Arc of ellipse detection for video image registration
Arnaud Le Troter, R´ emy Bulot, Jean-Marc Boi, Jean Sequeira
Laboratoire des Sciences de l’Information et des Syst` emes (LSIS - UMR 6168)
Equipe LXAO (ESIL) - case 925 - 163, avenue de Luminy
13288 Marseille cedex 9, France
Abstract—In this paper, we give a detailed presentation of a
robust algorithm for detecting arcs of ellipse in a binary image.
The characterization of such arcs of ellipse enables the identifica-
tion between some video image elements and the corresponding
landmarks in a 3D model of the scene to be represented. This
algorithm is based on a classical ellipse property that enables
its parameters separation. It provides interesting results even in
noisy images or when these arcs are small and partially hidden.
The Simulfoot project has been developed in the LXAO
group of the LSIS laboratory with the participation of research
scientists in the fields of Computer and Cognitive Sciences.
The goal of this project is to provide a support for team sport
analysis using video sequences, with dedicated applications to
A key step of this process is the 2D-3D registration that
consists in identifying a set of specific elements within the
images and associating them with the corresponding ones in
the 3D model, all these landmarks being referenced in the 2D
model of the field.
This problem can be handled in various ways depending
on video capture conditions. We suppose that we do not have
any knowledge on the capture parameters: the camera has not
been calibrated, it can move and zoom without any constraint,
and we can skip from a camera to another one within a video
sequence. Thus, we will not base the registration process on
the sequence coherence but only on the detection of landmarks
as straight and circular lines that have been drawn on the field
and that appear as straight and elliptic lines in the images.We
take advantage of homography classical properties  and the
representation of these transformations as linear applications
in the homogeneous space to perform the transformation from
the images to the 2D model of the field. A 3 lines and 3
columns matrix represents this transformation.
Thus, our problem is:
• To automatically detect the image area corresponding to
the field (a 2D space in the 3D one).
• To find the matrix that performs the transformation be-
tween the points of the image area and the 2D model.
Research works have been developed in the frame of this
project to automatically detect the Region of Interest (the field)
and the straight lines in this area . When the number of
straight lines in this area is too small, we need to find other
relevant features such as arcs of ellipses that are the projection
of circular lines.
We find points of the primary field itself (i.e. the grass, or
the earth) through the characterization of color coherence in
the region of interest . Thus, by setting to 0 all the points
selected as primary field and all the points that lay out of the
region of interest, we obtain a binary image in which points
to 1 may be associated with the players, the referee, the ball
and the lines drawn on the field . Once straight lines have
been detected in this binary image, we can produce another
binary image in which the points associated with these lines
have been retrieved.
Our goal is to extract arcs of ellipses from this binary image.
II. ARC OF ELLIPSE DETECTION
Many algorithms for detecting ellipses in images have
been developed and published. Most of them use variable
ellipses that automatically match the data (,). We have
developed an algorithm based on the Hough transform applied
to two subsets of separated variables.The most general ellipse
equation is expressed with six parameters and a proportionality
relation on them: that means that ellipses are defined by 5
effective parameters (or by using 5 points). We could think
to use a ”5 to 1” Hough transform to provide such detection
but it would not be acceptable for complexity (the parameter
space would be R5) and non-homogeneity reasons.
Fig. 1.The center O of the ellipse belongs to the line IJ
We have taken advantage of an ellipse geometrical property
to separate this research into two other ones, one in R2and one
in R3), both of them in parameter spaces that have a correct
homogeneity. This property is expressed as follows: ”Let M1
and M2be two points of the ellipse, and let T1and T2be the
tangent lines to the ellipse in these two points. Let I be the
intersection point of T1 and T2, and let J be the middle of
M1M2. Then the IJ line contains the center O of the ellipse”.
This property has already been used for detecting ellipses in