Learning About Map Projections

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[edit] What is a Map?

A map is a two dimensional representation of a three dimensional object such as a sphere, ellipsoid (egg-shape), or an irregular shaped body. For planetary maps, these 3-D objects are the planets, their moons, and irregular bodies such as asteroids. Maps allow scientists and researchers to analyze and measure characteristics of features on the body such as area, distance, and direction. See Map (Wikipedia) for a detailed description of maps.

uploaded image: Example of a map made using data from the Mars Orbiter Laser Altimeter (MOLA)
Example of a map made using data from the Mars Orbiter Laser Altimeter (MOLA)


[edit] What is a Map Projection?

A projection is an algorithm or equation for mapping a three dimensional body onto a two dimensional surface such as paper, a computer screen, or in our case, a digital image. There are many different types of projections.

uploaded image: Mercator Projection: The classic Mercator projection places a cylinder (rolled piece of paper) tangent to the equator.
Mercator Projection: The classic Mercator projection places a cylinder (rolled piece of paper) tangent to the equator.

For additional information on types and properties of map projections see Map Projections (USGS).


[edit] Isis Supported Projections

Isis currently supports the following projections:

  • Sinusoidal
  • Simple Cylindrical
  • Equirectangular
  • Polar Stereographic
  • Orthographic
  • Lambert Conformal Conic
  • Mercator
  • Transverse Mercator
  • and many more...


Related Resources

[edit] What is a Planetary Image Map?

A primary capability of Isis is to create map projected images of raw instrument data. This allows researchers to make fundamental measurements on and observations about the images.

The following is an example of a single Mars Global Surveyor (MGS) Mars Orbital Camera (MOC) instrument image that has been transformed to a planetary image map using the Sinusoidal projection.

uploaded image: MOC image before tranformation
MOC image before tranformation
uploaded image: MOC image after sinusoidal tranformation
MOC image after sinusoidal tranformation


[edit] What is a Planetary Image Mosaic?

Equally as important, Isis allows a collection of raw instrument images to be projected and stitched together (mosaicked) into large regional or global maps.

uploaded image: Five Mars Odyssey THEMIS instrument images that have been projected and mosaicked to generate a regional planetary image map using the Sinusoidal projection
Five Mars Odyssey THEMIS instrument images that have been projected and mosaicked to generate a regional planetary image map using the Sinusoidal projection


[edit] Defining a Map in Isis

In order to project an image, characteristics of the map must be established. They include the latitude/longitude coverage or ground range, the pixel resolution, the target body radii, latitude and longitude definitions, and the projection. In Isis we record all of this information in a Parameter Value Language (PVL) formatted map file. For example this MGS MOC image was projected using the following:

Group = Mapping
 TargetName         = Mars
 EquatorialRadius   = 3396190.0 <meters>
 PolarRadius        = 3376200.0 <meters>
 LatitudeType       = Planetocentric
 LongitudeDirection = PositiveEast
 LongitudeDomain    = 360

 ProjectionName     = Sinusoidal
 CenterLongitude    = 227.95679808356

 MinimumLatitude    = 10.766902750622
 MaximumLatitude    = 34.44419678224
 MinimumLongitude   = 219.7240455337
 MaximumLongitude   = 236.18955063342

 PixelResolution    = 426.87763879023 <meters/pixel>
End_Group
uploaded image: Image projected using the mapfile information displayed to the left.
Image projected using the mapfile information displayed to the left.

[edit] Target Shape Definition

The target shape must be defined in order to project an image. The shape is characterized by the equatorial and polar radii of the body. Depending on the projection, one or both of these values will be used. The chart to the right shows which projections are for a sphere only (use only the equatorial radius) and which work for ellipsoids:

Highlighted below are the PVL keywords used to define the target radii, which must be given in units of meters.

Group = Mapping
 TargetName         = Mars
 EquatorialRadius   = 3396190.0 <meters>
 PolarRadius        = 3376200.0 <meters>
 LatitudeType       = Planetocentric
 LongitudeDirection = PositiveEast
 LongitudeDomain    = 360

 ProjectionName     = Sinusoidal
 CenterLongitude    = 227.95679808356

 MinimumLatitude    = 10.766902750622
 MaximumLatitude    = 34.44419678224
 MinimumLongitude   = 219.7240455337
 MaximumLongitude   = 236.18955063342

 PixelResolution    = 426.87763879023 <meters/pixel>
End_Group
Projection Sphere Ellipsoid
Sinusoidal X
Simple Cylindrical X
Equirectangular X
Polar Stereographic X X
Orthographic X
Mercator X X
Transverse Mercator X X
Lambert Conformal X X

[edit] Interactive Planetary Radii Demonstration

User Defined Applet

[edit] Latitude Type

Latitudes can be represented either in planetographic or planetocentric form. The planetocentric latitude is the angle between the equatorial plane and a line from the center of the body. The planetographic latitude is the angle between the equatorial plane and a line that is normal to the body. In a quick summary, both latitudes are equivalent on a sphere (i.e., equatorial radius equal to polar radius); however, they differ on an ellipsoid (e.g., Mars, Earth).

