# imregicp

Surface registration using iterative closest point algorithm

Since R2022b

## Description

The imregicp function uses the iterative closest point (ICP) algorithm for rigid registration of surfaces. Use this function to register surfaces extracted from medical volumes.

regSurface = imregicp(movingSurface,fixedSurface) transforms the surface movingSurface, so that it is registered with the reference surface fixedSurface using the ICP algorithm. The function returns the registered surface regSurface.

example

regSurface = imregicp(movingSurface,fixedSurface,Name=Value) specifies options for the ICP algorithm using one or more optional name-value arguments.

[regSurface,tform] = imregicp(___) returns the transformation tform between the moving surface and the registered surface, in addition to any combination of input arguments from previous syntaxes.

[regSurface,tform,rmse] = imregicp(___) returns the root mean squared error (RMSE) rmse of the Euclidean distance between the inlier points of the aligned surfaces regSurface and fixedSurface, in addition to any combination of input arguments from previous syntaxes.

## Examples

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Load a MAT file containing intensity volume data into the workspace. Extract the volume data.

V = vol;

Specify an isovalue for isosurface extraction.

isovalue = 0.5;

Extract the isosurface of the reference volume at the specified isovalue.

[~,fixedSurface] = extractIsosurface(V,isovalue);

Display and inspect the reference isosurface.

figure
plot3(fixedSurface(:,2),fixedSurface(:,1),fixedSurface(:,3),"o")

Create a rigid transformation, as an affinetform3d object, for the reference volume.

theta = pi/18;
affineMatrix = [cos(theta)  sin(theta) 0  5; ...
-sin(theta) cos(theta) 0  5; ...
0           0          1  10; ...
0           0          0  1];
tform_rigid = affinetform3d(affineMatrix);

Transform the reference volume using the rigid transformation.

tformV = imwarp(V,tform_rigid);

Extract the isosurface of the transformed volume at the specified isovalue.

[~,movingSurface] = extractIsosurface(tformV,isovalue);

Display and inspect the transformed isosurface.

figure
plot3(movingSurface(:,2),movingSurface(:,1),movingSurface(:,3),"o")

Register the transformed isosurface with respect to the reference isosurface using surface registration.

regSurface = imregicp(movingSurface,fixedSurface,DistanceThreshold=30);
iterations = 1	Fitness = 1.0000	inlierRmse = 11.2506
iterations = 2	Fitness = 1.0000	inlierRmse = 8.7551
iterations = 3	Fitness = 1.0000	inlierRmse = 6.9022
iterations = 4	Fitness = 1.0000	inlierRmse = 5.5101
iterations = 5	Fitness = 1.0000	inlierRmse = 4.5163
iterations = 6	Fitness = 1.0000	inlierRmse = 3.7939
iterations = 7	Fitness = 1.0000	inlierRmse = 3.2680
iterations = 8	Fitness = 1.0000	inlierRmse = 2.8856
iterations = 9	Fitness = 1.0000	inlierRmse = 2.6002
iterations = 10	Fitness = 1.0000	inlierRmse = 2.3826
iterations = 11	Fitness = 1.0000	inlierRmse = 2.2116
iterations = 12	Fitness = 1.0000	inlierRmse = 2.0695
iterations = 13	Fitness = 1.0000	inlierRmse = 1.9479
iterations = 14	Fitness = 1.0000	inlierRmse = 1.8438
iterations = 15	Fitness = 1.0000	inlierRmse = 1.7478
iterations = 16	Fitness = 1.0000	inlierRmse = 1.6615
iterations = 17	Fitness = 1.0000	inlierRmse = 1.5823
iterations = 18	Fitness = 1.0000	inlierRmse = 1.5086
iterations = 19	Fitness = 1.0000	inlierRmse = 1.4390
iterations = 20	Fitness = 1.0000	inlierRmse = 1.3744

Display and inspect the registered isosurface.

figure
plot3(regSurface(:,2),regSurface(:,1),regSurface(:,3),"o")

## Input Arguments

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Surface to be registered, specified as an M-by-3 numeric matrix. M is the number of points in the surface. Each row contains the 3-D coordinates of a surface point.

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

Reference surface, specified as an M-by-3 numeric matrix. M is the number of points in the surface. Each row contains the 3-D coordinates of a surface point.

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

### Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: regSurface = imregicp(movingSurface,fixedSurface,Metric="pointToPlane") registers the surfaces using the "pointToPlane" minimization metric for the ICP algorithm.

Minimization metric, specified as "pointToPoint" or "pointToPlane".

When registering planar surfaces, you can use the "pointToPlane" metric to reduce the number of iterations in the algorithm, but at a higher computational complexity for each iteration.

Data Types: char | string

Maximum number of iterations for the ICP algorithm, specified as a positive integer.

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

Initial rigid transformation, specified as an affinetform3d object.

Parameters for outlier removal, specified as a two-element vector of the form [n r].

The function considers the surface points with fewer than n neighbors within a sphere of radius r to be outliers, and removes them from consideration for the registered surface. n must be a positive integer, and r must be positive. Specifying a high value for n with a low value for r causes the function to remove outliers aggressively.

Data Types: single | double

Distance threshold for closest point, specified as a positive scalar. The DistanceThreshold is the maximum distance at which the k-nearest neighbor search considers a point in movingSurface as a possible correspondent for a point in fixedSurface. Increasing the distance threshold can enable you to detect a correspondence in images with sparse surface points, but can also cause the algorithm to return false positives.

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

Number of points used for local plane fitting, specified as a positive integer greater than or equal to 3. To specify this argument, you must specify Metric as "pointToPlane". Smaller values of NumPoints can result in faster computation, but can reduce accuracy.

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

Progress information output, specified as a numeric or logical 1 (true) or 0 (false). Specify Verbose as true to display information such as the number of iterations, fitness score, and inlier RMSE value.

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

## Output Arguments

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Registered surface, returned as an M-by-3 numeric matrix. M is the number of points in the surface. Each row contains the 3-D coordinates of a surface point.

Data Types: double | single

Rigid transformation, returned as an affinetform3d object.

Root mean square error of the Euclidean distance between the inlier points of the aligned surfaces regSurface and fixedSurface, returned as a numeric scalar.

Data Types: double

## References

[1] Besl, P.J., and Neil D. McKay. “A Method for Registration of 3-D Shapes.” IEEE Transactions on Pattern Analysis and Machine Intelligence 14, no. 2 (February 1992): 239–56. https://doi.org/10.1109/34.121791.

## Version History

Introduced in R2022b