Post on 15-Nov-2015
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Introductions to Maps based on Prof. Ian Dowman 2009
Dietmar Backes
Content of this lecture: Fundamental definitions
Examples and Key-characteristics of maps
Methods of Mapping
Some accuracy measures for Maps
Geometric corrections and registrations of images
DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
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Terminology
Maps are traditionally paper documents. Now the information which used to be depicted on a paper map is stored
in digital form.
Image maps are now very common e.g. Google Earth. Subsequently we will use the term MAP to cover information stored in
both paper and digital form.
Digital data can be presented in paper form, but also in other ways such as perspective views, but these can still be referred to as maps.
Remark:
This Lectures gives a first glimpse on key issues which will be discussed in detail at later parts of this module.
DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
The role of Maps
A Map is a traditional method of recording and displaying objects and their spatial location and distribution
Maps are an indispensable aid for everyone from a scientist to a traveller
It serves as a means of communicating the spatial relationship and the forms of the objects
Many maps also give accurate location
Basic elements of a map Location and attribute to that location
Location means where in space
Attribute means what is it about or quality of that location
Types of map Based on the theme of the map
Based on the scale of the map
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DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Types of Maps
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DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Fit for Purpose
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We need to assess weather maps are suitable for the application in mind
We need to decide the best way to generate maps which satisfy the requirements of the intended application
DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Examples of different Maps and their key properties
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An ancient map of a city in
Mesopotamia on a clay tablet A section of first topographic map of Paris (good horizontal accuracy poor vertical accuracy)
DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
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Examples of different Maps and their key properties
DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
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Ordnance Survey 1:25 000 Ordnance Survey 1:50 000
Examples of different Maps and their key properties
Topographic Maps
DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Scale of the Map
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DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Global Map with 8 Layers
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DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Google Earth/Maps
Data from different sources
Example of image maps, produced from aerial photographs and satellite data
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DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Google Earth/Maps
Data acquired at different times
Multitemporal data collection
Seamlines in are a specific disadvantage of image maps
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DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Representing the 3rd dimension 2.5D elevation
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The representations introduced so far are 2D. Heights can be represented by:
Contours
Spot heights
Relief shading
Digital Elevation Models (DEMs)
(rasterised) digital elevation models are convenient for use in a computer and can be displayed in many ways.
We call such representations 2.5 D
DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
2.5D DEM of a large area
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DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Representing the 3rd dimension 3D point clouds
The Helicopter mounted ATLAS
system collects approximately
30,000 3D data points per
second.
Flying at an altitude of 150m and
60kph this translates to a density
of 30 points per square metre on
the ground. A typical swath width
at this altitude is 60m
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Example: ATLAS - High resolution Laser Terrain mapping
This area is subject
to rapid technical
advances!
DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Applications: 3D City Models
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Rendered LiDAR point clouds
Examples by Infoterra
DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
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Applications: 3D City Models
Example Microsoft Virtual World (Bing maps)
DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
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Applications: 3D City Models Example Virtual Berlin
courtesy of Prof. Kolbe
(in Google maps)
Today 3D visualisations are often
called 3D maps; however it is
more complex to represent and
model semantic information in 3D.
DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Example Deformation maps: DEMs showing differential movement using interferometric SAR (IfSAR)
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IZMIT Earthquake
Subsidence in urban areas
Examples by fNPA
Fringe vectors superimposed
onto Landsat TM
4m total displacement detected
Such maps providing millimetre precision in heights
based on complex analysis of Satellite imagery
DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Sources of Data Existing maps
Existing maps are very useful source of data. Currency of the map with respect to the dynamism of the theme of the map and the area has to be checked before utilising the existing maps
Ground survey Ground survey for some selected location or at random locations are required for
most of the surveying and mapping methods. Ground survey for the entire area is also applicable for certain types of maps
Ground survey is often used to fix Ground Control Points GPS (Global Positioning System) very useful
New Platforms and Mobile Mapping Low flying unmanned aerial vehicles (UAVs) and ground based vehicles are
currently developed and tested for rapid mapping. Such systems deploying a range of sensors. Currency of information will be very high.
Aerial photographs Currency of information available is high if the data is newly acquired
Satellite data Currency of information available is high as the data is available on repeated
coverage
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DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Methods of Mapping
Conventional ground surveying Using surveying and levelling instruments such as theodolites
and GPS receivers
Airborne and Spaceborne sensing Aerial photographs - Photogrammetry
Satellite data
Lidar data
Radar data (radargrammetry)
Interferometric data
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DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Comparison of methods of mapping
Conventional Ground Surveying Useful for highly accurate large scale maps
Highly labour intensive method and hence unsuitable for larger areal coverage and unsuitable for small scale maps
Airborne sensing (e.g. Photogrammetry from aerial photographs) Useful from large scale to small scale maps
Cost of data acquisition is high
High initial investment is required to derive maps
Requirement of specially trained labour
New techniques such as Lidar and Radar extend the scope
Space borne Sensing (e.g. Photogrammetry from satellite data) Cost of data acquisition is comparatively cheaper
Suitable for medium scale to small scale maps
Suitable for updating the existing maps as the repeated coverage is available
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DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Accuracy of maps
Absolute accuracy
depends on a grid being present.
