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2. IP07 - Map Projections. General ConceptsCharacteristicsReference ellipsoidsLatitude and longitude coordinatesDatumsCylindrical projectionsConic projectionsAzimuthal projectionsPseudo-cylindrical projectionsENVI map projection header informationImage display tools Cursor location Grid lines.
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1. EPSc 407 – IP07
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3. 3 Map projection general concepts Map projections attempt to display a portion of a planet's surface on a flat plane
Distortion in area, shape, scale, or direction occurs in creating the projection
There is no “best” map projection
Each projection is designed to minimize distortion in area, shape, scale, or direction
Projections that accurately portray area are known as equal-area projections
A circle placed on anywhere on map represents the same amount of area
Also known as equivalent projections
Conformal projections show objects on a map without shape distortion
All lines of latitude and longitude intersect at right angles
Local scale is the same in all directions around any point
Areas are generally distorted, except along certain lines
4. 4 Map projection general concepts Scale is the ratio of a distance portrayed on a map to the same distance on the planet
No map projection correctly shows scale throughout the map
Usually one or more lines on the map has a constant scale
Equidistant projections show true scale between the center of map and other points
Directions (azimuths) on a map are shown correctly relative to the center of the map on azimuthal projections
Some azimuthal projections are also equal-area, conformal, or equidistant
Some map projections have special characteristics
Lines of constant direction shown as straight lines (Mercator), good for navigating over long distances
Great circle arcs shown as straight lines (gnomonic) or as circles (stereographic)
5. 5 Map projection general concepts Reference ellipsoid used to approximate planets that are flattened at poles (polar axis is shorter than equatorial axis)
Reference ellipsoids can be designed for local or global applications
Earth ellipsoids for global use refined over past 200 years
Geopotential surface is the surface of equal gravity potential
Gravity vector is perpendicular to geopotential surface
Geoid is geopotential surface at mean sea level
Varies from ellipsoid by up to ± 100 m.
Elevations on maps are usually relative to a geoid; latitude, longitude, and planar coordinates are relative to reference ellipsoid
6. 6 Map projection general concepts Reference Ellipsoids
a = semi-major axis (ellipsoid equatorial radius)
b = semi-minor axis (ellipsoid polar radius)
f = flattening
e = eccentricity
7. 7 Selected reference ellipsoids
8. 8 Latitude and longitude coordinate systems Planetocentric is relative to ellipsoid center
Latitude is angle between equator and line from surface point to ellipsoid center
Longitude uses right-hand rule (east positive)
Planetographic (geodetic) is relative to ellipsoid normal
Latitude is angle between equator and normal to ellipsoid at a surface point
Longitude direction depends on planet rotation: west positive for prograde planets; Earth is east positive for global areas or west positive locally
Planet Centered Cartesian have x, y, z coordinates
9. 9 Geodetic datums Provides framework for referencing planar coordinates
Horizontal and/or vertical reference
Requires reference ellipsoid and coordinate system origin
Hundreds of datums in use for different regions of the Earth
Datums can differ from each other by up to one kilometer in x, y planar coordinates
Conversion from one datum to another will also change values of geodetic latitude and longitude.
It is important to know what datum is being used
Do not mix data that use different datums
Common datums for maps and remote sensing of North America
NAD27: Clark 1866 ellipsoid
WGS84: WGS84 ellipsoid
These differ by about 150 - 200 meters
10. 10 Datum conversion
11. 11 Map projections Projection Types
Cylindrical
Conic
Azimuthal
Pseudocylindrical
12. 12 Cylindrical projections Regular cylindrical projections partly formed by projecting points onto a cylinder wrapped around a globe at the equator
Longitude lines are equidistant parallel straight lines on the projection
Latitude lines cross longitude lines at right angles, but are not equally spaced
Oblique or transverse projections result from rotating the cylinder relative to the globe
13. 13 Mercator projection Longitude lines are vertical, equally spaced, and parallel to each other
Latitude lines are horizontal (cross longitude at right angles)
Spacing increases toward the poles so that the projection is conformal
Area is distorted, as is scale
Used for marine navigation because straight lines are lines of constant azimuth
Used to show large portions of globe, except for the poles
14. 14 Transverse Mercator projection Projection of the globe onto a cylinder tangent to a longitude line
Latitude and longitude lines are no longer straight lines
Distortion of scale, distance, direction, and area increase away from central longitude
15. 15 Universal Transverse Mercator (UTM) projection Special case of transverse Mercator
Widely used for designating rectangular coordinates (in meters) on large-scale maps
Earth divided into 60 zones (each 6° of longitude wide)
Scale variation within a zone is 1 part in 1,000
Zone origin is equator at central longitude, with x value of 500,000 m and y of 0 m for Northern Hemisphere
X increases to east, y to the north
16. 16 Cylindrical Equidistant projection Latitude and longitude lines are parallel, equidistant, straight lines, intersecting at right angles
Simple linear scaling of latitude and longitude
Also known as simple cylindrical or geographic lat/lon projection (ENVI)
Neither equal-area nor conformal
17. 17 Space Oblique Mercator Projection Modified cylindrical projection with map surface defined by satellite orbit
