worldToIntrinsic

Convert from world to intrinsic coordinates

Syntax

[xIntrinsic, yIntrinsic] = worldToIntrinsic(R,xWorld,yWorld)

[xIntrinsic,yIntrinsic,zIntrinsic] = worldToIntrinsic(R,xWorld,yWorld,zWorld)

Description

[xIntrinsic, yIntrinsic] = worldToIntrinsic(R,xWorld,yWorld) maps points from the 2-D world system (xWorld,yWorld) to the 2-D intrinsic system (xIntrinsic,yIntrinsic) based on the relationship defined by 2-D spatial referencing object R.

If the kth input coordinates (xWorld(k),yWorld(k)) fall outside the image bounds in the world coordinate system, worldToIntrinsic extrapolates xIntrinsic(k) and yIntrinsic(k) outside the image bounds in the intrinsic coordinate system.

[xIntrinsic,yIntrinsic,zIntrinsic] = worldToIntrinsic(R,xWorld,yWorld,zWorld) maps points from the world coordinate system to the intrinsic coordinate system using 3-D spatial referencing object R.

Examples

Convert 2-D World Coordinates to Intrinsic Coordinates

Read a 2-D grayscale image of a knee into the workspace.

m = dicominfo('knee1.dcm');
A = dicomread(m);

Create an imref2d object, specifying the size and the resolution of the pixels. The DICOM file contains a metadata field PixelSpacing that specifies the image resolution in each dimension in millimeters per pixel.

RA = imref2d(size(A),m.PixelSpacing(2),m.PixelSpacing(1))

RA = 
  imref2d with properties:

           XWorldLimits: [0.1562 160.1562]
           YWorldLimits: [0.1562 160.1562]
              ImageSize: [512 512]
    PixelExtentInWorldX: 0.3125
    PixelExtentInWorldY: 0.3125
    ImageExtentInWorldX: 160
    ImageExtentInWorldY: 160
       XIntrinsicLimits: [0.5000 512.5000]
       YIntrinsicLimits: [0.5000 512.5000]

Display the image, including the spatial referencing object. The axes coordinates reflect the world coordinates. Notice that the coordinate (0,0) is in the upper left corner.

figure
imshow(A,RA,'DisplayRange',[0 512])

Select sample points, and store their world x- and y- coordinates in vectors. For example, the first point has world coordinates (38.44,68.75), the second point is 1 mm to the right of it, and the third point is 7 mm below it. The last point is outside the image boundary.

xW = [38.44 39.44 38.44 -0.2];
yW = [68.75 68.75 75.75 -1];

Convert the world coordinates to intrinsic coordinates using worldToIntrinsic.

[xI, yI] = worldToIntrinsic(RA,xW,yW)

xI = 1×4

  123.0080  126.2080  123.0080   -0.6400

yI = 1×4

  220.0000  220.0000  242.4000   -3.2000

The resulting vectors are the intrinsic x- and y- coordinates in units of pixels. Note that the intrinsic coordinate system is continuous, and some returned intrinsic coordinates have noninteger values. Also, worldToIntrinsic extrapolates the intrinsic coordinates of the point outside the image boundary.

Convert 3-D World Coordinates to Intrinsic Coordinates

Read a 3-D volume into the workspace. This image consists of 27 frames of 128-by-128 pixel images.

load mri;
D = squeeze(D);
D = ind2gray(D,map);

Create an imref3d spatial referencing object associated with the volume. For illustrative purposes, provide a pixel resolution in each dimension. The resolution is in millimeters per pixel.

R = imref3d(size(D),2,2,4)

R = 
  imref3d with properties:

           XWorldLimits: [1 257]
           YWorldLimits: [1 257]
           ZWorldLimits: [2 110]
              ImageSize: [128 128 27]
    PixelExtentInWorldX: 2
    PixelExtentInWorldY: 2
    PixelExtentInWorldZ: 4
    ImageExtentInWorldX: 256
    ImageExtentInWorldY: 256
    ImageExtentInWorldZ: 108
       XIntrinsicLimits: [0.5000 128.5000]
       YIntrinsicLimits: [0.5000 128.5000]
       ZIntrinsicLimits: [0.5000 27.5000]

Select sample points, and store their world x-, y-, and z-coordinates in vectors. For example, the first point has world coordinates (108,92,52), the second point is 3 mm above it in the +z-direction, and the third point is 0.2 mm to the right of it in the +x-direction. The last point is outside the image boundary.

xW = [108 108 108.2 2];
yW = [92 92 92 -1];
zW = [52 55 52 0.33];

Convert the world coordinates to intrinsic coordinates using worldToIntrinsic.

[xI, yI, zI] = worldToIntrinsic(R,xW,yW,zW)

xI = 1×4

   54.0000   54.0000   54.1000    1.0000

yI = 1×4

   46.0000   46.0000   46.0000   -0.5000

zI = 1×4

   13.0000   13.7500   13.0000    0.0825

The resulting vectors are the intrinsic x-, y-, and z-coordinates in units of pixels. Note that the intrinsic coordinate system is continuous, and some returned intrinsic coordinates have noninteger values. Also, worldToIntrinsic extrapolates the intrinsic coordinates of the point outside the image boundary.

Input Arguments

R — Spatial referencing object

imref2d or imref3d object

Spatial referencing object, specified as an imref2d or imref3d object.

xWorld — Coordinates along the x-dimension in the world coordinate system

numeric scalar or vector

Coordinates along the x-dimension in the world coordinate system, returned as a numeric scalar or vector.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

yWorld — Coordinates along the y-dimension in the world coordinate system

numeric scalar or vector

Coordinates along the y-dimension in the world coordinate system, returned as a numeric scalar or vector. yWorld is the same length as xWorld.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

zWorld — Coordinates along the z-dimension in the world coordinate system

numeric scalar or vector

Coordinates along the z-dimension in the world coordinate system, returned as a numeric scalar or vector. zWorld is the same length as xWorld.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Output Arguments

xIntrinsic — Coordinates along the x-dimension in the intrinsic coordinate system

numeric scalar or vector

Coordinates along the x-dimension in the intrinsic coordinate system, specified as a numeric scalar or vector. xIntrinsic is the same length as xWorld.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

yIntrinsic — Coordinates along the y-dimension in the intrinsic coordinate system

numeric scalar or vector

Coordinates along the y-dimension in the intrinsic coordinate system, specified as a numeric scalar or vector. yIntrinsic is the same length as xWorld.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

zIntrinsic — Coordinates along the z-dimension in the intrinsic coordinate system

numeric scalar or vector

Coordinates along the z-dimension in the intrinsic coordinate system, specified as a numeric scalar or vector. zIntrinsic is the same length as xWorld and yWorld.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64