Automated electric wire extraction from LiDAR point cloud data · Automated electric wire...
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Automated electric wire extraction from LiDAR point cloud data Ajay Kumar Sharma, Wrick Hom Choudhury & Anand Mohan Singh (RMSI PRIVATE LIMITED)
Transcript of Automated electric wire extraction from LiDAR point cloud data · Automated electric wire...
Automated electric wire extraction from LiDAR point
cloud data
Ajay Kumar Sharma, Wrick Hom Choudhury
&
Anand Mohan Singh
(RMSI PRIVATE LIMITED)
www.rmsi.com
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Introduction
Acronym for light detection and
ranging (LiDAR).
Method for collecting very dense and
accurate elevation data.
It refers to a remote sensing
technology that emits intense, focused
beams of light and measures the time it
takes for the reflections to be detected by
the sensor.
Uses an active sensor to emit energy
(light) and detect returned energy.
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LiDAR Data
Airborne and Terrestrial capabilities
Combines GPS and an Inertial Measurement device to compute x,y,z
positions
Every point recorded has an x,y,z, and intensity value
Can be collected day or night)
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LiDAR Data Issues
Huge datasets
Cumbersome processing
Requires heavy computational power.
Availability of automated processing tools are less.
Automated classification in most software is restricted to ground point
classification and canopy classification.
Often object extraction tools are limited to buildings and trees extraction.
Even the extraction of these objects are not absolute.
Large amount of manual intervention is necessary for quality output.
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The Issue in Focus
Telephone wires, cables, low tension wires on the roadside are a
part of urban electrical utility infrastructure.
Often these wires pass through road side vegetation making
classification nearly impossible
Even if some points are selected through eyeballing there is
questionable veracity and limited certainty about the authenticity of
the capture.
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Wire passing through vegetation
Vegetation
Wire
Wire
Ground
Ground
Electric poles
It is possible to see the wire section passing through the vegetation but it is difficult to say for sure and capture
those points for classification
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How can we solve this?
The solution for the problem is to find a mathematical relation
between the points of the wire.
Since ideally a wire is a curve we will approach with a curve fit for
the wire points.
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Process
The following are the step by step approach for the processing :
Step 1: Capture and create a sample set
Step 2: Exporting it as a separate file
Step 3: Plane fit of the wire-points
Step 4: Curve fit of the wire-points
Step 5: Removing non-wire points
Step 6: Saving final file as a .las file
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Step 1: Capture and create a sample set
A mathematical relationship or logic has to be established between the
points (in this case the wire points )
To establish this relationship we need to capture a sample set using
which the equation can be established.
The creation of the sample training set is created by:
I. Using a standard GIS software which allows LIDAR processing (In
this case we have used Global Mapper 16 LIDAR suit)
II. The user needs to be able to identify some part of the wire that he
can capture and classify as wire
III. Once this step is done the user needs to be able to export the class
exclusively as a separate las file
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The original overhead view of the strip (normal view port of global mapper 16)
Using the sectional profile tool to select the strip for classification
The sectional view showing the wire points
Manually select the wire points The selected point are then classified under the power line classification .
Step by Step method of Mapper 16manual classification of points in Global
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Step 2: Exporting it as a separate file
The points classified as wire is then exported as an exclusive las
file.
This las file is plotted on a 3D plot in python
The importance of this part is that the algorithm can have a separate
dataset to develop the necessary mathematical relationship
effectively
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The exclusive wire point file read and plotted in python
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Step 3: Plane fit of the wire-points
Wires as we generally see is a curve in the xz plane while it is
generally a straight line in the xy plane (ideally).
Thus we will first try to fit a plane in the dataset containing the wire
points.
The main steps for the plane fit :
I. Select three points from the sample set which will be used to
create the plane
II. Find the plane equation
III. Find the allowable width
IV. Classify all the points that fall within the space defined by the
plane and the range
V. Create separate matrix containing these points (classified within
this space ) exclusively
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# 15
(note : for an ideal curve one of the ends is also obviously the highest point )
The plane equation requires three points for the plane
The three seemingly best from a curve would be
The lowest most point of the curve
The two end points of the curve
The three points
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Finding plane equation
Describing a plane through three points
Let p1=(x1, y1, z1), p2=(x2, y2, z2), and p3=(x3, y3, z3) be non-collinear
points.
From this we get the equation of the plane: ax+by+cz+d=0
d is found by solving the equation by any one of the three points.
