Two-Frame Optical Flow Formulation in an Unwarping Multiresolution Scheme C. Cassisa 1,2 , S. Simoens 1 , and V. Prinet 2 1 Lab. of Fluid Mechanics and Acoustics (LMFA), Ecole Centrale Lyon, France 2 Lab. of Informatics, Automatics and Applied Mathematics (LIAMA), Chinese Academy of Sciences, Beijing, Chine ccassisa@ec-lyon.fr Abstract. In this paper, we propose a new formulation of the Differ- ential Optical Flow Equation (DOFE) between two consecutive images considering spatial and temporal information from both. The displace- ment field is computed in a Markov Random Field (MRF) framework. The solution is done by minimization of the Gibbs energy using a Direct Descent Energy (DDE) algorithm. A hybrid multiresolution approach, combining pyramidal decomposition and two-step multigrid techniques, is used to estimate small and large displacements. A new pyramidal de- composition method without warping process between pyramid levels is introduced. The experiments carried out on benchmark dataset se- quences show the effectiveness of the new optical flow formulation using the proposed unwarped pyramid decomposition schema. Keywords: Optical flow estimation, RMF minimization, Multiresolu- tion technique. 1 Introduction Motion estimation has always been a major activity in computer vision commu- nity, with application in tracking, stereo matching, rigid and elastic motions, fluid propagation... Since early 80’s, it has been well studied and many approaches have been proposed. But it is still remaining challenging to this date. For details on existing algorithms, you can refer to Barron’s et al. [4]. Differential Optical Flow Equation (DOFE), introduced by Horn & Schunck [9], has proved to be very powerful in motion estimation. The DOFE is based on the hypothesis of illumination constancy over a small period of time. At the beginning, approaches were defined on a centered formulation of the DOFE that needs at least three successive images ([9,4]). Other approaches studied the case of only two successive frames and proposed a non-centered DOFE based on the first image ([5]) or on the second one ([11,13]). Recently the work of Alvarez et al. [1] imagines an intermediate image at the half way from the first to the second image and uses a symmetrical formulation of DOFE based on two images. However, this method needs many interpolation and warping steps that can affect the quality of the estimation. E. Bayro-Corrochano and J.-O. Eklundh (Eds.): CIARP 2009, LNCS 5856, pp. 790–797, 2009. c  Springer-Verlag Berlin Heidelberg 2009