Method for groupwise point set matching
A method for registering a collection of m input point sets or images {P 1 , P 2 , . . . , P m }, where m is an integer. The method identifies a set of m rigid (or affine) transformations {T 1 , T 2 , . . . , T m } aligning such images comprising determining a mean of the input point sets or images {P 1 , P 2 , . . . , P m } and aligning the images using the determined mean in performing the transformation alignment. The method extends image matching using only a pair of point sets (i.e., from registration of only a pair of images) to a collection of point sets (i.e., registration of more than a pair of images).
1 . A method for registering a collection of m input point sets {P 1 , P 2 , . . . , P m }, where m is an integer greater than 2, comprising:
identifying a set of m rigid or affine transformations {T 1 , T 2 , . . . , T m };
aligning such images comprising determining a mean of the m input point sets {P 1 , P 2 , . . . , P m } and aligning the images using the determined mean in performing the transformation alignment.
2 . The method recited in claim 1 wherein the method determines the closest points computed from a randomly selected one of the point sets {P 1 , P 2 , . . . , P m }, and from such determined point set, determines a transformation for each one of the point sets {P 1 , P 2 , . . . , P m } and updates the points sets {P 1 , P 2 , . . . , P m } iteratively a fixed number of times or until a change of a predetermined error criterion, such as for example the mean squared error or the maximum absolute error, is below a predetermined threshold.
3 . The method recited in claim 1 wherein the method determines the transformation that minimizes the mean squared distance between the elements of point sets {P 1 , P 2 , . . . , P m } and a weighted average of the closest points in all other ones of the point sets {P 1 , P 2 , . . . , P m }; and updates the set points {P 1 , P 2 , . . . , P m } iteratively a fixed number of times or until a change of the a predetermined error criterion, such as for example the mean squared error or the maximum absolute error, is below a predetermined threshold.
4 . A method for registering a collection of m input point sets {P 1 , P 2 , . . . , P m }, where m is an integer, comprising:
identifying a set of m rigid or affine transformations {T 1 , T 2 , . . . , T m };
aligning such images comprising determining a mean of the m input point sets {P 1 , P 2 , . . . , P m } and aligning the images using the determined mean in performing the transformation alignment; and
wherein the method includes determining the closest points computed from a randomly selected one of the point sets {P 1 , P 2 , . . . , P m }, and from such determined points, determining a transformation for each one of the point sets {P 1 , P 2 , . . . , P m } and updating the set points {P 1 , P 2 , . . . , P m } iteratively a fixed number of times or until a change of a predetermined error criterion is below a predetermined threshold.
5 . A method for registering a collection of m input point sets {P 1 , P 2 , . . . , P m }, where m is an integer, comprising:
identifying a set of m rigid or affine transformations {T 1 , T 2 , . . . , T m };
aligning such images comprising determining a mean of the m input point sets {P 1 , P 2 , . . . , P m } and aligning the images using the determined mean in performing the transformation alignment; and
wherein the method includes determining the transformation that minimizes the mean squared distance between the point set {P 1 , P 2 , . . . , P m } and a weighted average of the closest points in all other ones of the point sets {P 1 , P 2 , . . . , P m }; and updates the set points {P 1 , P 2 , . . . , P m } iteratively a fixed number of times or until a change of a predetermined error criterion is below a predetermined threshold.
6 . The method recited in claim 5 wherein the predetermined error criterion is mean square error.
7 . The method recited in claim 5 wherein the predetermined error criterion is maximum absolute error.