recalagerigide.c File Reference

rigid registration of two closed contours More...

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Detailed Description

rigid registration of two closed contours

Usage: recalagerigide in1 in2 out

Description:

Rigid registration of two closed contours. Let X and Y be two point sets, given respectively by in1 and in2. This procedure identifies the parameters of a rigid deformation R such that the "distance" between R(X) and Y is a local minimum. The distance D(Z,Y) between two sets Z and Y is defined by:

D(Z,Y) = sum { d2(z,Y) ; for all z in Z }

d2(z,Y) = min { d2(z,y) ; for all y in Y }

d2(z,y) = (z - y)^2 ; i.e., the square or the Euclidean distance between z and y.

The rigid deformation R is defined as the composition (in this order) of scalings, rotations and translations.

In 2d, the parameters are:

• sx : parameter for the scaling in direction x
• sy : parameter for the scaling in direction y
• theta : angle (in radians) of the rotation around the barycenter of X
• tx : parameter for the translation in direction x
• ty : parameter for the translation in direction y

In 3d, the parameters are:

• sx : parameter for the scaling in direction x
• sy : parameter for the scaling in direction y
• sz : parameter for the scaling in direction z
• theta : angle (in radians) of the rotation around the parallel to the the z axis passing by the barycenter of X
• phi : angle (in radians) of the rotation around the parallel to the the y axis passing by the barycenter of X
• tx : parameter for the translation in direction x
• ty : parameter for the translation in direction y
• tz : parameter for the translation in direction z

Types supported: byte 2d, byte 3d

Category: geo

Author:

Michel Couprie