Designed for displaying early Landsat images and other similar satellite data
Central line of projection is satellite groundtrack
Scale is true along groundtrack
Used only for narrow band along the groundtrack
18. 18 Conic projections Surface projected onto a cone that intersects planet at one or two latitude lines (known as standard parallels)
Scale is true along the standard parallels, but distorted elsewhere
Can also be conformal, equal-area, or equidistant in limited portions of the map
Used for areas of large east-west extent
19. 19 Lambert Conformal Conic projection Uses two standard parallels
Is conformal
Latitude lines are arcs of concentric circles with spacing decreasing toward center of map
Longitude lines are equally spaced and intersect latitudes at right angles
Scale is true along standard parallels
20. 20 Albers equal area projection Uses two standard parallels
Is equal-area
Latitude lines are arcs of concentric circles with spacing decreasing toward north and south edges of map
Longitude lines are equally spaced and intersect latitudes at right angles
Scale and shape are true along standard parallels
21. 21 Azimuthal projection Surface projected onto a plane, usually tangent to the planet
Direction or azimuth from the center of the projection to every other point on the map is correctly shown
For spherical form, great circles passing through the center of the map are shown as straight lines
22. 22 Orthographic projection Projection from a point infinitely far from the planet onto a plane tangent to the planet
Makes the planet appear like a globe
Latitude and longitude lines can be straight lines, ellipses, or circles
Neither conformal or equal-area
23. 23 Stereographic Projection Projection from a point on a planet to a plane tangent to the planet and on the opposite side from the projection point
A conformal projection
Often used to show polar areas with North or South Pole at the center of the map
24. 24 General perspective projection Projections of a planet onto a plane through a single point
Simulates the geometry of a framing camera
Neither conformal or equal-area
Other azimuthal projections are special cases of this projection
25. 25 Pseudocylindrical projections Resemble cylindrical projections
Latitude lines are straight and parallel
Longitude lines are curves
26. 26 ENVI map projection header information Map projection information stored in ENVI ASCII header file
Map info can be added by editing file
No registration is performed by editing the
Geographic Corners attribute
EM » File » Edit ENVI Header
27. 27 Image display tools Cursor Location/Value
IM » Tools » Cursor Location/Value…
Grid lines
IM » Overlay » Grid Lines…
Add grids for pixel, map, or geographic coordinate systems
Non-pixel coordinates require georeferenced image
28. 28 Grid line settings Save grid settings to file for later use
29. 29 Map coordinate converter EM » Map » Map Coordinate Converter
Change projections and datums to desired settings
Enter known coordinate
Calculate in forward or reverse direction
30. 30 ASCII coordinate converter EM » Map» ASCII Coordinate Conversion
Convert one or more files of coordinates or GCPs (ground control points)
31. 31 Resampling and warp methods Pixel resampling methods
Nearest neighbor uses the nearest pixel without any interpolation
Bilinear is a linear interpolation using 4 neighboring pixels
Cubic convolution uses 16 pixels to approximate the sine function using cubic polynomials; significantly slower than other methods
Warp methods
RST (rotation, scaling and translation), requires at least four GCPs
Polynomial, sometimes called ‘rubbersheeting’
Degree of polynomial is dependent upon number of GCPs selected: #GCPs > (degree + 1)^2
Delaunay triangulation fits triangles to the irregularly spaced GCPs and interpolates values to the output grid.
32. 32 Projection conversion: reverse mapping Projection conversion employs reverse mapping to derive output
Example: take an input grid and convert to a different projection
33. 33 Projection conversion: bilinear interpolation Bilinear interpolation resampling is used to better approximate output
Example:
34. 34 Projection converstion: bilinear interpolation
35. 35 Changing map projections and datums EM » Map » Convert Map Projection
Select file and target projection
Optionally save warp points to GCP file
Set warping and resampling parameters
36. 36 Ground control points A set of image coordinates for an unregistered image corresponding to a known set of locations
Sources of known locations may vary
Registered images
Maps
DLGs (digital line graphs)
GPS field readings
Unregistered images (special case)
GCPs saved in ASCII format
37. 37 Georeferencing—GCP collection GCPs required to register image to a map projection
Warp (unregistered) image must be displayed to collect GCPs
“Image to Map” for registering to DLGs or field readings
EM » Map » Registration » Select GCPs: Image to Map
Destination projection, datum, and pixel size are specified
“Image to Image” for registering to another image
EM » Map » Registration »
Select GCPs: Image to Image
38. 38 Georeferencing—GCP collection GCPs are entered and managed through GCP selection dialog
39. 39 Georeferencing—GCP collection Collected GCPs are displayed on warp image
Map locations may be entered by hand, or automatically entered from vector window or existing registered image
ENVI will predict warp image location given map location after four GCPs have been entered
GCPs may be updated or deleted to minimize error
For best results RMS error < 1.5
Save GCPs to file for later use
40. 40 Georeferencing—image warping Register image from GCP selection dialog
Options » Warp Displayed Band… or
Options » Warp File…
or from ENVI menu
EM » Map » Registration » Warp from GCPs: Image to Map or
EM » Map » Registration » Warp from GCPs: Image to Image
41. 41 Help Help viewing this document
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