LocalWeightedMeanTransformation2D

2-D local weighted mean geometric transformation

Description

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

Creation

You can create a LocalWeightedMeanTransformation2D object using the following methods:

• The fitgeotrans function, which estimates a geometric transformation that maps pairs of control points between two images.

• The images.geotrans.LocalWeightedMeanTransformation2D described here. This function creates a LocalWeightedMeanTransformation2D object using coordinates of fixed points and moving points, and a specified number of points to use in the local weighted mean calculation.

Syntax

tform = images.geotrans.LocalWeightedMeanTransformation2D(movingPoints,fixedPoints,n)

Description

tform = images.geotrans.LocalWeightedMeanTransformation2D(movingPoints,fixedPoints,n) creates a LocalWeightedMeanTransformation2D object given control point coordinates in movingPoints and fixedPoints, which define matched control points in the moving and fixed images, respectively. The n closest points are used to infer a second degree polynomial transformation for each control point pair.

Input Arguments

movingPoints — x- and y-coordinates of control points in the moving image

m-by-2 matrix

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

fixedPoints — x- and y-coordinates of control points in the fixed image

m-by-2 matrix

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

n — Number of points to use in local weighted mean calculation

numeric value

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

Properties

Dimensionality — Dimensionality of the geometric transformation

2

Dimensionality of the geometric transformation for both input and output points, specified as the value 2.

Object Functions

outputLimits	Find output spatial limits given input spatial limits
transformPointsInverse	Apply inverse geometric transformation

Examples

Fit Set of Fixed and Moving Control Points Using Second Degree Polynomial

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 the LocalWeightedMeanTransformation2D object at the control points.

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

Algorithms

The local weighted mean transformation infers 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.