fitgeotform2d
Syntax
Description
tform = fitgeotform2d(movingPoints,fixedPoints,tformType)tformType to the control
point pairs movingPoints and fixedPoints.
tform = fitgeotform2d(movingPoints,fixedPoints,"polynomial",degree)degree to the control point
pairs movingPoints and fixedPoints. Specify the
degree of the polynomial transformation degree, which can be 2, 3, or
4.
tform = fitgeotform2d(movingPoints,fixedPoints,"pwl")movingPoints and fixedPoints. This
transformation creates a Delaunay
triangulation of the fixed control points, and maps moving control points to the
corresponding fixed control points. A different affine transformation maps control points in
each local region. The mapping is continuous across the control points, but is not
continuously differentiable.
tform = fitgeotform2d(movingPoints,fixedPoints,"lwm",n)movingPoints and fixedPoints. The local weighted
mean transformation creates a mapping by inferring a polynomial at each control point using
neighboring control points. The mapping at any location depends on a weighted average of
these polynomials. The function uses the n closest points to infer a
second degree polynomial transformation for each control point pair.
Examples
Create a checkerboard image and rotate it to create a misaligned image.
I = checkerboard(40);
J = imrotate(I,30);
imshowpair(I,J,"montage")
Define some matching control points on the fixed image (the checkerboard) and moving image (the rotated checkerboard). You can define points interactively using the Control Point Selection tool.
fixedPoints = [41 41; 281 161]; movingPoints = [56 175; 324 160];
Create a similarity geometric transformation that you can use to align the two images.
tform = fitgeotform2d(movingPoints,fixedPoints,"similarity");Use the tform estimate to resample the rotated image to register it with the fixed image. The regions of color (green and magenta) in the false color overlay image indicate error in the registration. This error comes from a lack of precise correspondence in the control points.
Jregistered = imwarp(J,tform,OutputView=imref2d(size(I))); imshowpair(I,Jregistered)
Input Arguments
Output Arguments
More About
The table lists the transformation types supported by fitgeotform2d
in order of complexity.
Transformation Type | Description | Minimum Number of Control Point Pairs | Example |
|---|---|---|---|
"similarity" | Use this transformation when shapes in the moving image are unchanged, but the image is distorted by some combination of translation, rotation, and isotropic scaling. Straight lines remain straight, and parallel lines are still parallel. | 2 |
|
"reflectivesimilarity" | Same as "similarity", with the addition of optional
reflection. | 3 |
|
"affine" | Use this transformation when shapes in the moving image exhibit shearing or anisotropic scaling. Straight lines remain straight, and parallel lines remain parallel, but rectangles become parallelograms. | 3 |
|
"projective" | Use this transformation when the scene appears tilted. Straight lines remain straight, but parallel lines converge toward a vanishing point. | 4 |
|
"polynomial" | Use this transformation when objects in the image are curved. The higher the order of the polynomial, the better the fit, but the result can contain more curves than the fixed image. | 6 (order 2) 10 (order 3) 15 (order 4) |
|
"pwl" | Use this transformation (piecewise linear) when parts of the image appear distorted differently from each other. | 4 |
|
"lwm" | Use this transformation (local weighted mean) when the distortion varies locally and piecewise linear is not sufficient. | 6 (12 recommended) |
|
The first five transformations, "similarity",
"reflectivesimilarity", "affine",
"projective", and "polynomial", are global
transformations. In these transformations, a single mathematical expression applies to an
entire image. The last two transformations, "pwl" (piecewise linear) and
"lwm" (local weighted mean), are local transformations. In these
transformations, different mathematical expressions apply to different regions within an
image. When exploring how different transformations affect the images you are working with,
try the global transformations first. If these transformations are not satisfactory, try the
local transformations: the piecewise linear transformation first, and then the local
weighted mean transformation.
References
[1] Goshtasby, Ardeshir. “Piecewise Linear Mapping Functions for Image Registration.” Pattern Recognition 19, no. 6 (January 1986): 459–66. https://doi.org/10.1016/0031-3203(86)90044-0.
[2] Goshtasby, Ardeshir. “Image Registration by Local Approximation Methods.” Image and Vision Computing 6, no. 4 (November 1988): 255–61. https://doi.org/10.1016/0262-8856(88)90016-9.
