependency

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Mac OSX

1. Download and install the latest python 2.7 release here and install it. Depending on whether you have access to easy_install or curl, run one of the following

   sudo easy_install pip
   curl https://bootstrap.pypa.io/ez_setup.py -o - | python
   

   (More detailed instructions on how to get pip can be found here).

2. For numpy (and some other libraries) you will need the python-dev package, get it by running

   sudo apt-get install python-dev 
   

   Now you have pip, it should be easy to install most of the other libraries. For example to install networkx, simply run

   pip install networkx
   

   Repeat this process with scipy, matplotlib, cython, scikit-image, pillow, meshpy and shapely. To install opencv, either use brew or follow the instructions detailed here or scroll to the bottom of the installation instructions for some notes on how to install openCV.

3. Navigate to the folder /NET and run

   python setup_C_net_functions.py build_ext --inplace
   

   This should create two files called C_net_functions.so and C_net_functions.c, the first you need, the latter you can safely delete.

Known issues

When running NET within a virtualenv on mac the matplotlib backend is not found correctly. This is a known issue which unfortunately prevents NET from running. It can be fixed by switching to the qt4 backend. In the code you have to replace:

import matplotlib.pyplot as plt

with

import matplotlib
matplotlib.use('qt4agg')
import matplotlib.pyplot as plt

This affects all the scripts from the /validation and /GeGui folders. The appropriate lines are already added to the scripts. If you run into this problem, just uncomment them in the beginning of the affected scripts.

Some notes on installing OpenCV for Linux

OpenCV is a powerful library for image processing and computer vision written in C. For this application we use the python wrapper for the library. Nevertheless before we can wrap it in python, we first need to install the library itself. To do this, you can follow the instructions provided below.

1. Download the source files and unpack them.

2. Run

sudo apt-get install build-essential
sudo apt-get install cmake git libgtk2.0-dev pkg-config libavcodec-dev libavformat-dev libswscale-dev
sudo apt-get install python-dev python-numpy libtbb2 libtbb-dev libjpeg-dev libpng-dev libtiff-dev libjasper-dev libdc1394-22-dev
mkdir opencv2.4-make
cd opencv2.4-make
cmake -D CMAKE_BUILD_TYPE=RELEASE ..path/to/opencv2.4.10 (the folder you just unpacked)

This will compile openCV which will take a while. Now run

make

which will build openCV - might also take a while. Finally run

sudo make install

Now you have resolved the openCV dependency of the wrapper and

import cv2

should work inside a python shell.

Important note: NET does only work with openCV versions 2.x as in 3.x the syntax of the find contour function changes.

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Extracting network data using the NET framework

The network extraction and analysis tool (NET) is intended for the extraction of network data from images which can later be analyzed easily. The workflow is broken down into four steps represented by four processing scripts

1. Segment the original image into foreground and background and therefore create a binary image using binarize.py
2. Extract the network from the binary image unsing net.py
3. Optional: manually correct errors in the network or remove artifacts using the graph-edit GUI gegui.py
4. Analyze basic characteristics of the network with analyze.py

binarize

To get from a grayscale to a suitable binary image can be tricky. I have provided rudimentary scripts which do some contrast improvement and thresholding for different kinds of images (binarize_tracheole.py for tracheoles, binarize_crack.py for cracks and binarize_leaf.py for leaves). All scripts take the path to the image as required arguments as well as some optional arguments to modify their behaviour. Imput images can be of several formats (read the PIL Image file formats documentation for reference). Common formats like .png, .jpg and .tif are supported in any case.

