 
Summary: Curvaturebased signatures for object description and recognition
Elli Angelopoulou, James P. Williams, Lawrence B. Wolff
Computer Vision Laboratory, Department of Computer Science,
The Johns Hopkins University, Baltimore, MD 21218, USA
email: {angelop, jimbo, wolff}@cs.jhu.edu
ABSTRACT
An invariant related to Gaussian curvature at an object point is developed based upon the covariance matrix of photo
metric values within a local neighborhood about the point. We employ three illumination conditions, two of which are com
pletely unknown. We never need to explicitly know the surface normal at a point. The determinant of the covariance matrix
of the intensity threetuples in the local neighborhood of an object point is shown to be invariant with respect to rotation and
translation. A way of combining these determinants to form a signature distribution is formulated that is rotation, translation,
and scale invariant. This signature is shown to be invariant over large ranges of poses of the same objects, while being sig
nificantly different between distinctly shaped objects. A new object recognition methodology is proposed by compiling sig
natures for only a few viewpoints of a given object.
Keywords: object representation, object recognition, Gaussian curvature, covariance matrix
1. INTRODUCTION
The recognition of threedimensional objects using twodimensional images and the efficient representation of the
shape information are of fundamental importance in computer vision and robotics. A typical approach is to extract a set of
highlevel features from input images and associate these features with the geometry of the objects in the scene. Such fea
tures can vary from simple primitives like 2D points14, junctions23 and 2D curves11 to complex structures like deformable
