transformPointsInverse

Apply inverse geometric transformation

Syntax

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

[u,v,w] = transformPointsInverse(tform,x,y,z)

U = transformPointsInverse(tform,X)

Description

[u,v] = transformPointsInverse(tform,x,y) applies the inverse transformation of 2-D geometric transformation tform to the points specified by coordinates x and y.

[u,v,w] = transformPointsInverse(tform,x,y,z) applies the inverse transformation of 3-D geometric transformation tform to the points specified by coordinates x, y, and z.

U = transformPointsInverse(tform,X) applies the inverse transformation of tform to the input coordinate matrix X and returns the coordinate matrix U. transformPointsInverse maps the kth point X(k,:) to the point U(k,:).

Examples

Apply Inverse Transformation of 2-D Geometric Transformation

Define a 3-by-3 geometric transformation matrix. This example specifies a matrix for an affine transformation consisting of vertical shear and horizontal stretch.

A = [1.5 0 0; 0.8 1 0; 0 0 1];

Create an affinetform2d object from the transformation matrix.

tform = affinetform2d(A);

Apply the inverse geometric transformation to a point.

x = 7.5;
y = 14;
[u,v] = transformPointsInverse(tform,x,y)

u = 
5

v = 
10

Transform Packed Coordinates Using Custom 2-D Transformation

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

Apply Inverse Transformation of 3-D Geometric Transformation

Define a rigid geometric transformation consisting only of translation.

t = [10 20.5 15];
tform = transltform3d(t);

Apply the forward geometric transformation to an input point.

x = 11;
y = 21.5;
z = 16.01;
[u,v,w] = transformPointsInverse(tform,x,y,z)

u = 
1

v = 
1

w = 
1.0100

Transform Packed Coordinates Using Custom 3-D Transformation

Specify the packed (x,y,z) coordinates of five input points. The packed coordinates are stored as a 5-by-3 matrix, where the first, second, and third columns contain the x-, y-, and z- coordinates,respectively.

XYZ = [5 25 20;10 5 25;15 10 5;20 15 10;25 20 15];

Define an inverse mapping function that accepts and returns points in packed (x,y,z) format.

inverseFcn = @(c) [c(:,1)+c(:,2),c(:,1)-c(:,2),c(:,3).^2];

Create a 3-D geometric transformation object, tform, that stores this inverse mapping function.

tform = geometricTransform3d(inverseFcn)

tform = 
  geometricTransform3d with properties:

        InverseFcn: @(c)[c(:,1)+c(:,2),c(:,1)-c(:,2),c(:,3).^2]
        ForwardFcn: []
    Dimensionality: 3

Apply the inverse transformation of this 3-D geometric transformation to the input points.

UVW = transformPointsInverse(tform,XYZ)

UVW = 5×3

    30   -20   400
    15     5   625
    25     5    25
    35     5   100
    45     5   225

Input Arguments

tform — Geometric transformation

geometric transformation object

Geometric transformation, specified as a geometric transformation object listed in the table.

Geometric Transformation Object	Description
2-D Linear Geometric Transformations
transltform2d	Translation transformation
rigidtform2d	Rigid transformation: translation and rotation
simtform2d	Similarity transformation: translation, rotation, and isotropic scaling
affinetform2d	Affine transformation: translation, rotation, anisotropic scaling, reflection, and shearing
projtform2d	Projective transformation
3-D Linear Geometric Transformations
transltform3d	Translation transformation
rigidtform3d	Rigid transformation: translation and rotation
simtform3d	Similarity transformation: translation, rotation, and isotropic scaling
affinetform3d	Affine transformation: translation, rotation, anisotropic scaling, reflection, and shearing
Nonlinear Geometric Transformations
geometricTransform2d	Custom 2-D geometric transformation using point-wise mapping functions
geometricTransform3d	Custom 3-D geometric transformation using point-wise mapping functions
LocalWeightedMeanTransformation2D	2-D local weighted means transformation
PiecewiseLinearTransformation2D	2-D piecewise linear transformation
PolynomialTransformation2D	2-D polynomial transformation

Note

You can also specify tform as an object of type rigid2d, rigid3d, affine2d, affine3d, or projective2d. However, these objects are not recommended. For more information, see Version History.

x — x-coordinates of points to be transformed

m-by-n or m-by-n-by-p numeric array

x-coordinates of points to be transformed, specified as an m-by-n or m-by-n-by-p numeric array. The number of dimensions of x matches the dimensionality of tform.

Data Types: single | double

y — y-coordinates of points to be transformed

m-by-n or m-by-n-by-p numeric array

y-coordinates of points to be transformed, specified as an m-by-n or m-by-n-by-p numeric array. The size of y must match the size of x.

Data Types: single | double

z — z-coordinates of points to be transformed

m-by-n-by-p numeric array

z-coordinates of points to be transformed, specified as an m-by-n-by-p numeric array. z is used only when tform is a 3-D geometric transformation. The size of z must match the size of x.

Data Types: single | double

X — Coordinates of points to be transformed

l-by-2 or l-by-3 numeric array

Coordinates of points to be transformed, specified as an l-by-2 or l-by-3 numeric array. The number of columns of X matches the dimensionality of tform.

The first column lists the x-coordinate of each point to transform, and the second column lists the y-coordinate. If tform represents a 3-D geometric transformation, X has size l-by-3 and the third column lists the z-coordinate of the points to transform.

Data Types: single | double

Output Arguments

u — x-coordinates of points after transformation

m-by-n or m-by-n-by-p numeric array

x-coordinates of points after transformation, returned as an m-by-n or m-by-n-by-p numeric array. The number of dimensions of u matches the dimensionality of tform.

Data Types: single | double

v — y-coordinates of points after transformation

m-by-n or m-by-n-by-p numeric array

y-coordinates of points after transformation, returned as an m-by-n or m-by-n-by-p numeric array. The size of v matches the size of u.

Data Types: single | double

w — z-coordinates of points after transformation

m-by-n-by-p numeric array

z-coordinates of points after transformation, returned as an m-by-n-by-p numeric array. The size of w matches the size of u.

Data Types: single | double

U — Coordinates of points after transformation

numeric array

Coordinates of points after transformation, returned as a numeric array. The size of U matches the size of X.

The first column lists the x-coordinate of each point after transformation, and the second column lists the y-coordinate. If tform represents a 3-D geometric transformation, the third column lists the z-coordinate of the points after transformation.

Data Types: single | double

Version History

Introduced in R2013a

R2022b: Supports new geometric transformation objects

Starting in R2022b, most Image Processing Toolbox™ functions create and perform geometric transformations using the premultiply convention. Accordingly, you can now specify tform as a geometric transformation object that uses the premultiply convention, such as an affinetform2d object.

Although transformPointsInverse still supports objects that use the postmultiply convention, such as an affine2d object, these objects are not recommended. You can streamline your geometric transformation workflows by switching to the new premultiply geometric transformation objects. For more information, see Migrate Geometric Transformations to Premultiply Convention.

There is no change to the support for nonlinear geometric transformation objects.