Image Processing Toolbox

Advanced Spatial Transformation Techniques

The following functions, when used in combination, provide a vast array of options for defining and working with 2-D, N-D, and mixed-D spatial transformations:

• maketform
• fliptform
• tformfwd
• tforminv
• findbounds
• makeresampler
• tformarray
• imtransform

The imtransform, findbounds, and tformarray functions use the tformfwd and tforminv functions internally to encapsulate the forward transformations needed to determine the extent of an output image or array and/or to map the output pixels/array locations back to input locations. You can use tformfwd and tforminv to explore the geometric effects of a transformation by applying them to points and lines and plotting the results. They support a consistent handling of both image and pointwise data.

The previous example, Performing the Transformation, used the makeresampler function with a standard interpolation method. You can also use it to obtain special effects or custom processing. For example, you could specify your own separable filtering/interpolation kernel, build a custom resampler around the MATLAB interp2 or interp3 functions, or even implement an advanced anti-aliasing technique.

And, as noted, you can use tformarray to work with arbitrary-dimensional array transformations. The arrays do not even need to have the same dimensions. The output can either have a lower or higher number of dimensions than the input.

For example, if you are sampling 3-D data on a 2-D slice or manifold, the input array might have a lower dimensionality. The output dimensionality might be higher, for example, if you combine multiple 2-D transformations into a single 2-D to 3-D operation.

Performing General Spatial Transformations

Image Registration