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images.geotrans.LocalWeightedMeanTransformation2D class

Package: images.geotrans

2-D local weighted mean geometric transformation

Description

A LocalWeightedMeanTransformation2D object encapsulates a 2-D local weighted mean geometric transformation.

You can create a LocalWeightedMeanTransformation2D object using the following methods:

  • fitgeotrans — Returns a LocalWeightedMeanTransformation2D object that maps control point pairs using a local weighted mean transformation

  • The LocalWeightedMeanTransformation2D class constructor

Construction

tform = images.geotrans.LocalWeightedMeanTransformation2D(movingPoints,fixedPoints,n) constructs a LocalWeightedMeanTransformation2D object given m-by-2 matrices movingPoints and fixedPoints, which define matched control points in the moving and fixed images, respectively. 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 n closest points are used to infer a second degree polynomial transformation for each control point pair. n can be as small as 6, but making it small risks generating ill-conditioned polynomials.

Input Arguments

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x- and y-coordinates of control points in the moving image, specified as an m-by-2 matrix. The number of control points m must be greater than or equal to n.

Data Types: double | single

x- and y-coordinates of control points in the fixed image, specified as an m-by-2 matrix. The number of control points m must be greater than or equal to n.

Data Types: double | single

Number of points to use in local weighted mean calculation, specified as a numeric value. n can be as small as 6, but making n small risks generating ill-conditioned polynomials

Data Types: double | single | uint8 | uint16 | uint32 | uint64 | int8 | int16 | int32 | int64

Properties

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Describes the dimensionality of the geometric transformation for both input and output points.

Methods

images.geotrans.LocalWeightedMeanTransformation2d.outputLimitsFind output limits of geometric transformation
images.geotrans.LocalWeightedMeanTransformation2d.transformPointsInverseApply inverse geometric transformation

Copy Semantics

Value. To learn how value classes affect copy operations, see Copying Objects (MATLAB) in the MATLAB® documentation.

Examples

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Fit a local weighted mean transformation to a set of fixed and moving control points that are actually related by a global second degree polynomial transformation across the entire plane.

Set up variables.

x = [10, 12, 17, 14, 7, 10];
y = [8, 2, 6, 10, 20, 4];
 
a = [1 2 3 4 5 6];
b = [2.3 3 4 5 6 7.5];
 
u = a(1) + a(2).*x + a(3).*y + a(4) .*x.*y + a(5).*x.^2 + a(6).*y.^2;
v = b(1) + b(2).*x + b(3).*y + b(4) .*x.*y + b(5).*x.^2 + b(6).*y.^2;
 
movingPoints = [u',v'];
fixedPoints = [x',y'];

Fit local weighted mean transformation to points.

tformLocalWeightedMean = images.geotrans.LocalWeightedMeanTransformation2D(movingPoints,fixedPoints,6);

Verify the fit of our LocalWeightedMeanTransformation2D object at the control points.

movingPointsComputed = transformPointsInverse(tformLocalWeightedMean,fixedPoints);
 
errorInFit = hypot(movingPointsComputed(:,1)-movingPoints(:,1),...
                       movingPointsComputed(:,2)-movingPoints(:,2))
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