Related to the scale of the map. The horizontal accuracy is usually represented as width of line as the smallest feature that can be interpreted from a map, which is 0.3 mm to 0.5 mm on the map.
hence on 1:50,000 map
0.3 mm to 0.5 mm = 15m to 25m
The horizontal accuracy of 1:50,000 map is 15m to 25m.
The vertical accuracy is usually represented with respect to the contour interval, which in turn depends on the scale of the map and the type of the terrain.
The contour interval for 1:50,000 scale map is 20m and the vertical accuracy of that map is 6m to 10m. The contour interval for 1:50000 scale map can be 10m as well, if the terrain is relatively smoothly undulating and then the expected accuracy of that map is 3m to 5m.
Note also Digital Elevation Models
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DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Accuracy of maps
Relative accuracy
Accuracy of an object with reference to another object
irrespective of the absolute accuracy of either of the objects or
accuracy of one location with respect to another location in the same map irrespective of absolute accuracy of either of the
locations
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DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Factors affecting the accuracy of the map
Scale
Method of compilation
Generalisation/presentation
Some features are omitted in the map
Some are exaggerated and presented
Some are approximated and presented
Generalisation / Presentation depends on the scale of the
map, type and purpose of the map
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DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Generalisation - effect of the Scale of the Map
26 IGN 1:25,000 IGN 1:100,000 IGN 1:250,000
DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Generalisation - Feature selection or elimination
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1:10,000 1:25,000 1:50,000 1:100,000
Imhof (1968)
The concept of Mapping will be discussed in detail later in the course.
DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Assessing accuracy The accuracy can be determined by calculating the closeness of measured co-
ordinates (on the map) to the true value. This is measured by root mean square error.
where v is the residual error and n is the number of points.
The precision of a set of observation - the closeness of measurements to each other - is estimated by the standard deviation ():
where is the mean difference
Reliability is a measure of accuracy given by the proportion of points which fall outside a given limit. The rule of thumb usually applied is that 95% of points will have a
precision of 2 and 99% will have a precision of 3 .
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n
vv
1
( )2
n
vv
nrmse v
)(2
DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Absolute Accuracy of UK topographic maps from
Ordnance Survey
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Scale and method of
original survey
Expected absolute accuracy
at differing confidence level
68% 95% 99%
1:1250 0.5m 0.8m 1.0m
1:2500
Resurveyed / reformed 1.1m 1.9m 2.4m
1:2500
overhaul 2.8m 4.8m 6.0m
1:10000 4.1m 7.1m 8.8m
The detail may be less accurate than these values.
DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Relative Accuracy of UK topographic maps from
Ordnance Survey
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Scale and method of
original survey
Expected relative accuracy at
differing confidence level
68% 95% 99%
1:1250 0.4m 0.8 1.0m
1:2500
Resurvey/reformed 1.1m 1.8m 2.3m
1:2500
Overhaul 1.2m 2.3m 3.0m
1:10000 3.5m 6.7m 8.8m
The detail may be less accurate than these values.
DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Geometric correction and registration of earth
observation data for mapping (e.g. Satellite
images)
Motivation:
As seen in previous section, images collected by airborne
and space borne sensors but also from the Ground are an
efficient data source for mapping.
Fundamental Problem:
How can images, captured from a airborne camera, related to
the maps projected to the curved surface of our Earth?
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Show Example!
DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
A Spherical earth is presented on a two dimensional flat paper map (most of the time), which needs projection
techniques
This projections cause some distortions will be discussed in the Foundation module in detail
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Geometric correction and registration of images Mapping on the earth surface
DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Geometric correction and registration of images Principles of image formation
A frame may be formed in three ways:
1.As a single exposure - that is with no significant movement of the sensor whilst
the image is formed as in the case of a frame camera.
2. As a series of lines almost normal to the track of the sensor. In this case a
single line can be considered without a time parameter but time must be
considered in constructing a full frame. The push broom scanners fall into this
category.
3. As a series of points each recorded at a separate time. This is the most
distorted type of image requiring the most complex mathematical model. The
scanner systems and microwave systems fall into this category.
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DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Geometric correction and registration of images Principles of image formation
Single Exposure
With a central projection the whole image is exposed at once.
This ensures no distortion due to movement.
