P2-7-1 
A Comparative Study on Techniques for Optical Flow Estimation 
: On the Application to Vehicle Motion Analysis 
Takashi FUSE and Eihan SHIMIZU 
Department of Civil Engineering 
University of Tokyo 
JAPAN 
fuse@planner.t.u-tokyo.ac.jp, shimizu@planner.t.u-tokyo.ac.jp 
KEY WORDS: Optical Flow, Gradient-Based Approach, Vehicle Motion Analysis. 
ABSTRACT 
The most readily available motion parameter from sequential image is optical flow. Among various optical flow 
estimation techniques, gradient-based approach is common. This approach is based on the assumption that the brightness 
of a point in the image remains constant during a short time interval, while the location of that point in the image may 
change due to motion. This assumption leads to a single local constraint on the optical flow at a certain point in the image. 
It is, however, ill-posed as the constraint constitutes only one equation of two unknowns, that is, x-component and y- 
component of the flow vector. In order to solve this problem, various methods have been proposed. There are, however, 
only a few comparative studies from the viewpoint of the application to the specific and practical motion analysis. This 
paper compiles the gradient-based approaches and compares their performance empirically from the point of view of 
application to vehicle motion analysis. The basic methods of gradient-based approach are compiled as follows: (1) 
Increase in the number of observation equations by the assumption that a constant velocity over each spatial neighborhood 
(spatial local optimization method), by a constant velocity over temporal neighborhood (temporal local optimization 
method), by use of three channels (RGB, HSI) of each pixel (multispectral constraints method) and by their combination; 
(2) Imposition of a condition, such as spatial smoothness of optical flow (spatial global optimization method), temporal 
smoothness (temporal global optimization method) and their combination. The result of empirical comparison shows the 
difficulty of estimation of precise and dense optical flow by ordinary gradient-based approaches, when sequential images 
are taken at an interval about 1/30 seconds. It argues that the results which are solved by spatial local optimization 
method are better than by other gradient-based approaches, and the method can track vehicles on 2D screen. Moreover, it 
is difficult to analyze vehicle motion by using ordinary gradient-based approaches, when sequential images are taken at an 
interval about 1/30 seconds. 
1. INTRODUCTION 
Sequential image processing techniques have made 
progress for motion analysis under the improved 
performances of optical sensor and personal computers. 
3D reconstruction and structure from motion have been 
attempted, and the attempts will develop into computer 
vision or robot vision. For 3D reconstruction and 
structure from motion, stereo sequential images are 
employed. Stereo matching requires displacement 
vectors at feature points. In order to acquire the 
displacement vectors, the extraction techniques of the 
displacement vectors have been investigated. Optical 
flow is usually used as the displacement vector and 
gradient-based approach is common technique for optical 
flow estimation. This approach is based on the 
assumption that the brightness of a point in the image 
remains constant during a short time interval, while the 
location of that point in the image may change due to 
motion. This assumption leads to a single local constraint 
on the optical flow at a certain point in the image (Horn 
and Schunck, 1981). It is, however, ill-posed as the 
constraint constitutes only one equation of two unknowns, 
that is, x-component and y-component of the flow vector. 
Further constraints are, therefore, necessary to solve for 
two unknowns. In order to solve this problem, various 
methods have been proposed. It is said that these 
approaches have large influence upon the result. 
On the other hand, there have been only a few comparative 
studies from the viewpoint of the application to the specific 
and practical motion analysis. This paper compiles the 
gradient-based approaches and compares their performance 
empirically from the point of view of application to vehicle 
motion analysis. 
2. GRADIENT-BASED APPROACH 
2.1 Gradient Constraint Equation 
An equation that relates the change in image brightness at a 
point to the motion of the brightness pattern was derived 
by Horn and Schunck (1981). Let the image brightness at 
the point (x, y) in the image plane at time t be denoted by