**Multiple Range Data Set Registration**

**Figures 1a and 1b: Two sets of range data
taken from the same scene (click any figure for more detail)**
The Problem:

When obtaining range and color information, taking data from one position
in a scene cannot completely represent everything in that scene.
The data obtained by the laser from each position only contains information
about the first surface the laser beam encountered, creating shadows where
other surfaces are occluded from the viewpoint. By taking multiple
sets of data from different positions (figures **1a** and **1b**)
and registering them with one another, the occluded areas can be minimized
in the final rendering. The goal of this registration process is
to find a transformation matrix that will map the coordinate system of
one data set onto that of another. We register these data sets in
pairs until they all can be transformed to a single coordinate system.

Our Method:

The first step in registering two data sets is to manually identify
corresponding planar surfaces in the range data. After transforming
the points from the spherical coordinates of the laser into Cartesian
coordinates in 3-space, we select (in each data set) points in three planar
surfaces that exist in both. The best-fit plane (in the least
squares sense) is then determined for each of the selected sets of points
(figures **2a** and **2b**).

**Figures 2a and 2b: With the three matching
planar surfaces selected in each set**
Once these planes are known it takes one rotation to make the first
plane from each set parallel to each other, a second rotation to make the
other two planes as nearly parallel as is possible, and then a translation
to register the planes and therefore the sets. Figure **3a** shows
the sets and their respective planes aligned, and figure **3b** shows
in red and green which points in the final data set came from which initial
set.

**Figures 3a and 3b: After aligning the coresponding
planes, and with colors to show the original data sets**
This approach allows us several advantages. First, one difficulty
in using just points to align two data sets is that it is unlikely for
any point in set A that there is a corresponding point in set B.
Secondly, the use of a best-fit approximation to a planar surface helps
minimize the effect of the noise in the range data. Finally, the transformation
matrix we obtain via the registration process is useful later on when these
sets will be rendered, as knowing the transformations between camera positions
helps us determine which data sets should currently be rendered.

### Research Sponsors

Maintained by Chris McCue

Last Modified 18 February 1999