Tracheoles and Cracks

The two scripts behave similarly with regards to their processing methods. I have separated the scripts nevertheless to improve clarity and enable diversification later on. Available parameters are

• -g kernel size of the gaussian blur applied to reduce noise in the image at the beginning. g should be significantly smaller than the smallest structure in the image you want to resolve. If g = 0, no gaussian blur will occur.
• -t value for the threshold used for dividing the image into background and foreground (black and white). E.g. if t = 100, all pixels with a value smaller or equal t will be mapped to zero (black) and all pixels larger than t will be mapped to one (white). t should be choosen in a way that all important structures are present and connected while everything that belongs to the background vanishes.
• -s kernel size of the binary opening and closing operators applied to smoothen the contours of the foreground. s should be considerably smaller than the diameter of the thinnest network part. If s is too high, information is lost as foreground structures vanish. If s is too small, the operation has close to no effect. If s = 0, no smoothing will occur.
• -m minimum size of features (in pixels) that will be preserved in the image. This will remove artifacts and noise that are disconnected from the main network. If for example m = 5000, structures composed of less than 5000 pixels will be removed from the image. In general, I advise to set m smaller than 1/10th of the total number of pixels in the image. If m is choosen to high, the main structure might vanish. If m is choosen too low, atrifacts and noise might remain in the image.

To segment an image of a tracheole (for example tracheole1.png) with parameters g = 0 (no blurring), t = 110, s = 3 and m = 500, run

python binarize_tracheole.py ../data/originals/tracheole1.png -g 0 -t 110 -s 3 -m 500

To segment an image of a crack pattern (for example cracks2.png) with parameters g = 3, t = 150, s = 2 and m = 10000, run

python binarize_crack.py ../data/originals/cracks2.png -g 3 -t 150 -s 2 -m 10000

Leaves

This script behaves a bit differently as in addition to thresholding and smoothing it also tries to increase the contrast in the image. Available parameters are

• -g as before: the kernel size of the gaussian blur operation.
• -eq the kernel size of the local histogram equalization applied to increase contrast. If eq = 0, no local histogram equalization will occur.
• -r After local histogram equalization has been applied, a fraction of the processed image is recombined with a fraction of the original image. r determines said fraction. Therefore if r = 0.3, the outcome of the recombination process will be 0.3 x equalized image + 0.7 x original image.
• -o The threshold for thresholding the image to create a binary image is determined automatically using Otsu's method. o controls an offset to the automatically determined threshold. Therefore if o = 10 and the threshold calculated via Otsu's method equals 125, the image will be thresholded with a threshold t = 135 (also allows for negative values of o).
• -s as before: kernel size of the binary opening and closing operators for smoothing.
• -m as before: minimum feature size.

To segment an image of a leaf venation pattern (for example leaf1.png) with parameters g = 5, eq = 11, r = 0.5, o = 25, s = 3 and m = 50000, run

python binarize_leaf.py ../data/originals/leaf1.png -g 5 -eq 11 -r 0.5 -o 25 -s 3 -m 50000

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NET

Extraction of network data is done with the net.py script. NET takes the path to a binary (black and white) image as required command line argument and extracts a graph (networkx graph-object) from the largest connected component in the image. The format of the binary image needs to be pixel based (vector graphics need to be converted first) but other than that, all formats supported by the PIL library are possible. NET's behaviour can be modified by several parameters and switches:

• -source Required argument. The path to the image you want to process, for example ../data/originals/tracheole3.png. Either a relative path to the processing script or a total path works.
• -help displays all available options with a short description in the command line.
• -dest (default = source) If you want to save NET's results in a different folder than source, specify the dest argument. If for example you want to process leaf1.png from the /data/originals folder but save the resulting network in the /NET folder, specify -dest ../NET/. Either a relative path to the processing script or a total path works.
• -v (default = False) NET is run via the command line but by default it will not produce any command line output to avoid spam. If you enable verbosity by specifying v, NET will report on its current processing state and output some information on how long it took the script to complete the previous processing step.
• -d (default = False) If something goes wrong, NET crackes or the output is not what you expected, it might help to enable the debugging mode by specifying d. This will further increase the verposity of the script. Moreover, NET will save visualizations of intermediate processing steps so you can have a look and maybe figure out what is going wrong. The visualizations include a plot of the extracted contours, the triangulation and an overlay of the contours, triangulation, distance map and extracted network.
• -plt (default = False) Plotting and saving images (especially really large ones like NET is accustomed to dealing with) takes a lot of time. This is why by default visualization of the extracted networks is disabled. If you want to see what NET extracted, specify plt. By default, NET will save plots in .pdf format. This can take ages for graphs with more than ~1000 nodes. If you want to change the plot file format, specify the fformat argument.
• -fformat (default = .pdf) File format of the plots if plt is enabled. To display all available formats for your platform, start a python interpreter (for example by typing 'python' in your terminal) and run

import matplotlib.pyplot as plt
plt.gcf().canvas.get_supported_filetypes()

... If you want do visualize a really large graph, I would recommend to set fformat to .png and crank up the resolution of the image by specifying dpi so details are still recognizeable.

• -dpi (default = 500) If saving plots in non-vector-graphics formats like .png or .jpg you can change the resolution by specifying the dpi argument.
• -gformat (default = .gpickle) If you want to change the format the extracted graph is saved in, specify the gformat argument. For a list of supported formats, have a look at the networkx reading and writing graphs documentation. The default .gpickle format is a dump of a python object (in this case a networkx.Graph object). It is handy as all our processing is done in python and it can easily be read again to be the same python object it was before saving to the harddrive. For a cross-program format .gml most likely is the best choice as it is widely used and simple.
• -r (default r = 0) During the extraction process, the graph is made up of many points originally stemming from the triangles making up the contstrained delaunay triangulation at the heart of the vectorization process. Most of these points are not important for the topology of the graph (we therefore call them "redundant") as they lie on long stretches of the network that do neither represent junctions nor tips. These points are only there to support the geometry of the network. By specifying r you can decide how many of these redundant points you want to keep in your final representation. If r = 0 only nodes and tips will be saved and all redundant points will be discarded - this is nice if you don't care about geometry and want to save some time and disk space. If r = 1, approximately half of the redundant points will be kept. This is a good compromise between an acceptable approximation of the network's geometry and speed/size. If r = 2, all redundant points will be saved. This produces large files and the resulting graphs might take some time to load and analyze but it also has by far the best approximation of the network's geometry.
• -p (default p = 3) If the edges of your binary image are noisy, jagged or especially wiggly (which is the case for most images of biological networks), this might lead to the emergence of spurious branches in the extracted networks. These branches are extremely short and therefore easily recognizeable. By pruning away all branches that are shorter than p points (see the definition of redundant points in the description of the r parameter), we get rid of spurious branches. Treat p with care as you might lose information if p is too high (genuine branches are pruned away) and if p is too low, spurious branches might remain. p should be choosen considerably smaller than the average edge length, commonly between 2 and 6.
• -m (default m = False) If you are given a binary image that was maybe not processed with one of the binarize scripts and with whose quality you are not satisfied, you can use the m parameter, to remove disconnected artifacts and noise from the image (as described in the binarize section).
• -s (default s = False) As with the m parameter, by specifying s you can do some improvement of your binary image by smoothing contours before you start processing (as described in the binarize section).
• -dm (default dm = False) If you want to save the distance map that is created during the graph extraction process, enable dm. If you want to later open and edit the graph with GeGUI, you will need the distance map so better save it right away, it will be created anyways.

If you want to extract a graph from the image /data/binaries/tracheole6.png, set pruning to 5, save all redundant nodes, enable verbosity and additionally save a visualization of the graph in .png format with a resolution of 2000 dpi, run

python net.py ../data/binaries/tracheole6.png -p 5 -r 2 -v -plt -fformat png -dpi 2000

