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Apply spatial transformation to N-D array





B = tformarray(A,T,R,TDIMS_A, TDIMS_B,TSIZE_B,TMAP_B,F) applies a spatial transformation to array A to produce array B.


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Create a 2-by-2 checkerboard image where each square is 20 pixels wide and display it.

I = checkerboard(20,1,1);

Transform the checkerboard with a projective transformation. First create the spatial transformation structure (TFORM).

T = maketform('projective',[1 1; 41 1; 41 41;   1 41],...
                           [5 5; 40 5; 35 30; -10 30]);

Create a resampler. Use the pad method 'circular' when creating a resampler, so that the output appears to be a perspective view of an infinite checkerboard.

R = makeresampler('cubic','circular');

Perform the transformation, specifying the TFORM and the resampler. Swap the output dimensions. Specify a 100-by-100 output image. Leave TMAP_B empty, since you specify TSIZE_B. Leave the fill value empty since it won't be needed.

J = tformarray(I,T,R,[1 2],[2 1],[100 100],[],[]);

Input Arguments

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Input image, specified as a nonsparse numeric array, that can be real or complex.

Data Types: single | double | int8 | int16 | int32 | uint8 | uint16 | uint32 | logical

Spatial transformation, specified as a spatial transformation structure, called a TFORM. You typically use the maketform function to create a TFORM structure. tformarray uses T and the function tforminv to compute the corresponding location in the input transform subscript space for each location in the output transform subscript space. tformarray defines the input transform space by TDIMS_B and TSIZE_B and the output transform subscript space by TDIMS_A and size(A).

If T is empty, tformarray operates as a direct resampling function. It applies the resampler defined in R to compute values at each transform space location defined in TMAP_B. If TMAP_B is empty, tformarray applies the resampler at each location in the output transform subscript grid.

Data Types: struct

Resampler, specified as a structure. A resampler structure defines how to interpolate values of the input array at specified locations. R is created with makeresampler, which allows fine control over how to interpolate along each dimension. makeresampler also controls what input array values to use when interpolating close to the edge of the array.

Data Types: struct

Input transform dimensions, specified as a row vector of finite, positive integers.

TDIMS_A and TDIMS_B indicate which dimensions of the input and output arrays are involved in the spatial transformation. Each element must be unique, and must be a positive integer. The entries need not be listed in increasing order, but the order matters. It specifies the precise correspondence between dimensions of arrays A and B and the input and output spaces of the transformer T. length(TDIMS_A) must equal T.ndims_in, and length(TDIMS_B) must equal T.ndims_out.

For example, if T is a 2-D transformation, TDIMS_A = [2 1], and TDIMS_B = [1 2], then the column dimension and row dimension of A correspond to the first and second transformation input-space dimensions, respectively. The row and column dimensions of B correspond to the first and second output-space dimensions, respectively.

Data Types: double

Size in the transform dimensions, specified as a row vector of finite, positive integers. For more information, see TDIMS_A.

Data Types: double

Size of the output array transform dimensions, specified as a row vector of finite, positive integers. The size of B along nontransform dimensions is taken directly from the size of A along those dimensions. For example, if T is a 2-D transformation, size(A) = [480 640 3 10], TDIMS_B is [2 1], and TSIZE_B is [300 200], then size(B) is [200 300 3].

Data Types: double

Point locations in output space, specified as a nonsparse, finite real-valued array. TMAP_B is an optional argument that provides an alternative way of specifying the correspondence between the position of elements of B and the location in output transform space. TMAP_B can be used, for example, to compute the result of an image warp at a set of arbitrary locations in output space. If TMAP_B is not empty, then the size of TMAP_B takes the form

 [D1 D2 D3 ... DN L]

where N equals length(TDIMS_B). The vector [D1 D2 ... DN] is used in place of TSIZE_B. If TMAP_B is not empty, then TSIZE_B is [].

The value of L depends on whether T is empty. If T is not empty, then L is T.ndims_out, and each L-dimension point in TMAP_B is transformed to an input-space location using T. If T is empty, then L is length(TDIMS_A), and each L-dimensional point in TMAP_B is used directly as a location in input space.

Data Types: double

Fill values, specified as an array. The fill values in F can be used in three situations:

  • When a separable resampler is created with makeresampler and its padmethod is set to either 'fill' or 'bound'.

  • When a custom resampler is used that supports the 'fill' or 'bound' pad methods (with behavior that is specific to the customization).

  • When the map from the transform dimensions of B to the transform dimensions of A is deliberately undefined for some points. Such points are encoded in the input transform space by NaNs in either TMAP_B or in the output of TFORMINV.

In the first two cases, fill values are used to compute values for output locations that map outside or near the edges of the input array. Fill values are copied into B when output locations map well outside the input array. See makeresampler for more information about 'fill' and 'bound'.

F can be a scalar (including NaN), in which case its value is replicated across all the nontransform dimensions. F can also be a nonscalar, whose size depends on size(A) in the nontransform dimensions. Specifically, if K is the Jth nontransform dimension of A, then size(F,J) must be either size(A,K) or 1. As a convenience to the user, tformarray replicates F across any dimensions with unit size such that after the replication size(F,J) equals size(A,K).

For example, suppose A represents 10 RGB images and has size 200-by-200-by-3-by-10, T is a 2-D transformation, and TDIMS_A and TDIMS_B are both [1 2]. In other words, tformarray applies the same 2-D transform to each color plane of each of the 10 RGB images. In this situation you have several options for F:

  • F can be a scalar, in which case the same fill value is used for each color plane of all 10 images.

  • F can be a 3-by-1 vector, [R G B]'. tformarray uses the RGB value as the fill value for the corresponding color planes of each of the 10 images.

  • F can be a 1-by-10 vector. tformarray uses a different fill value for each of 10 images, with that fill value being used for all three color planes.

  • F can be a 3-by-10 matrix. tformarray uses a different RGB fill color for each of the 10 images.

Data Types: double

Output Arguments

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Transformed image, returned as an array.

Introduced before R2006a

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