An Effective Rigidity Constraint for Improving RANSAC in Homography Estimation - Advanced Concepts for Intelligent Vision Systems - page 202

An Effective Rigidity Constraint for Improving
RANSAC in Homography Estimation

David Monnin, Etienne Bieber, Gwenaël Schmitt, and Armin Schneider

French-German Research Institute of Saint-Louis (ISL), 5 rue du Général Cassagnou,
PO Box 70034, 68300 Saint-Louis, France
[e-mail]

Abstract. A homography is a projective transformation which can re-
late two images of the same planar surface taken from two different points
of view. Hence, it can be used for registering images of scenes that can
be assimilated to planes. For this purpose a homography is usually es-
timated by solving a system of equations involving several couples of
points detected at different coordinates in two different images, but lo-
cated at the same position in the real world. A usual and ecient way
of obtaining a set of good point correspondences is to start from a pu-
tative set obtained somehow and to sort out the good correspondences
(inliers) from the wrong ones (outliers) by using the so-called RANSAC
algorithm. This algorithm relies on a statistical approach which neces-
sitates estimating iteratively many homographies from randomly chosen
sets of four-correspondences. Unfortunately, homographies obtained in
this way do not necessarily reflect a rigid transformation. Depending on
the number of outliers, evaluating such degenerated cases in RANSAC
drastically slows down the process and can even lead to wrong solutions.
In this paper we present the expression of a lightweight rigidity con-
straint and show that it speeds up the RANSAC process and prevents
degenerated homographies.

1 Introduction

In the field of computer vision, homographies are widely used to relate images
of scenes assimilable to planar surfaces. All typical homography applications
from the computation of camera motion to image mosaicing, video stabilization,
augmented reality, image rectification or sub-pixel resolution extrapolation rely
in a way on image registration. Homographies are consequently expected to
reflect a mapping from one image plane to another which corresponds to a rigid-
body transformation. It is therefore assumed that a rigid body keeps its shape
during the acquisition of images to be related and that only its projection on
the image plane changes when the camera view changes.
The homogeneous coordinates representation used in projective geometry,
which is briefly described hereafter, allows a very synthetic and convenient ma-
trix representation of a homography. Unlike in Euclidean geometry, a combina-
tion of 3D rotation and translation necessitates only one matrix multiplication.