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A COMPUTER VISION METHOD FOR MOTION 
DETECTION USING COOPERATIVE KALMAN FILTERS 
Florence GERMAIN and Thomas SKORDAS 
ITMI 
11, Chemin des Prés, BP 87 
F-38243 Meylan cédex 
France 
e-mail: f.germain@itmi.fr, t.skordas@itmi.fr 
ABSTRACT : 
In this paper, we describe a method for the computation of the optical flow in a sequence of images 
acquired by a moving camera. The method is guided by the simultaneous satisfaction of two op- 
posite constraints introduced by the regularization process used to remove the underdetermination 
related to the aperture phenomenon. Two cooperative Kalman filters are used which allow us to 
compute the motion information present in the images. Such a method is particularly well suited 
to deal with outdoor scenes and some real experiments are presented which highlight its validity. 
KEY WORDS: Computer Vision, Motion detection and estimation, Kalman filtering. 
1 Introduction 
In the context of a rapidly growing demand for a computer 
based interpretation of images, motion analysis plays a ma- 
jor role. Image motion is mainly used: 
1. as a meaningful information on objects motion in the 
context of scene behavioral analysis [4]; 
2. as a model of the space-time redundancy in an image 
sequence, in the context of coding for image transmis- 
sion [3]. 
Motion analysis is commonly based on a pixel per pixel 
estimation of the instantaneous displacement of the under- 
lying physical points. The resulting dense field, estimated 
from each pair of consecutive images in a sequence of images 
acquired through a single CCD camera, is commonly named 
the optical flow. 
1.1 Explicit motion information 
The optical flow estimation relies on the local information 
which is intrinsically part of the image. In the following, we 
will refer to it as the explicit motion information. 
The explicit motion information has a local nature. The 
extraction process, at a given pixel, of a motion information 
is conditioned by the existence of a non zero spatial gradient. 
Therefore, the explicit information is available only inside a 
non homogeneous area of an image. 
Moreover, explicit information, when it does exist, is in- 
complete. It only provides a partial view of the underlying 
motion, depending on the spatial gradient orientation at the 
considered pixel. Most of the time, it amounts to the projec- 
tion of the searched displacement along the local spatial gra- 
dient of the intensity. This projection is commonly known 
as the orthogonal displacement. The underdetermination 
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which comes from the lack of a second projection illustrates 
a physical phenomenon known as the aperture phenomenon 
[5]. The ensued ambiguity summarizes the difficulties which 
are faced when estimating the motion in image sequences. 
1.2 The regularization operation 
Due to the incomplete nature of the explicit motion infor- 
mation, the optical flow estimation implies a spatial integra- 
tion of the local information, in order to remove, when this 
is possible, the underdetermination related to the aperture 
phenomenon. This operation, usually named regularization, 
requires an accurate determination of the spatial scope of 
integration. Intuitively, this integration must respect the 
boundaries between two homogeneously moving image ar- 
eas. Therefore, every qualitative change in the displacement 
vector field must be effectively detected. 
The quality of a regularization operator will be judged 
on both its integration capability and its ability to detect a 
qualitative change of the estimated vector field. The antag- 
onistic nature of these two constraints plays a major role in 
the choice of a regularization method. 
We propose an estimation of the optical flow to be used 
for the analysis of moving scenes. Our approach is guided by 
the simultaneous satisfaction of the opposed constraints put 
by the regularization. It is based on the use of a parametric 
estimator built on a Kalman filtering process which is similar 
to the one proposed by Stuller and Krishnamurthy [1]. 
2 A parametric Kalman model for 
the motion estimation 
The parametric Kalman model which has been introduced 
in [1] generates a parameterized family of optical flow esti- 
mators. The motion is estimated using a line-based scanning