Adv. Appl. Cliﬀord Algebras 27 (2017), 1961–1976
2017 The Author(s) This article is an open access
published online February 16, 2017
Applied Cliﬀord Algebras
Object Detection in Point Clouds Using
Conformal Geometric Algebra
, Adam Leon Kleppe, Lars Tingelstad and
Abstract. This paper presents an approach for detecting primitive geo-
metric objects in point clouds captured from 3D cameras. Primitive
objects are objects that are well deﬁned with parameters and math-
ematical relations, such as lines, spheres and ellipsoids. RANSAC, a
robust parameter estimator that classiﬁes and neglects outliers, is used
for object detection. The primitives considered are modeled, ﬁltered
and ﬁtted using the conformal model of geometric algebra. Methods
for detecting planes, spheres and cylinders are suggested. Least squares
ﬁtting of spheres and planes to point data are done analytically with
conformal geometric algebra, while a cylinder is ﬁtted by deﬁning a non-
linear cost function which is optimized using a nonlinear least squares
solver. Furthermore, the suggested object detection scheme is combined
with an octree sampling strategy that results in fast detection of multi-
ple primitive objects in point clouds.
There has been an increase in the use of 3D cameras in robotic vision appli-
cations due to the availability of commercial products with high accuracy.
The advantage of 3D cameras compared to 2D cameras is the additional
depth information, which can provide information about size and position of
objects in a scene, where a scene is the environment captured by the camera.
The depth information from 3D cameras can be represented as point clouds,
which is a set of points in Euclidean space given by the x, y, z coordinates
for each point. Object detection in point clouds can be diﬃcult due to noise,
outliers and complexity in the data.
There exists several approaches for describing the underlying features
and geometry represented in a point cloud. In  features such as curvature,
surface normals and edges are extracted and objects are described in terms