Image Processing Toolbox User's Guide

Defining the Transformation Data

Before you can perform a spatial transformation, you must first define the parameters of the transformation. The following sections describe two ways you can define a spatial transformation.

• Using a Transformation Matrix
• Using Sets of Points

With either method, you pass the result to the maketform function to create the TFORM structure required by imtransform.

Using a Transformation Matrix

The maketform function can accept transformation matrices of various sizes for N-D transformations. Because imtransform only performs 2-D transformations, you can only specify 3-by-3 transformation matrices.

For example, you can use a 3-by-3 matrix to specify any of the affine transformations. For affine transformations, the last column must contain 0 0 1 ([zeros(N,1); 1]). You can specify a 3-by-2 matrix. In this case, imtransform automatically adds this third column.

The following table lists the affine transformations you can perform with imtransform along with the transformation matrix used to define them. You can combine multiple affine transformations into a single matrix.

Affine Transform	Example	Transformation Matrix
Translation			tx specifies the displacement along the x axis ty specifies the displacement along the y axis.
Scale			sx specifies the scale factor along the x axis sy specifies the scale factor along the y axis.
Shear			shx specifies the shear factor along the x axis shy specifies the shear factor along the y axis.
Rotation			q specifies the angle of rotation.

Using Sets of Points

Instead of specifying a transformation matrix, you optionally use sets of points to specify a transformation and let maketform infer the transformation matrix.

To do this for an affine transformation, you must pick three non-collinear points in the input image and in the output image. (The points form a triangle.) For a projective transformation, you must pick four points. (The points form a quadrilateral.)

This example picks three points in the input image and three points in the output image created by the translation performed in Example: Performing a Translation. The example passes these points to maketform and lets maketform infer the transformation matrix. The three points mark three corners of one of the checkerboard squares in the input image and the same square in the output image.

• in_points = [11 11;21 11; 21 21]
  
  out_points = [51 51;61 51;61 61]
  
  tform2 = maketform('affine',inpts,outpts)
  

To view the transformation matrix created by maketform, look at the tdata field of the TFORM structure. The following shows the transformation matrix for the forward transformation that is stored in the T field of the tdata structure. Note that maketform created the same as transformation matrix as the one created in Step 2: Define the Spatial Transformation. For more information about the TFORM structure, see Contents of a TFORM Structure.

• tform2.tdata.T
  
  ans =
  
       1     0     0
       0     1     0
      40    40     1
  

Example: Performing a Translation

Creating TFORM Structures

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