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# 17
Fitting a plane through three points
Plotting all the points along with the plane .
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Find allowable width
Once the plane equation is found it is clear that the wire points are
not really on a single plane but they are in close proximity of the
plane since they are not in 2d but 3d. The point actually lie over the
wire surface
The wire with the laser dots along its sides
The laser markers showing lateral width
Laser points along the wire showing direction of scan
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Thus the need to accommodate the allowable width arises
These changes the 2 dimensional plane into a very narrow 3d space
Wire with the laser marker on the sides
Wire with plane fit through it
The markers and the plane
Normal distance from the markers onto the plane
(This is also called the residuals )
The range of all the residuals decides the
allowable width
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# 20
All the points that lie within the limits of that range are classified separately
A separate matrix containing only the points lying within these limits is also created
The points in green are within the plane limits
One thing to be noticed here is that the wire has been extracted along with other points in the plane
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Step 4: Curve fit of the wire-points
The method of fitting the curve would be based on the method of
least squares.
The curve would be 3rd degree polynomial
2D curve fit is used since it is easier and would not hamper the
output authenticity
We will use the X and Z coordinates only for processing the curve and
the residuals. Y coordinate is not required since it’s a 2D curve fit
and we have already segregated the wire points and other points in
the plane
This is also one reason why the plane fit was done in the first place
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The sample training set is referred again for the development of the
curve equation.
Using least square approach
i
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i
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The third degree polynomial in the equation in a matrix form
5
5 6
=
Total j+1 equation are created for (j=3) for a 3rd degree polynomial
The resultant equation will give us the value of the three coefficients and the constant
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Step 5: Removing non-wire points
Now we have a plane that contains the wire and all other points in
the plane
The objective now is to process the curve fit equation and try it with
only the points in the plane dataset and not the entire dataset
The main steps are
I. Find the range of allowable residuals using the training set
II. Process the residuals of all the points lying within the plane and then remove the
points whose residual is out of range
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Once the curve fit equation is found for the sample set unlike the plane fit (where the plane actually passes through at least the three points ) The curve is a best fit and does not pass through any of the wire points (ideally)
Thus the residual range (in the xz plane) for the wire points are calculated and stored
This becomes the allowable range for the wire points only
The best fit curve equation
Wire points
Perpendicular distance onto the equation to ascertain the residual range
Finding the residual range
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In one of the earlier slides it was already established that the wire was already extracted in the plane along with other points
Since it was a plane fit the computer did not differentiate between the wire and the rest of the points in that plane
All the plane points
Wire points
Other points in the plane
The plane points without the wire
Only wire points
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Step 6: Saving final file as a .las file
Now we are left with only the wire points in the entire dataset this is
then written in a .las file and saved.
This file can be opened in any standard lidar processing software.
This file contains the original dataset with the wires classified in the
designated class
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Before processing with our process , …wire passing through the vegetation cannot be captured
After processing the dataset using our process the entire wire can be clearly seen
It can be seen that the auto process has clearly captured the wire points passing through the vegetation
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General Observations
• We can see that this process can extract one single wire passing through vegetation.
• It is often seen that one wire passing across two poles is actually rarely a reality
• In reality there is a bunch of wire passing across the poles and often in very
disorganized manner.
• Now it should be mentioned that the process was carried out using an edited dataset
to focus on the process and the effectiveness of the math behind it.
• We can now take a look at the original data set and we see that there are many wires
passing through the roadside trees.
• These wires has to be sampled individually and processed individually and then the
final results from each process should be combined together into one single .las file
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The original dataset containing all the wire passing through the vegetation
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There are twelve wires
Separately sampled
Separately processed
Finally all the final outputs combined together in one output
We can clearly see that the wires points passing through the trees has been classified.
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This is a separate las file containing the electrical utility only.(which are wires and poles only)
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The file without using our process has large parts of the wire missing
Same file after using our process shows much more detailed wire.
We can clearly see the depth of extraction of the wire points that can be achieved using automated algorithms over manual approach
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Precautions
It is difficult to obtain samples from disorganized wire combinations
Every wire must be sampled individually.
Limitations
Benefits
Requires careful sampling by the user
Any mistake on the sampling part will reflect in the output
Reduce manual intervention
Increase processing efficiency
Reduce human error in manual sampling
Automatic selection of points passing through vegetation
Points so classified cannot be questioned for their veracity
Automation requires much less time.
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Thank You