Group = Mapping
 TargetName         = Mars
 EquatorialRadius   = 3396190.0 <meters>
 PolarRadius        = 3376200.0 <meters>
 LatitudeType       = Planetocentric
 LongitudeDirection = PositiveEast
 LongitudeDomain    = 360

 ProjectionName     = Sinusoidal
 CenterLongitude    = 227.95679808356

 MinimumLatitude    = 10.766902750622
 MaximumLatitude    = 34.44419678224
 MinimumLongitude   = 219.7240455337
 MaximumLongitude   = 236.18955063342
 
 PixelResolution    = 426.87763879023 <meters/pixel>
End_Group


[edit] Quick Tips

  • The latitude type will affect how other PVL keywords such as MinimumLatitude, CenterLatitude are interpreted.
  • Projections such as Sinusoidal, Simple Cylindrical, and Equirectangular will place pixels differently in the image depending on the latitude type. Pixel placement for other projections is not affected. The Latitude Type keyword must be either Planetocentric or Planetographic.


[edit] Interactive Planetocentric and Planetographic Demonstration

User Defined Applet

[edit] Longitude Direction and Domain

Two keywords indicate how longitude is defined on the target body and must be specified. The longitude direction indicates whether longitude increases to the east or west, that is, positive to the east or positive to the west. The longitude domain specifies how longitudes should be interpreted 0° to 360° or -180° to 180°. In both cases, these specifications affect other keywords and the interpretation of other keywords, such as MinimumLongitude and CenterLongitude.

The longitude direction keyword must be either PositiveEast or PositiveWest, while the longitude domain keyword must be 180 or 360. These keywords are highlighted in the example below.

Group = Mapping
 TargetName         = Mars
 EquatorialRadius   = 3396190.0 <meters>
 PolarRadius        = 3376200.0 <meters>
 LatitudeType       = Planetocentric
 LongitudeDirection = PositiveEast
 LongitudeDomain    = 360

 ProjectionName     = Sinusoidal
 CenterLongitude    = 227.95679808356

 MinimumLatitude    = 10.766902750622
 MaximumLatitude    = 34.44419678224
 MinimumLongitude   = 219.7240455337
 MaximumLongitude   = 236.18955063342

 PixelResolution    = 426.87763879023 <meters/pixel>
End_Group

[edit] Interactive Longitude Direction of Domain Demonstration

User Defined Applet

[edit] Ground Range

The ground range defines the extent of the map. That is, the minimum and maximum latitude/longitude values. Recall that these are in terms of the latitude system, longitude direction, and longitude domain. In the keywords below, the keywords highlighted define the ground range of the map.

Group = Mapping
 TargetName         = Mars
 EquatorialRadius   = 3396190.0 <meters>
 PolarRadius        = 3376200.0 <meters>
 LatitudeType       = Planetocentric
 LongitudeDirection = PositiveEast
 LongitudeDomain    = 360

 ProjectionName     = Sinusoidal
 CenterLongitude    = 227.95679808356

 MinimumLatitude    = 10.766902750622
 MaximumLatitude    = 34.44419678224
 MinimumLongitude   = 219.7240455337
 MaximumLongitude   = 236.18955063342

 PixelResolution    = 426.87763879023 <meters/pixel>
End_Group

[edit] Interactive Ground range demonstration

User Defined Applet

[edit] Pixel Resolution

The pixel resolution defines the size of pixels in a map projected image in either meters per pixel, or pixels per degree. In the example below is the highlighted keyword used to define the pixel resolution in meters per pixel.

Group = Mapping
 TargetName         = Mars
 EquatorialRadius   = 3396190.0 <meters>
 PolarRadius        = 3376200.0 <meters>
 LatitudeType       = Planetocentric
 LongitudeDirection = PositiveEast
 LongitudeDomain    = 360

 ProjectionName     = Sinusoidal
 CenterLongitude    = 227.95679808356

 MinimumLatitude    = 10.766902750622
 MaximumLatitude    = 34.44419678224
 MinimumLongitude   = 219.7240455337
 MaximumLongitude   = 236.18955063342

 PixelResolution    = 426.87763879023 <meters/pixel>
End_Group

Alternately the resolution can be defined as pixels per degree. For example

Group = Mapping
 TargetName         = Mars
 EquatorialRadius   = 3396190.0 <meters>
 PolarRadius        = 3376200.0 <meters>
 LatitudeType       = Planetocentric
 LongitudeDirection = PositiveEast
 LongitudeDomain    = 360

 ProjectionName     = Sinusoidal
 CenterLongitude    = 227.95679808356

 MinimumLatitude    = 10.766902750622
 MaximumLatitude    = 34.44419678224
 MinimumLongitude   = 219.7240455337
 MaximumLongitude   = 236.18955063342

 Scale              = 138.85641255722 <pixels/degree>
End_Group

[edit] Interactive Example of pixel resolutions

User Defined Applet

[edit] Projection and Parameters

The final information required in the map file is the projection for mapping the body to a two dimensional surface. In addition to the projection name, projection-specific parameters must be provided. For example, Sinusoidal requires the center Longitude. The following table outlines the keywords required for each projection:

