# Human supervisory approach to modeling industrial scenes using geometric primitives Page: 4 of 9

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Because of the large extent of errors in real-world data

and the lack of reliability in autonomous methods, we have

opted to use a human supervisor to guide the modeling

process. The underlying approach is to use geometric

primitives to fuse and segment the range imagery, and then

use the segmented data to refine the parameters of the geo-

metric primitive. Geometric primitives are ideal for mod-

eling industrial environments since they require very little

memory for large world maps, and are easy to store and

manipulate. Once the parameters for all the surfaces in the

scene are found and refined, the geometric models are

extrapolated to build the final world model. The world

model is then exported to a CAD system.

From the supervisor's point of view, the modeling

system consists of two windows and a few controls on a

workstation. The first window displays range imagery

from the structured lighting system, and the second win-

dow contains the world model built from the range imag-

ery. The range imagery appears in the window as a

collection of points in space. The supervisor selects initial-

ization points on the surface of an object, and instructs the

computer to fuse, segment and model the object. As an

object is modeled, the data associated with the object is

highlighted in the data window. When the operator is satis-

fied with the fusion and segmentation, the model is refined

and the surface represented by the model appears in the

model window. The points associated with the object in

the data window are also removed, allowing the supervisor

to easily monitor progress. After the range data has been

fused, segmented and modeled, the operator extrapolates

surfaces in the model window until a fully defined world

model is produced.

With regards to geometric primitives used to model

the surfaces, casual observation of industrial environments

reveals that a few types of surfaces can be used to model a

wide range of industrial scenes. Bounded planes, for

example, can be used to model walls, ceilings and floors,

and combined to model cabinets, desks, crates and other

items. Finite-length cylinders can be used to model venti-

lation ducts, chemical storage drums, electrical conduit

among other objects. A final type of surface, a random sur-

face, can be used to model objects such as sand heaps or a

pile of debris. The details of how we fuse, segment and

model these surfaces are described next.

2.0 DETAILED DESCRIPTION

Let Si = {(xk, Yk, Zk)} be the i' set of range sam-

ples collected from surfaces in an environment. The sam-

ples Si are typically collected from a ranging system (e.g.,

structured lighting) and provide a single view of the envi-

ronment. Consider the union of N sets of range samples of

the same scene but collected from different viewpoints.

The set of range samples, S = St v S2- - SN, thus rep-

resent samples of surfaces in the environment. Our objec-

tive is to build a reliable scene model from the data in S.2.1 Planes

The supervisor typically starts by fusing, segmenting

and modeling the planes in S. A bounded plane is

described by a set of parameters p = {a, b, c, d} which

define the (infinite) plane ax + by + cz = d, and a set of

edge points e = {(xk, yk, Zk)}, that lie in the plane and

represent the vertices of the plane's boundary. The prob-

lem is now one of determining plane parameters p and

edge points e. An estimate of p is found as the least-

squares solution to a system of equations formed from a

set of initialization points u = { (xk, yk, Zk) }, selected by

the supervisor. Typically, the supervisor randomly selects

four to ten initialization points scattered around the plane

and its periphery. After parameters p have been estimated,

a new (primed) coordinate system is established such that

the z' = 0 plane of the new coordinate system coincides

with the plane represented by the estimated parameters in

p . The data in S is then rotated from the world coordinate

system into the primed coordinate system and denoted as

S'. The standard deviation az'(u') of the perpendicular

distance of the rotated initialization points to the plane

z' = 0 is now estimated. A new set of points, T' c S' is

derived from S' such that

T' = {(xk', Yk" Zk IZkI < Xa z'(4u')

whete X is a tuning parameter used to fuse misregistered

planes. By correctly adjusting X, data from misregistered

planes can be assimilated into a single plane. Effectively, a

one-dimensional (i.e., along the z' coordinate) segmenta-

tion of the data in S' is performed. The next task is to seg-

ment the data in T' along the x' and y' coordinates.

Two dimensional segmentation of the remaining

points in T' begins by forming a bounding box B of

width Ax' and height Ay' around the initialization points

u0= { (xi', Yk', 0) } . The width and height of the bound-

ing box is then expanded to 2Ax' and 2Ay' respectively,

and points in T' that are exterior to the expanded bound-

ing box are discarded. This simple operation is adequate

for isolated planes, e.g., the top of a box, but inadequate

for planes touching other surfaces, e.g., the side of a box

sitting on a floor. Thus, additional steps are performed on

the data in T' to correctly segment planes such as the lat-

ter. To start with, all remaining points in T' are projected

onto the x' axis, and a ten-bin histogram over the region

of support of the distribution is calculated. If a bin con-

tains less than 15% of the peak value of the histogram, the

points in that bin and all points from that bin to the current

plane boundary are discarded. The same process then

occurs on the y' axis. If points are discarded, the histo-

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Luck, J.P.; Little, C.Q. & Roberts, R.S. Human supervisory approach to modeling industrial scenes using geometric primitives, article, November 19, 1997; California. (digital.library.unt.edu/ark:/67531/metadc709270/m1/4/: accessed October 16, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.