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)

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)

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)

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)