estimateGeometricTransform3D
Estimate 3-D geometric transformation from matching point pairs
Syntax
Description
tform = estimateGeometricTransform3D(matchedPoints1,matchedPoints2,transformType)matchedPoints1 to the inliers in the matched points
from the other set of 3-D points matchedPoints2.
[
additionally returns a vector specifying each matched point pair as either an
inlier or an outlier using the input arguments from the previous syntax.tform,inlierIndex]
= estimateGeometricTransform3D(___)
[
additionally returns a status code indicating whether or not the function could
estimate a transformation and, if not, why it failed. If you do not specify the
tform,inlierIndex,status] = estimateGeometricTransform3D(___)status output, the function instead returns an error
for conditions that cannot produce results.
[___] = estimateGeometricTransform3D(___,
specifies additional options using one or more name-value pair arguments in
addition to any combination of arguments from previous syntaxes. For example,
Name,Value)'Confidence',99 sets the confidence value for finding the
maximum number of inliers to 99.
Examples
Estimate Transformation Between Two Point Clouds
Load a point cloud file into the workspace.
ptCloud1 = pcread('teapot.ply')ptCloud1 =
pointCloud with properties:
Location: [41472×3 single]
Count: 41472
XLimits: [-3 3.4340]
YLimits: [-2 2]
ZLimits: [0 3.1500]
Color: []
Normal: []
Intensity: []
ptCloud1 = pcdownsample(ptCloud1,'random',0.25); Create a rigid 3-D transformation object with a 30-degree rotation.
theta = 30; % degrees rot = [cosd(theta) sind(theta) 0; ... -sind(theta) cosd(theta) 0; ... 0 0 1]; trans = [0 0 0]; tform = rigid3d(rot,trans);
Transform the point cloud using the transformation object.
ptCloud2 = pctransform(ptCloud1,tform);
To introduce noise, add random points to both point clouds.
noise1 = rescale(rand(1000,3),-2,2); ptCloud1 = pointCloud([ptCloud1.Location;noise1]); noise2 = rescale(rand(1000,3),-2,2); ptCloud2 = pointCloud([ptCloud2.Location;noise2]);
Visualize the noisy point clouds.
figure
pcshowpair(ptCloud1,ptCloud2)
title('Point Clouds With Added Noise')
Extract matched points from the point clouds.
matchedPoints1 = ptCloud1.Location; matchedPoints2 = ptCloud2.Location;
Estimate the rigid transformation between the point clouds.
[tformEst,inlierIndex] = estimateGeometricTransform3D(matchedPoints1, ... matchedPoints2,'rigid');
Extract the inlier points.
inliersPtCloud1 = transformPointsForward(tformEst,matchedPoints1(inlierIndex,:)); inliersPtCloud2 = matchedPoints2(inlierIndex,:);
Visualize the inliers of the aligned point clouds.
figure
firstPtCloud = pointCloud(inliersPtCloud1);
secondPtCloud = pointCloud(inliersPtCloud2);
pcshowpair(firstPtCloud,secondPtCloud)
title('Aligned point clouds')
Input Arguments
matchedPoints1 — First set of matched 3-D points
M-by-3 matrix of
[x,y,z]
coordinates
First set of matched 3-D points, specified as an M-by-3 matrix in which each row is a set of (x,y,z) coordinates and M is the number of matched points.
matchedPoints2 — Second set of atched 3-D points
M-by-3 matrix of
[x,y,z]
coordinates
Second set of matched 3-D points, specified as an M-by-3 matrix in which each row is a set of (x,y,z) coordinates and M is the number of matched points.
transformType — Transformation type
'rigid' | 'similarity'
Transformation type, specified as 'rigid' or
'similarity'. Each transform type requires a minimum
number of matched pairs of points to estimate a transformation. You can
generally improve the accuracy of a transformation by using a larger number
of matched pairs of points. This table shows the type of object associated
with each transformation type and the minimum number of matched pairs of
points the transformation requires.
transformType | tform Object | Minimum Number of Matched Pairs of Points |
|---|---|---|
'rigid' | rigid3d | 3 |
'similarity' | affine3d | 3 |
Data Types: string
Name-Value Pair Arguments
Specify optional
comma-separated pairs of Name,Value arguments. Name is
the argument name and Value is the corresponding value.
Name must appear inside quotes. You can specify several name and value
pair arguments in any order as
Name1,Value1,...,NameN,ValueN.
'Confidence',99 sets the confidence
value for finding the maximum number of inliers to
99.'MaxNumTrials' — Maximum random trials
1000 (default) | positive integer
Maximum number of random trials, specified as the comma-separated pair
consisting of 'MaxNumTrials' and a positive
integer. This value specifies the number of randomized attempts the
function makes to find matching point pairs. Specifying a higher value
causes the function to perform additional computations, which increases
the likelihood of finding inliers.
Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64
'Confidence' — Confidence of finding maximum number of inliers
99 (default) | positive numeric scalar
Confidence of finding the maximum number of inliers, specified as the
comma-separated pair consisting of 'Confidence' and
a positive numeric scalar in the range (0, 100). Increasing this value
causes the function to perform additional computations, which increases
the likelihood of finding a greater number of inliers.
Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64
'MaxDistance' — Maximum distance from point to projection
1.5 (default) | positive numeric scalar
Maximum distance from a point to the projection of the corresponding
point, specified as the comma-separated pair consisting of
'MaxDistance' and a positive numeric scalar.
'MaxDistance' specifies the maximum distance,
in pixels, that a point can differ from the projected location of its
corresponding point to be considered an inlier. The corresponding
projection is based on the estimated transform.
The function checks for a transformation from
matchedPoints1 to
matchedPoints2, and then calculates the distance
between the matched points in each pair after applying the
transformation. If the distance between the matched points in a pair is
greater than the 'MaxDistance' value, then the
pair is considered an outlier for that transformation. If the distance
is less than 'MaxDistance', then the pair is
considered an inlier.
Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64
Output Arguments
Algorithms
The function excludes outliers using the M-estimator sample consensus (MSAC) algorithm. The MSAC algorithm is a variant of the random sample consensus (RANSAC) algorithm. Results may not be identical between runs due to the randomized nature of the MSAC algorithm.
References
[1] Hartley, Richard, and Andrew Zisserman. Multiple View Geometry in Computer Vision. 2nd ed. Cambridge, UK ; New York: Cambridge University Press, 2003.
[2] Torr, P.H.S., and A. Zisserman. “MLESAC: A New Robust Estimator with Application to Estimating Image Geometry.” Computer Vision and Image Understanding 78, no. 1 (April 2000): 138–56. https://doi.org/10.1006/cviu.1999.0832.