U.S. Department of the InteriorU.S. Geological Survey

Reprojecting Raster Data of Global Extent

Auto-Carto 2005: A Research Symposium21 - 23 March, 2005Las Vegas, Nevada

E. Lynn Useryusery@usgs.gov

Reprojecting Raster Data of Global Extent Daniel R. Steinwand,

Science Applications International Corp., USGS National Center for Earth Resources Observation and Science (EROS), Sioux Falls, SD

Michael P. Finn, Jason R. Trent, E. Lynn Usery, and Robert A. Buehler,

USGS, Mid-Continent Mapping Center, Rolla, MO

Outline

Objectives Approach Methods

Coordinate Transformations Framing (Output Frame) Forward vs. Inverse Mapping (Reprojection) Wraparound Resampling

Implementing a map image projection program Conclusions

Objectives

Solve problems associated with projection of global raster datasets and corresponding errors to global environmental models

Provide a software package that better handles known problems (including raster categorical resampling) for wide use in the modeling community

Approach

Expand on previous research Handle identified issues and problems Chain various geospatial, computational, and

map projection methods into a solution framework

Implement a software package to handle the reprojection of global raster datasets

Methods

Coordinate Transformations Framing

Output Frame (Geographic MinBox and Direct Specification)

Forward vs. Inverse Mapping Reprojection (Algorithm)

Wraparound Resampling

Categorical Resampling

Coordinate Transformations

Subroutine packages usually operate on a point-by-point basis

General Cartographic Transformation Package (GCTP) Point-by-point basis C programming language

Works for both vector and raster data Datum transformations usually included

Framing

Extent of the image (raster data) in projection space Where and how that space is aligned with the image

coordinate system First-order transformation (translation and scaling) Tie two coordinate systems together

UL image pixel to center of UL pixel in projection space Equations (image to/ from projection coordinates) Determine Output Image Frame

Framing EquationsImage to/ from projection coordinates

X = ULprojX + (sample – 1) * pixelSizeX Y = ULprojY – (line – 1) * pixelSizeY

Line = (ULprojY – Y)/pixelSizeY + 1 Sample = (X – ULprojX)/PixelSizeX + 1

(Upper Left image pixel is pixel (1,1), i.e., 1-relative coordinates)

Determine Output Image Frame

The geographic extent of the (re)projection output image In units of the output image projection system

Common MethodsThe geographic MinBoxDirect specification of output projection extent

Determine Output Image Frame The Geographic MinBox User defines output

image extent with UpperLeft and LowerRight geographic coordinates

Determine Output Image Frame The Geographic MinBox The frame is

conceptualized in geographic space (with grid lines added for clarification)

Determine Output Image Frame The Geographic MinBox This space is

converted to the output projection.

Corners & Sides of the frame are converted (piecewise) and projection coordinate minimums and maximums are recorded.

Determine Output Image Frame The Geographic MinBox Locations of the

min/max projection coordinates are noted.

Determine Output Image Frame The Geographic MinBox The minimum and

maximum extents form the MinBox—this is the extent of the output image.

The number of lines and samples are determined by dividing these dimensions by the pixel size.

Determine Output Image Frame The Geographic MinBox If the MinBox

algorithm is not applied, and only the UL and LR geographic coordinates are used to determine projection min/max, clipping of the frame can occur.

Determine Output Image Frame Direct specification of projection extent

User specifies the min and max coordinates of the output spaceOr, alternatively: Specify the UL corner of the

image and the number of lines and samples

Forward vs. Inverse Mapping

Inverse mapping algorithmSteps through the output image space and

calculates the corresponding coordinates in the input image; then selects the pixel value (and perhaps neighboring values) at those input coordinates

Inverse Mapping AlgorithmPseudo Code Simplest case: point-by-point, nearest neighbor For each line in the output image: For each pixel in this output image line:

Determine the output space projection coordinate for this pixel

Convert the coordinate to the input space projection Determine the input space image coordinate Grab the image value(s) at the input image coordinate

The Wraparound Problem

Resampling

Geospatial data of global extent can suffer from great geometric distortions when being reprojected

Errors associate with these distortions and scale changes affect resampling within the reprojection function, especially for categorical data

ResamplingNearest Neighbor 1 point in the output space image and map

that point into the input image space (via the inverse mapping algorithm)

ResamplingNearest Neighbor If the resolution of the output imagery is

reduced (downsampling), adjacent pixels in the output may fall more the 1 pixel away in the input (via the inverse mapping algorithm)

Categorical Resampling New resampling algorithm treats pixels as areas (not points,

Steinwand (2003))

4 corners of each pixel are mapped into the input space Many pixels involved

Can apply simple statistical methods to determine output image pixels based on the area the pixel coverage in the input image

MapImg: An ImplementationTypical Output

Solves wraparound problem

Extreme Downsampling and Reprojection with the Nearest Neighbor

MapImg: Output

Can provide better categorical resampling in extreme downsampling

MapImgStand-Alone Program Multiplatform

MS WindowsUNIX (many variants)

Linux User interface (startup

screen)

MapImgProgram controls Via dialog boxes

Data type User’s projection

choices All parameter

entries Provides user’s

with Reprojected image A metadata file Summary window Optional log file

MapImgC and C++

GCTP at the core

Software design =>

MapImgMetadata (.info) File

Data Parameter Comments

Rows & Columns Space delimited integers

Projection Number GCTP code for the map projection

Zone Number For UTM projection

Unit Type For length measurements (currently only supports meters)

Spheroid Number GCTP code for datum (currently only supports sphere of radius 6370997 meters)

Pixel Size Scale width of a pixel in areas of true scale

Upper Left Longitude/ Upper Left Latitude

Geographic coordinates of corner

15 GCTP parameters Space delimited real number (floating point) values

Data type Pre-defined string

MapImgTechniques, I/O, Data Structures, Algorithms

Utilizes multiple techniques for input, storage, and output of various data files (primarily generic binary raster images)

3 primary data structures IMGINFO structure The projinfo class The GUI

2 major algorithms within mapimg.exe mapframeit() mapimg()

mapimg.exe

mapframeit algorithm Calculates the row and column dimension Caluclates the UL corner for a given projection

mapimg algorithm Loops through every row and column in the output

raster and loads the appropriate value Checks for fill values and wraparound Controls I/O buffering for time optimization

Conclusions

Projection of global raster data is a significant problem

Categorical resampling with modal categories yields better results than nearest neighbor methods

MapImg program provides solutions to raster data reprojection for a variety of computer architectures and is freely available

U.S. Department of the InteriorU.S. Geological Survey

Reprojecting Raster Data of Global Extent

Auto-Carto 2005: A Research Symposium21 - 23 March, 2005Las Vegas, Nevada

http://carto-research.er.usgs.gov/projection/index.html