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Title
Proceedings International Workshop on Mobile Mapping Technology
Author
Li, Rongxing

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