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geometricTransform2d

2-D geometric transformation object

Description

A geometricTransform2d object defines a custom 2-D geometric transformation using point-wise mapping functions.

Creation

Description

example

tform = geometricTransform2d(inverseFcn) creates a geometricTransform2d object and sets the inverse mapping InverseFcn property.

tform = geometricTransform2d(inverseFcn,forwardFcn) also sets the forward mapping property, ForwardFcn.

Properties

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Inverse mapping function, specified as a function handle. The function should accept and return coordinates as a n-by-2 numeric matrix representing the packed (x,y) coordinates of n points.

For more information about function handles, see Create Function Handle.

Example: ifcn = @(xy) [xy(:,1).^2, sqrt(xy(:,2))];

Forward mapping function, specified as a function handle. The function should accept and return coordinates as a n-by-2 numeric matrix representing the packed (x,y) coordinates of n points.

For more information about function handles, see Create Function Handle.

Example: ffcn = @(xy) [sqrt(xy(:,1)),(xy(:,2).^2)];

Object Functions

transformPointsForwardApply forward geometric transformation
transformPointsInverseApply inverse geometric transformation

Examples

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Specify the packed (x,y) coordinates of five input points. The packed coordinates are stored in a 5-by-2 matrix, where the x-coordinate of each point is in the first column, and the y-coordinate of each point is in the second column.

XY = [10 15;11 32;15 34;2 7;2 10];

Define the inverse mapping function. The function accepts and returns points in packed (x,y) format.

inversefn = @(c) [c(:,1)+c(:,2),c(:,1)-c(:,2)]
inversefn = function_handle with value:
    @(c)[c(:,1)+c(:,2),c(:,1)-c(:,2)]

Create a 2-D geometric transform object, tform, that stores the inverse mapping function.

tform = geometricTransform2d(inversefn)
tform = 
  geometricTransform2d with properties:

        InverseFcn: @(c)[c(:,1)+c(:,2),c(:,1)-c(:,2)]
        ForwardFcn: []
    Dimensionality: 2

Apply the inverse geometric transform to the input points.

UV = transformPointsInverse(tform,XY)
UV = 5×2

    25    -5
    43   -21
    49   -19
     9    -5
    12    -8

Specify the x- and y-coordinates vectors of five points to transform.

x = [10 11 15 2 2];
y = [15 32 34 7 10];

Define the inverse and forward mapping functions. Both functions accept and return points in packed (x,y) format.

inversefn = @(c) [c(:,1).^2,sqrt(c(:,2))];
forwardfn = @(c) [sqrt(c(:,1)),c(:,2).^2];

Create a 2-D geometric transform object, tform, that stores the inverse mapping function and the optional forward mapping function.

tform = geometricTransform2d(inversefn,forwardfn)
tform = 
  geometricTransform2d with properties:

        InverseFcn: @(c)[c(:,1).^2,sqrt(c(:,2))]
        ForwardFcn: @(c)[sqrt(c(:,1)),c(:,2).^2]
    Dimensionality: 2

Apply the inverse geometric transform to the input points.

[u,v] = transformPointsInverse(tform,x,y)
u = 1×5

   100   121   225     4     4

v = 1×5

    3.8730    5.6569    5.8310    2.6458    3.1623

Apply the forward geometric transform to the transformed points u and v.

[x,y] = transformPointsForward(tform,u,v)
x = 1×5

    10    11    15     2     2

y = 1×5

   15.0000   32.0000   34.0000    7.0000   10.0000

Define an inverse mapping function that applies anisotropic scaling. The function must accept and return packed (x,y) coordinates, where the x-coordinate of each point is in the first column, and the y-coordinate of each point is in the second column.

xscale = 0.3;
yscale = 0.5;
inversefn = @(xy) [xscale*xy(:,1), yscale*xy(:,2)];

Create a 2-D geometric transform object, tform, that stores the inverse mapping function.

tform = geometricTransform2d(inversefn)
tform = 
  geometricTransform2d with properties:

        InverseFcn: @(xy)[xscale*xy(:,1),yscale*xy(:,2)]
        ForwardFcn: []
    Dimensionality: 2

Read an image to be transformed.

I = imread('cameraman.tif');
imshow(I)

Figure contains an axes object. The axes object contains an object of type image.

Use imwarp to apply the inverse geometric transform to the input image. The image is enlarged vertically by a factor of 2 (the inverse of yscale) and horizontally by a factor of 10/3 (the inverse of xscale).

Itransformed = imwarp(I,tform);
imshow(Itransformed)

Figure contains an axes object. The axes object contains an object of type image.

Define an inverse mapping function that accepts packed (x,y) coordinates, where the x-coordinate of each point is in the first column, and the y-coordinate of each point is in the second column. The inverse mapping function in this example takes the square of the polar radial component.

r = @(c) sqrt(c(:,1).^2 + c(:,2).^2);
w = @(c) atan2(c(:,2), c(:,1));
f = @(c) [r(c).^2 .* cos(w(c)), r(c).^2 .* sin(w(c))];
g = @(c) f(c);

Create a 2-D geometric transform object, tform, that stores the inverse mapping function.

tform = geometricTransform2d(g);

Read a color image to be transformed.

I = imread('peppers.png');
imshow(I)

Figure contains an axes object. The axes object contains an object of type image.

Create an imref2d object, specifying the size and world limits of the input and output images.

Rin = imref2d(size(I),[-1 1],[-1 1]);
Rout = imref2d(size(I),[-1 1],[-1 1]);

Apply the inverse geometric transform to the input image.

Itransformed = imwarp(I,Rin,tform,'OutputView',Rout);
imshow(Itransformed)

Figure contains an axes object. The axes object contains an object of type image.

Introduced in R2018b