In: Stilla U, Rottensteiner F, Paparoditis N (Eds) CMRT09. IAPRS, Vol. XXXVIII, Part 3/W4 — Paris, France, 3-4 September, 2009 
TRAJECTORY-BASED SCENE DESCRIPTION AND CLASSIFICATION BY ANALYTICAL 
FUNCTIONS 
D. Pfeiffer 3 , R. Reulke b * 
1 Akeleiweg 46D, 12487 Berlin, Germany - david@dltmail.de 
h Humboldt-University of Berlin, Computer Science Department, Computer Vision, Rudower Chaussee, Berlin, 
Germany - reulke@infonnatik.hu-berlin.de 
Commission III, WG III/4 and III/5 
KEY WORDS: Object recognition, Scene Analysis, statistical and deterministic trajectory models 
ABSTRACT: 
Video image detection systems (VIDS) provide an opportunity to analyse complex traffic scenes that are captured by stationary video 
cameras. Our work concentrates on the derivation of traffic relevant parameters from vehicle trajectories. This paper examines dif 
ferent procedures for the description of vehicle trajectories using analytical functions. Derived conical sections (circles, ellipses and 
hyperboles) as well as straight lines are particularly suitable for this task. Thus, it is possible to describe a suitable trajectory’ by a 
maximum of five parameters. A classification algorithm uses these parameters and takes decisions on the turning behaviour of vehi 
cles. 
A model based approach is following. The a-priori knowledge about the scene (here prejudged and verified vehicle trajectories) is 
the only required input into this system. One confines himself here to straight lines, circles, ellipses and hyperboles. Other common 
functions (such as clothoids) are discussed and the choice of the function is being justified. 
1. INTRODUCTION 
1.1 Motivation 
Traffic management is based on an exact knowledge of the 
traffic situation. Therefore, traffic monitoring at roads and 
intersections is an essential prerequisite. Inductive loops and 
microwave radar systems are the most common detection and 
surveillance systems to measure traffic flow on public roads. 
VIDS that operate with real time image processing tech 
niques became more attractive during the last 15 years 
(Michalopoulos 1991), (Wigan 1992), (Setchell et al. 2001), 
(Kastrinaki et al. 2003). Traditional traffic parameters like 
presence, vehicle length, speed as well as time gap between 
two vehicles and vehicle classification (Wei et al. 1996) can 
be determined. In contrast to other sensors, the use of local 
cameras makes a two-dimensional observation possible and 
thus can determine new traffic parameters like congestion 
length, source-destination matrices, blockage or accidents 
and therefore support the estimation of travel times. Multi 
camera systems extend some limitations of single camera 
systems (e.g. occlusions, reliability) and enlarge the observa 
tion area (Reulke et al. 2008a). 
We proposed a framework that autonomously detects atypi 
cal objects, behavior or situations even in crowded and com 
plex situations (Reulke et al. 2008b). Extracted object data 
and object trajectories from multiple sensors have to be 
fused. An abstract situational description of the observed 
scene is obtained from the derived trajectories. The first step 
in describing a traffic scene is to ascertain the normal situa 
tion by statistical means. In addition, semantic interpretation 
is also derived from statistical information (such as direction 
and speed). Deviations of the inferred statistics are inter 
preted as atypical events, and therefore can be used to detect 
and prevent dangerous situations. These options allow the 
detection of sudden changes as well as atypical or threatening 
events in the scene. Atypical or threatening events are gener 
ally defined as deviations from the normal scene behavior or 
have to be defined by a rule based scheme. Red light runners 
and incident detection systems are an example for a self- 
evident road traffic application. 
The trajectories of street vehicles are smooth and homogene 
ous over a large scale. Therefore, a mathematical description 
by elementary functions is appropriate for these trajectories. 
Thus, dramatic reductions of the bandwidths are achieved for 
a full scene transmission. The basic step to determine the 
driver intentions is to fit the trajectories to the analytical 
functions. 
This paper is organized as follows: After an overview of 
situation analysis and atypical event detection the approach is 
introduced. Then, an example installation is described and its 
results are presented. The mathematical fundamentals of the 
adaptation of formerly derived trajectories of turning vehicles 
by hyperbolas, ellipsoids, spheres and straight lines are 
sketched. The derived information is very comprehensive but 
compact and permits downcast to other representations like 
source destination matrices. The paper closes with a sum 
mary and an outlook. 
1.2 Situation Analysis and Atypical Event Detection 
Scene description and automatic atypical event detection are 
issues of increasing importance and an interesting topic in 
many scientific, technical or military fields where complex 
situations (i.e. scenes containing many objects and interac- 
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