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Learning About Map Projections


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.

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)

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.

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 Projection (USGS).

ISIS3 Supported Projections


ISIS3 currently supports the following projections:

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

Related Resources

What is a Planetary Image Map?


A primary capability of ISIS3 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.

MOC image before transformation MOC image after sinusoidal transformation
MOC image before transformation MOC image after sinusoidal transformation

What is a Planetary Image Mosaic?


Equally as important, ISIS3 allows a collection of raw instrument images to be projected and stitched together (mosaicked) into large regional or global maps.

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

Sample_mosaic_themis.jpg

Defining a Map in ISIS3


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 ISIS3 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

Image projected using the above mapfile
Image projected using the above mapfile

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 below shows which projections are for a sphere only (use only the equatorial radius) and which work for ellipsoids:

Marked 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

Interactive Planetary Radii Demonstration

INSERT INTERACTIVE DEMO HERE

Latitude Type


Latitudes can be represented either in planetocentric or planetographic 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

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 LatitudeType keyword must be either Planetocentric or Planetographic.

Interactive Planetocentric and Planetographic Demonstration

PLACE INTERACTIVE DEMO HERE

Longitude Direction and Domain


Two keywords indicate how longitude is defined on the target body and must be specified. The LongitudeDirection keyword indicates whether longitude increases to the east or west, that is, positive to the east or positive to the west. The LongitudeDomain keyword 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 LongitudeDirection keyword must be either PositiveEast or PositiveWest, while the LongitudeDomain keyword must be 180 or 360. These keywords are marked 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

Interactive Longitude Direction of Domain Demonstration

PLACE INTERACTIVE DEMO HERE

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 marked 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

Interactive Ground range demonstration

PLACE INTERACTIVE DEMO HERE

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 marked 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

Alternatively, 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

Interactive Example of pixel resolutions

PLACE INTERACTIVE DEMONSTRATION HERE

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 CenterLongitude. 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

Projecting a Camera Cube


To project a raw instrument (camera) cube to a map projected image you must use the ISIS3 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 Automatically computed using information from the camera model
PixelResolution Automatically computed using information from the camera model
EquatorialRadius, PolarRadius, LatitudeSystem, LongitudeRange, LongitudeDomain Automatically computed using the TargetName from the cube labels.
CenterLatitude, CenterLongitude, and other projection specific parameters Automatically computed using the middle of the ground range
Cam2map_screenshot.jpg
A screen shot of the cam2map application

Quick Tips

  • cam2map requires the input to be a camera cube and therefore ISIS3 must support the camera model in order for this program to be successful.
  • spiceinit must be run on the input cube as well.

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 following example.

When a camera acquires image data it is stored in a certain domain:

Mars_sphere_illustration.png

When an image is created from the acquired data using the same domain, the correct image is generated:

180_domain_correct.png

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):
360_domain_incorrect.png

These illustrate the problems that can arise when working with images that cross the longitude seam.

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.

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:

SimpleCylindrical.jpg Blue_right_arrow.gif SinusodialProjection.jpg

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,

Simple_135-110.jpg
Simple Cylindrical
Sinusodial_135-110.jpg
Sinusoidal
Mosaic_sinus.jpg
Sinusoidal Mosaic from Mars

The program for reprojecting an image map is map2map.

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 below

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

  ProjectionName     = Sinusoidal
  CenterLongitude    = 354.0

  PixelResolution    = 100.0 <meters/pixel>
 End_Group
 End
Mosaic after
THEMIS Mosiac

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.

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.

Mercator.gif View (21.1 KB) Kristin Berry, 2016-05-31 01:54 PM

Mola_of_sheet2a_thumb.jpg View (186 KB) Kristin Berry, 2016-05-31 01:54 PM

MOC1.jpg View (12.2 KB) Kristin Berry, 2016-05-31 01:59 PM

SinuMOC1.jpg View (56.9 KB) Kristin Berry, 2016-05-31 01:59 PM

Sample_mosaic_themis.jpg View (19.3 KB) Kristin Berry, 2016-05-31 02:17 PM

Cam2map_screenshot.jpg View (179 KB) Kristin Berry, 2016-05-31 02:46 PM

180_domain_correct.png View (248 KB) Kristin Berry, 2016-05-31 02:56 PM

360_domain_incorrect.png View (5.15 KB) Kristin Berry, 2016-05-31 02:56 PM

Mars_sphere_illustration.png View (476 KB) Kristin Berry, 2016-05-31 02:56 PM

Blue_right_arrow.gif View (1.25 KB) Kristin Berry, 2016-05-31 03:05 PM

SimpleCylindrical.jpg View (337 KB) Kristin Berry, 2016-05-31 03:05 PM

SinusodialProjection.jpg View (269 KB) Kristin Berry, 2016-05-31 03:05 PM

Simple_135-110.jpg View (136 KB) Kristin Berry, 2016-05-31 03:07 PM

Mosaic_sinus.jpg View (223 KB) Kristin Berry, 2016-05-31 03:07 PM

Sinusodial_135-110.jpg View (123 KB) Kristin Berry, 2016-05-31 03:07 PM

Mosaic_after.jpg View (10.1 KB) Kristin Berry, 2016-05-31 03:14 PM