ProjectionName CenterLongitude CenterLatitude FirstStandardParallel SecondStandardParallel ScaleFactor
Sinusoidal X
SimpleCylindrical X
Equirectangular X X
PolarStereographic X X
Orthographic X X
LambertConformal X X X X
Mercator X X
TransverseMercator X X X

[edit] Projecting a Camera Cube

uploaded image: The above image is a screen shot of the cam2map application
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The above image is a screen shot of the cam2map application

To project a raw instrument (camera) cube to a map projected image you must use the Isis program cam2map. The program allows you to enter a map file to specify the projection, ground range, resolution, and target definition. If a map file is not supplied the program will provide the following defaults:

Parameters Default Value
  • MinimumLatitude, MaximumLatitude, MinimumLongitude, MaximumLongitude
  • PixelResolution
  • EquatorialRadius, PolarRadius, LatitudeSystem, LongitudeRange, LongitudeDomain
  • CenterLatitude, CenterLongitude, and other projection specific parameters
  • Automatically computed using information from the camera model
  • Automatically computed using information from the camera model
  • Automatically computed using the TargetName from the cube labels.
  • Automatically computed using the middle of the ground range


[edit] Quick Tips

  • cam2map requires the input to be a camera cube and therefore Isis must support the camera model in order for this program to be successful.
  • spiceinit must be run on the input cube as well.

[edit] Problems at the Longitude Seams

Problems can occur when working on images that cross the longitude seam. For example, choosing a map file with:

LongitudeDomain = 360

A map file combined with an image that was viewed over the 0°/360° seam will visually look like:

The cam2map program has an option which automatically changes the longitude domain if it detects the image crossing the seam. If you turn this option off, be aware you can generate large images with mostly NULL data. Note that a similar problem occurs at the -180°/180° longitude boundary if LongitudeDomain = 180.


uploaded image:
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uploaded image:
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These illustration the problems that can arise when working with images that cross the longitude seam. When a camera acquires image data (left) it is stored in a certain domain. When an image is created from the acquired data using the same domain, the correct image is generated (above). When an image is created in a different longitude domain, the resulting image is incorrect (below, this image was scaled down to fit on the screen).
uploaded image:
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[edit] Power Tip: Reprojecting an Image Map

Occasionally the need arises to reproject an image map. For example, converting from a simple cylindrical to Sinusoidal projection:


uploaded image:
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uploaded image:
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Another purpose for reprojecting an image map is to get all the images with the same projection, parameters, resolution, latitude system, etc in order to mosaic. For example,


uploaded image: Simple Cylindrical
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Simple Cylindrical
uploaded image: Sinusoidal
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Sinusoidal
uploaded image: Sinusoidal Mosaic from Mars.
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Sinusoidal Mosaic from Mars.


The program for reprojecting an image map is map2map.


[edit] Power Tip: Making Mosaics

In order to mosaic a set of cubes they must all be projected in cam2map or map2map using the SAME pixel resolution, target definition, and projection and parameters (e.g., center longitude, etc). Note the ground range does not need to be the same. This is fairly straight-forward as you can project all the images with the same map file, just leave out the MinimumLatitude, MinimumLongitude, MaximumLatitude, MaximumLongitude parameters.

In the example below, we see the mapping file used to project the five images in the THEMIS mosaic on the right

Group = Mapping
 LatitudeType       = Planetocentric
 LongitudeDirection = PositiveEast
 LongitudeDomain    = 360

 ProjectionName     = Sinusoidal
 CenterLongitude    = 354.0

 PixelResolution    = 100.0 <meters/pixel>
End_Group
End
uploaded image:
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[edit] Creating a mosaic

-The most convenient way to mosaic a number of map projected images is to use the automos application. Automos reads a list of input images, computes the latitude and longitude coverage of all the images and creates the output mosaic.

-The mapmos application mosaics one image at a time. Remember to set create=true the first time mapmos is run with the first image in order to create the output mosaic file.

-It is possible to mosaic images together by specifying the output pixel coordinate placement using the handmos application. This would be for any ISIS3 image cubes that do not have a camera model or cartographic mapping information that is required by mapmos and automos.

[edit] Other Hints and Tips

  • In lieu of using a standard text editor, the programs maptemplate or mosrange can be used to assist in the building of map files.
  • A map projected image can be used as a map file. For example, a Viking and MOC image taken of the same area can be projected by running cam2map on the Viking image using the defaults and then the MOC image projected using the Viking image as the map file. The MOC image will have the same projection, target definition, resolution, and ground range so that the images can be easily compared.
  • In general, the pixel resolution of the image map is only accurate in certain portions of the image; however, this is entirely dependent upon the projection you select. The labels of the output cube will have a keyword called TrueScaleLatitude and/or TrueScaleLongitude and these represent where the resolution is accurate. The accuracy may be true along that meridian or parallel or point. Again this depends upon the projection.
  • The output map image size will vary depending on ground range and pixel resolution. Care should be taken to ensure your output image is not too large. You can check the size of image that will produced with a fully-defined map file by using the mapsize program.
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