# Compute Umeyama Transform¶

## Group (Subgroup)¶

DREAM3D Review (Registration)

## Description¶

This Filter computes the Umeyama transform between two unstructured Geometries. An "unstructured" Geometry is any geometry that requires explicit definition of Vertex positions. Specifically, Vertex, Edge, Triangle, Quadrilateral, and Tetrahedral Geometries are considered unstructured Geometries. The Umeyama transform estimates the affine transformation that maximizes the similarity (specifically, the covariance) between two n-dimensional point sets. For two unstructured Geometries, this has the effect of estimating, in closed form, the affine transformation that best brings the Vertices of the moving Geometry into the reference frame of the Vertices of the fixed Geometry. The algorithm may optionally incorporate scaling into the computation of the affine transformation matrix.

The moving and fixed unstructured Geometries do not need to be the same type, since only the Vertex positions are considered; however, the two unstructured Geometries need to share the same number of Vertices. This Filter will create an Attribute Matrix located in the Data Container of the moving Geometry in which to store the transformation matrix. Note that the stored transformation matrix will be in row major order.

## Parameters¶

Name Type Description
Use Scaling bool Whether to include scaling into the transformation matrix

## Required Geometry¶

Any unstructured Geometry

## Required Objects¶

Kind Default Name Type Component Dimensions Description
Moving Data Container None N/A N/A The Data Container holding the moving Geometry
Fixed Data Container None N/A N/A The Data Container holding the fixed Geometry

## Created Objects¶

Kind Default Name Type Component Dimensions Description
Generic Attribute Matrix TransformationData Generic N/A The Attribute Matrix used to store the computed transformation matrix
Attribute Array TransformationMatrix float (2, 4) The computed transformation matrix

## References ##¶

[1] Least-squares estimation of transformation parameters between two point patterns, S. Umeyama, PAMI 1991, DOI: 10.1109/34.88573

## Example Pipelines¶

Please see the description file distributed with this plugin.

## DREAM3D Mailing Lists¶

If you need more help with a filter, please consider asking your question on the DREAM3D Users mailing list: