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II-LK – A Real-Time Implementation for Sparse
Optical Flow
Tobias Senst, Volker Eiselein, and Thomas Sikora
Technische Universit¨at Berlin
Communication Systems Group
{senst,eiselein,sikora}@nue.tu-berlin.de
http://www.nue.tu-berlin.de
Abstract. In this paper we present an approach to speed up the com-
putation of sparse optical flow fields by means of integral images and
provide implementation details. Proposing a modification of the Lucas-
Kanade energy functional allows us to use integral images and thus to
speed up the method notably while affecting only slightly the quality of
the computed optical flow. The approach is combined with an efficient
scanline algorithm to reduce the computation of integral images to those
areas where there are features to be tracked. The proposed method can
speed up current surveillance algorithms used for scene description and
crowd analysis.
Keywords: Lucas-Kanade, optical flow, fast implementation, integral
images, optimization, real-time.
1 Introduction
Computation of optical flow is a common topic in the computer vision community
whose applications range from motion estimation to point tracking. There are
many different approaches to compute optical flow, among them the classical
Lucas-Kanade method [12].
Introduced in 1981, it still has many applications ([1]) and is a popular method
to compute the movement of sparse feature points from one video frame to the
next. This is often used for tracking objects or persons directly as e.g. in [11]
or [9]. As another approach based on the idea of individual motion, [5] builds
trajectories from sparse feature tracks which are afterwards clustered to obtain
the number of persons in a scene. Similarly, yet in a different context, crowds
are described in [14] by their pointwise motion which yields information on their
activity and on abnormal events. Other applications are 3D pose and camera
parameter estimation as e.g. in [10]. The Lucas-Kanade method also inspired
other more recent algorithms as e.g. [7], [6] or [3].
Formulating brightness constancy between two points in consecutive images
leads to an equation in two unknowns and cannot be solved as such. This is
commonly known as the aperture problem. As a solution, the Lucas-Kanade
method assumes constant flow for a window around the current pixel and solves
A. Campilho and M. Kamel (Eds.): ICIAR 2010, Part I, LNCS 6111, pp. 240–249, 2010.
c
Springer-Verlag Berlin Heidelberg 2010