Converting projected coordinate system worldfile to geographic coordinate system worldfile?

Question

I have an image with the worldfile like this:

0.298582141739
0.000000000000
0.000000000000
-0.298582141739
1283836.327077804830
6134835.890168172310

I think it is the projected coordinate system. I want to convert it to geographic coordinate system, because I want to know the latitude/longitude of each pixel of the image. How to convert that? I check the worldfileread in the matlab, it can read both. But I did not find how to convert.

Could anyone know about that?

Answer 1

The world file encodes the Northing (N) and Easting (E) values relative to a UTM grid, sub-region of the earth in the Universal Transverse Mercator coordinate system.

The wikipedia page for UTM provides the conversions: https://en.wikipedia.org/wiki/Universal_Transverse_Mercator_coordinate_system#Notation

See specifically the section on From UTM coordinates (E,N,Zone,Hemi) to latitude, longitude for the conversion.

Answer 2

The world file format indicates the Northing and Easting values, the last two lines, should be UTM.

Conversion would depend on what software you're using. You indicate MATLAB, so this m-script at the File Exchange would probably work for you:

https://www.mathworks.com/matlabcentral/fileexchange/37605-utm2latlong-geotiff-converter/content/utm2latlong.m

function utm2latlong(source,output,tfwFlag,zone,varargin)

%UTM2LATLONG - converts a tiff file from UTM coordinates into a Lat/Long
%GeoTIFF
%
% This tool converts a UTM GeoTIFF, or tiff with corresponding UTM world
% file, into a Lat/Long GeoTIFF. This function does not require any of
% MATLAB's Mapping Toolbox functions. It uses MATLAB's base functions to
% rewrite the file in the Lat/Long projection. The source tiff file is read
% in and a new GeoTIFF is created with the geographic directory
% information.
%
% However, this function does utilize a few functions currently found on
% MATLAB's File Exchange website (see Required Subfunctions). You should be
% able to search and download these functions on the File Exchange website
% and then run this tool.
%
% Required Subfunctions:
%   geotiffwrite.m by Jimmy Shen (File ID: #27959)
%   utm2ell.m by Mike Craymer (included in his Geodetic Toolbox #15285)
%   rad2deg.m by Mike Craymer (included in his Geodetic Toolbox #15285)
%
% Inputs:
%   source   - string; path to source GeoTiff
%   output   - string; path to output GeoTiff
%   tfwFlag  - logical; indicates whether an accompanying world file is
%                       located in the same directory
%   zone     - scalar; UTM zone (e.g. 4 to indicate Oahu)
%   x_pixel  - scalar; pixel scaling in the x-direction
%   y_pixel  - scalar; pixel scaling in the y-direction (almost always negative)
%   Easting  - scalar; Easting (upper left corner)
%   Northing - scalar; Northing (upper left corner)
%
% Usage:
%   utm2latlong(source,output,tfwFlag,zone,[x_pixel,y_pixel,Easting,Northing])
%
% Example:
%   Consider the NOAA landsat GeoTiff for Oahu found on the following website:
%   http://www.soest.hawaii.edu/coasts/data/oahu/landsat.html
%   It's projection is in UTM coordinates. It has a corresponding .tfw
%   world file. The following converts the file to a Lat/Long GeoTiff:
%
%     source = 'C:\GIS\OAHU\oahu.tif';
%     output = 'C:\GIS\LatLong\oahu_LL.tif';
%     tfwFlag = 1;  % .tfw file included
%     zone = 4;
%     utm2latlong(source,output,tfwFlag,zone);

% Ver. 1.0
% July 23, 2012

% NOTE: MATLAB's imread function does not read in the coordinate
% information from geotiff files.  Thus, a corresponding world file  (.tfw)
% must accompany the .tif file or you must know the information (x_pixel,
% y_pixel, Easting, Northing).

if nargin < 4
    disp('Not enough input arguments. Type help utm2latlong for more information.')
    return
end

%% Get data from .tif and .tfw files
Info = imfinfo(source);
data = imread(source);
if tfwFlag
    % Load .tfw world file
    source_tfw = [source(1:end-3) 'tfw'];
    world_file_data = load(source_tfw);
    % From .tfw world file, we know the pixel scaling and UTM coordinates
    x_pixel = world_file_data(1);   % pixel scale in x-direction
    rot1 = world_file_data(2);      % rotation about y-axis
    rot2 = world_file_data(3);      % rotation about x-axis
    y_pixel = world_file_data(4);   % pixel scale in y-direction
    E1 = world_file_data(5);        % Easting (upper left pixel)
    N1 = world_file_data(6);        % Northing (upper left pixel)
else
    % Check the number of input arguments
    if nargin ~= 8
        disp(['The number of inputs does not match what was expected. ',...
            'Type help utm2latlong for more information.'])
        return
    end
    % Read data from input
    x_pixel = varargin(1);
    y_pixel = varargin(2);
    E1 = varargin(3);
    N1 = varargin(4);
end

% Check that there is no rotation
if (rot1 ~= 0) || (rot2 ~= 0)
    disp('Rotation detected in the .tfw file.  Rotations are not supported.')
    return
end

%% Calculate extent of the image in UTM coordinates
E2 = E1 + x_pixel*Info.Width;
N2 = N1 + y_pixel*Info.Height;

% Convert to lat/long
[lat1,long1] = utm2ell(N1,E1,zone);
lat1 = rad2deg(lat1);
long1 = rad2deg(long1);
[lat2,long2] = utm2ell(N2,E2,zone);
lat2 = rad2deg(lat2);
long2 = rad2deg(long2);

%% Create geotiff file
% (We could use the make_option GUI that comes with the geotiffwrite.m file,
% but to save time this has already been done. The data below is the output
% from calling make_option.)
% [option bbox] = make_option([long1, lat2; long2, lat1]);
bbox = [long1, lat2; long2, lat1];
option.GTModelTypeGeoKey = 2;       % Geographic latitude-longitude System 
option.GTRasterTypeGeoKey = 1;      % Raster pixel is area
option.GeographicTypeGeoKey = 4326; % Geographic Coordinate System - WGS84
option.GTCitationGeoKey = 'Created using the geotiffwrite.m matlab function';
option.FullColor = 1;
geotiffwrite(output, bbox, data, 16, option)

disp(['File saved to: ',output]);

(Code included in case the link goes stale. Full credit to the author Kyle Mayer. Code license)