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a
bc
d
A
BC
D
S
f
H
n
N N
n
DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Cross track (whisk broom) and
along track (pushbroom) scanners
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Geometric correction and registration of images Principles of image formation
DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Geometric correction and registration of images Sources of errors in airborne and satellite imagery
Effects caused by the earth:
earth rotation,
earth curvature,
relief.
Effects caused by movement of the platform:
position,
attitude.
Effects caused by the operation of the sensor:
panoramic effect,
rotation of the mirror,
non-linearity of the mirror movement.
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DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
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imaged
recorded
Earth rotation
Earth curvature a a
a a = dr radial displacement
Geometric correction and registration of images Effects due to the Earth
DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
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Geometric correction and registration of images Effects due to the Earth
a a' n
f
A
h
H
Displacement due to relief
aa/an = h/H dr/r = h/H
dr = r.(h/H)
DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Geometric correction and registration of images Effects due to the Earth
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Sensor Altitude (km) Half swath (km) dr for h= 500m Pixels
1. Aerial camera with
f=150mmm
10 4 200 133
2. Metric camera on
Spacelab
f=300mm
250 90 180 5
3. Landsat 705 90 64 2
4. SPOT nadir 830 30 18 2
5. SPOT 27 830 450 271 27
Examples of relief distortion from various sensors
DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Geometric correction and registration of images GEOMETRIC DISTORTIONS DUE TO EARTH ROTATION AND
MOVEMENT OF THE PLATFORM
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Earth rotation Altitude variation Spacecraft velocity
Pitch variation Roll variation Yaw variation
DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Geometric correction and registration of images Correction of distortions
The systematic effects can be corrected by applying a mathematical transformation based on polynomials
Error due to relief cannot be corrected by this method
Also known as rubber sheeting or rubber sheet wrapping
Use of these method requires ground control points (GCPs)
GCPs must be carefully selected and must be evenly distributed over the image
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DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Geometric correction and registration of images transforming image to map
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Similarity transformation
Affine transformation
Polynomial transformation
dbyaxY
cbyaxX
ybxbbY
yaxaaX
210
210
5
2
4
2
3210
5
2
4
2
3210
bybxbybxbbY
ayaxayaxaaX
DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Geometric correction and registration of images 2D Similarity transformation 4 Parameter
This transformation is to relate any two-dimensional rectangular co-ordinate
system to any other two-dimensional rectangular co-ordinate system. It preserves
the internal geometry of the transformed system. Two control points required
(minimum).
X = ax - by + c
Y = bx + ay + d
A similarity transformation is performed by applying:
- 1 scale factor ( m = (a2 + b2)),
- 1 rotation angle (tan = b/a),
- 2 translations (c and d).
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DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Geometric correction and registration of images 2D affine transformation 6 Parameter
An affine transformation enables adjustment to be applied independently in each
direction. Thus for scanner images, it corrects first-order distortions such as
affinity due to non-orthogonality and scale difference between scan along track
directions which may be caused by earth rotation, map projection and other
geometric distortions.
Three ground control points, at least, are required.
X = ao + a1x + a2y
Y = bo + b1x + b2y
A affine transformation is performed by applying:
- 2 scale factor,
- 2 rotation angle,
- 2 translations.
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DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Geometric correction and registration of images Second-order Polynomials 12 Parameter
Polynomials in the form:
X = ao + a1x + a2y + a3x2 + a4y2 + a5xy
Y = bo + b1x + b2y + b3x2 + b4y2 + b5xy
If polynomials are used great care must be taken to ensure that a sufficient number of
control points are available and that they are distributed over the whole area to be
transformed. A minimum of six ground control points are necessary .
Additional terms may be added to equations 6 to correct for higher order distortions, the
need for care in use of control points is greater for higher orders.
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DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
In order to create a new, corrected, image it is necessary to transform each
pixel individually. The transformation will not generate integer values for the new
row and column positions in the corrected image, hence the density value from
the original image must be assigned to the nearest row and column position in
the new image. This is known as resampling.
Resampling is commonly carried out using
one of three methods:
1.NEAREST NEIGHBOUR
straightforward and computationally economic but
may produce shifts in position and poor visual impression.
1.BILINEAR INTERPOLATION
an acceptable compromise.
1.CUBIC CONVOLUTION
smooths the image but computationally intensive.
ALL RESAMPLING DEGRADES THE IMAGE TO SOME EXTENT.
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Geometric correction and registration of images Resampling
DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
Following Practical's are offered on a voluntary base:
Character and Key parameter of Maps
Image registration and Geo-referencing
Excel Spreadsheet transformation
Geo-referencing a image in ArcGIS
Information can be found on Moodle
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Geometric correction and registration of images
Exercises:
DJB2011
UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science
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Any Questions ?