imregicp

Surface registration using iterative closest point algorithm

Since R2022b

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Syntax

regSurface = imregicp(movingSurface,fixedSurface)

regSurface = imregicp(movingSurface,fixedSurface,Name=Value)

[regSurface,tform] = imregicp(___)

[regSurface,tform,rmse] = imregicp(___)

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.

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

example

[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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Surface Registration of Isosurfaces

Open Live Script

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

load(fullfile(toolboxdir("images"),"imdata","BrainMRILabeled","images","vol_001.mat"));
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")

Figure contains an axes object. The axes contains a line object which displays its values using only markers.

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")

Figure contains an axes object. The axes contains a line object which displays its values using only markers.

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")

Figure contains an axes object. The axes contains a line object which displays its values using only markers.

Input Arguments

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`movingSurface` — Surface to be registered
M-by-3 numeric matrix

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.

`fixedSurface` — Reference surface
M-by-3 numeric matrix

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.

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.

`Metric` — Minimization metric
`"pointToPoint"` (default) | `"pointToPlane"`

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

`MaxIterations` — Maximum number of iterations
`20` (default) | positive integer

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

`InitialTransform` — Initial rigid transformation
`affinetform3d()` (default) | `affinetform3d` object

Initial rigid transformation, specified as an affinetform3d object.

`OutlierRemoval` — Parameters for outlier removal
`[20 2]` (default) | two-element vector

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

`DistanceThreshold` — Distance threshold for closest point
`0.1` (default) | positive scalar

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.

`NumPoints` — Number of points used for local plane fitting
`6` (default) | positive integer greater than or equal to `3`

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.

`Verbose` — Progress information output
`true` or `1` (default) | `false` or `0`

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.

Output Arguments

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`regSurface` — Registered surface
M-by-3 numeric matrix

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

`tform` — Rigid transformation
`affinetform3d` object

Rigid transformation, returned as an affinetform3d object.

`rmse` — Root mean square error
numeric scalar

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

imregicp

Syntax

Description

Examples

Surface Registration of Isosurfaces

Input Arguments

`movingSurface` — Surface to be registered
M-by-3 numeric matrix

`fixedSurface` — Reference surface
M-by-3 numeric matrix

Name-Value Arguments

`Metric` — Minimization metric
`"pointToPoint"` (default) | `"pointToPlane"`

`MaxIterations` — Maximum number of iterations
`20` (default) | positive integer

`InitialTransform` — Initial rigid transformation
`affinetform3d()` (default) | `affinetform3d` object

`OutlierRemoval` — Parameters for outlier removal
`[20 2]` (default) | two-element vector

`DistanceThreshold` — Distance threshold for closest point
`0.1` (default) | positive scalar

`NumPoints` — Number of points used for local plane fitting
`6` (default) | positive integer greater than or equal to `3`

`Verbose` — Progress information output
`true` or `1` (default) | `false` or `0`

Output Arguments

`regSurface` — Registered surface
M-by-3 numeric matrix

`tform` — Rigid transformation
`affinetform3d` object

`rmse` — Root mean square error
numeric scalar

References

Version History

See Also

Functions

Objects

Topics

imregicp

Syntax

Description

Examples

Surface Registration of Isosurfaces

Input Arguments

movingSurface — Surface to be registered M-by-3 numeric matrix

fixedSurface — Reference surface M-by-3 numeric matrix

Name-Value Arguments

Metric — Minimization metric "pointToPoint" (default) | "pointToPlane"

MaxIterations — Maximum number of iterations 20 (default) | positive integer

InitialTransform — Initial rigid transformation affinetform3d() (default) | affinetform3d object

OutlierRemoval — Parameters for outlier removal [20 2] (default) | two-element vector

DistanceThreshold — Distance threshold for closest point 0.1 (default) | positive scalar

NumPoints — Number of points used for local plane fitting 6 (default) | positive integer greater than or equal to 3

Verbose — Progress information output true or 1 (default) | false or 0

Output Arguments

regSurface — Registered surface M-by-3 numeric matrix

tform — Rigid transformation affinetform3d object

rmse — Root mean square error numeric scalar

References

Version History

See Also

Functions

Objects

Topics

`movingSurface` — Surface to be registered
M-by-3 numeric matrix

`fixedSurface` — Reference surface
M-by-3 numeric matrix

`Metric` — Minimization metric
`"pointToPoint"` (default) | `"pointToPlane"`

`MaxIterations` — Maximum number of iterations
`20` (default) | positive integer

`InitialTransform` — Initial rigid transformation
`affinetform3d()` (default) | `affinetform3d` object

`OutlierRemoval` — Parameters for outlier removal
`[20 2]` (default) | two-element vector

`DistanceThreshold` — Distance threshold for closest point
`0.1` (default) | positive scalar

`NumPoints` — Number of points used for local plane fitting
`6` (default) | positive integer greater than or equal to `3`

`Verbose` — Progress information output
`true` or `1` (default) | `false` or `0`

`regSurface` — Registered surface
M-by-3 numeric matrix

`tform` — Rigid transformation
`affinetform3d` object

`rmse` — Root mean square error
numeric scalar