If you have a noisy binary that you want to smooth and clear up (like /data/binaries/tracheole8.png), you want no pruning, are content with only some redundant nodes, want to have a visualization of intermediate steps, verbosity and a distance map but no plot of the final graph, then run

python net.py ../data/binaries/tracheole8.png -s 2 -m 1000 -p 0 -r 1 -d -v -dm

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gegui

I have been dealing with networks extracted from pseudo 2D structures a lot (especially the tracheole dataset). These images are projections onto a plane and therefore might contain network "crossings" which arent real but just created by superposition of two branches. To correct these spurious junctions I have written the GeGUI (graph edit GUI) which allows you to load the extracted graph object, superimpose it onto the original image and modify the graph's structure by manually deleting and creating nodes and edges. The script to start the GUI is called gegui.py but all the functionality is placed in the three sub-scripts InterActor.py (dealing with user-interaction), GraphHandler.py (dealing with manipulations of the graph object) and PlotHandler.py (dealing with the dynamic display of changes to the graph on the screen). To run the GeGUI you need to specify a folder in which the graph you want to process is located. For the GeGUI to properly start the folder also needs to contain an euclidean distance map of the binary the graph was extracted from and the original image. Therefore the folder should look like this:

/resultdir
----original_image_orig.png
----extracted_graph_r1.gpickle
----distance_map_dm.png

I the /data/results folder I have prepared several such folders (e.g. tracheole1, tracheole2 and tracheole3) to test GeGUI. If you want to load and process for example the graph extracted from tracheole1.png, run

python gegui.py ../data/results/tracheole1

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analyze

The analyze.py script is a very simple script that loads a graph, calculates some basic statistics of the graph and saves them to a text-file. The statistics are in no way complete and are just intended to give you a quick overview over the properties of the graph and enable you to sanity-check the results NET produced. To analyze your graph (currently reads only .gpickle format), run the script with the path to the graph as argument. If you for example want to analyze the graph of tracheole1 we already used in the GeGUI example, you need to run

python analyze.py ../data/results/tracheole1/tracheole1_graph_red1.gpickle

This command will have created a file called tracheole1_network_statistics.txt in the directory that holds the source-graph. As before, you can specify a separate target directory for the output via command line option. Therefore if we wanted to save the statistics file in the /data/results folder, we would need to run

python analyze.py ../data/results/tracheole1/tracheole1_graph_red1.gpickle ../data/results

The analyze.py script is made up of a series of functions that calculate each individual statistic. Each function then gets called once and writes its result to a textfile. It therefore is very easy to extend or adapt the script by adding new functions or removing existing functions. Just make sure you call your function at the end of the script and write the result into the file. The statistics calculated by the script as is are:

• Number of junctions in the network. Every node that has more than two neighbors is considered to be a junction (also called branching point).
• Number of tips in the network. Every node that has exactly one neighbor is considered to be a tip (also called endpoints).
• Total length of the network: The total length is the sum over all individual edge-lengths. It therefore has the dimension [pixels].
• Average edge length: The average edge length is the average of all individual edge-lengths. It therefore has the dimension [pixels].
• Average edge radius: The average edge radius is the average of all individual edge-radii. It therefore has the dimension [pixels].
• Total network area: The total network area is the sum of all individual edge-lengths times individual edge-radii. It therefore has the dimension [pixels^2].
• Area of the convex hull of the network: If we consider all nodes within the networks to be a point cloud and then calculate the convex hull of this point cloud, this is the area of this convex hull. It therefore has the dimension [pixels^2].
• Number of cycles in the network: A cycle in a network is a closed path. Here we do NOT calculate all possible closed paths but calculate the size of the cycle basis of the network. A basis for cycles of a network is a minimal collection of cycles such that any cycle in the network can be written as a sum of cycles in the basis. Therefore the cycle basis of the olympic rings has size 9 (5 rings + 4 overlaps).

TODO

• package NET as a python package
• sort NET's options in a comprehensible way
• refer to the methods paper as soon as it is in the ArXiv
• implement an option to modify the node size in plots
• specify how gegui selects the right files in a folder
• add markdown example processings for binarize, NET and maybe also analyze including images
• maybe add screenshots to geguis description