estgeotform2d

Estimate 2-D geometric transformation from matching point pairs

Since R2022b

Syntax

tform = estgeotform2d(matchedPoints1,matchedPoints2,transformType)

[tform,inlierIndex] = estgeotform2d(___)

[tform,inlierIndex,status] = estgeotform2d(___)

[___] = estgeotform2d(___,Name=Value)

Description

tform = estgeotform2d(matchedPoints1,matchedPoints2,transformType) estimates a 2-D geometric transformation between two images by mapping the inliers in the matched points from one image matchedPoints1 to the inliers in the matched points from another image matchedPoints2.

[tform,inlierIndex] = estgeotform2d(___) 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,status] = estgeotform2d(___) 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 status output, the function instead returns an error for conditions that cannot produce results.

[___] = estgeotform2d(___,Name=Value) specifies additional options using one or more name-value arguments in addition to any combination of arguments from previous syntaxes. For example, Confidence=99 sets the confidence value for finding the maximum number of inliers to 99.

Examples

Fit 2-D Geometric Transformation to SURF Feature Points

Read an image and display it.

original = imread("cameraman.tif");
imshow(original)
title("Original Image")

Distort and display the transformed image.

distorted = imresize(original,0.7); 
distorted = imrotate(distorted,31);

imshow(distorted)
title("Transformed Image")

Detect and extract features from the original and the transformed images.

ptsOriginal  = detectSURFFeatures(original);
ptsDistorted = detectSURFFeatures(distorted);
[featuresOriginal,validPtsOriginal] = extractFeatures(original,ptsOriginal);
[featuresDistorted,validPtsDistorted] = extractFeatures(distorted,ptsDistorted);

Match and display features between the images.

index_pairs = matchFeatures(featuresOriginal,featuresDistorted);
matchedPtsOriginal  = validPtsOriginal(index_pairs(:,1));
matchedPtsDistorted = validPtsDistorted(index_pairs(:,2));
 
showMatchedFeatures(original,distorted,matchedPtsOriginal,matchedPtsDistorted)
title("Matched SURF Points With Outliers")

Exclude the outliers, estimate the transformation matrix, and display the results.

[tform,inlierIdx] = estgeotform2d(matchedPtsDistorted,matchedPtsOriginal,"similarity");
inlierPtsDistorted = matchedPtsDistorted(inlierIdx,:);
inlierPtsOriginal  = matchedPtsOriginal(inlierIdx,:);
 
showMatchedFeatures(original,distorted,inlierPtsOriginal,inlierPtsDistorted)
title("Matched Inlier Points")

Use the estimated transformation to recover and display the original image from the distorted image.

outputView = imref2d(size(original));
Ir = imwarp(distorted,tform,"OutputView",outputView);
 
imshow(Ir) 
title("Recovered Image")

Input Arguments

matchedPoints1 — Matched points from first image

M-by-2 matrix | point feature object

Matched points from the first image, specified as an M-by-2 matrix of M number of [x y] coordinates, or as one of the point feature objects described in Point Feature Types.

matchedPoints2 — Matched points from second image

M-by-2 matrix | point feature object

Matched points from the first image, specified as an M-by-2 matrix of M number of [x y] coordinates, or as one of the point feature objects described in Point Feature Types.

transformType — Transformation type

"rigid" | "similarity" | "affine" | "projective" | "translation"

Transformation type, specified as "rigid", "similarity", "affine", "projective", or "translation". 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.

Transformation Type	tform Object	Minimum Number of Matched Pairs of Points
"rigid"	rigidtform2d	2
"similarity"	simtform2d	2
"affine"	affinetform2d	3
"projective"	projtform2d	4
"translation"	transltform2d	1

Data Types: string

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: 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 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 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 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

tform — Geometric transformation

rigidtform2d object | simtform2d object | affinetform2d object | projtform2d object | transltform2d object

Geometric transformation, returned as a rigidtform2d, simtform2d, affinetform2d, projtform2d, or transltform2d object.

The returned geometric transformation matrix maps the inliers in matchedPoints1 to the inliers in matchedPoints2. The function returns an object specific to the transformation type specified by the transformType input argument.

transformType	Geometric Transformation Object
"rigid"	rigidtform2d
"similarity"	simtform2d
"affine"	affinetform2d
"projective"	projtform2d
"translation"	transltform2d

inlierIndex — Index of inliers

M-by-1 logical vector

Index of inliers, returned as an M-by-1 logical vector, where M is the number of point pairs. Each element contains either a logical 1 (true), indicating that the corresponding point pair is an inlier, or a logical 0 (false), indicating that the corresponding point pair is an outlier.

Data Types: logical

status — Status code

0 | 1 | 2

Status code, returned as 0, 1, or 2. The status code indicates whether or not the function could estimate the transformation and, if not, why it failed.

Value	Description
0	No error
1	matchedPoints1 and matchedPoints2 inputs do not contain enough points
2	Not enough inliers found

If you do not specify the status code output, the function returns an error if it cannot produce results.

Data Types: int32

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.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• You cannot use a SURFPoints object as an input to estgeotform2d. See the Introduction to Code Generation with Feature Matching and Registration example for details on how to use SURFPoints with estgeotform2d in code generation.

Version History

Introduced in R2022b

R2022b: Recommended over estimateGeometricTransform2D

Starting in R2022b, many Computer Vision Toolbox™ functions create and perform geometric transformations using the premultiply convention. However, the estimateGeometricTransform2D function estimates geometric transformations using the old postmultiply convention. Although there are no plans to remove estimateGeometricTransform2D at this time, you can streamline your geometric transformation workflows by switching to the estgeotform2d function, which supports the premultiply convention. For more information, see Migrate Geometric Transformations to Premultiply Convention.