SIViP DOI 10.1007/s11760-015-0772-6 ORIGINAL PAPER Optical flow estimation based on the structure–texture image decomposition I. Bellamine 1 · H. Tairi 1 Received: 4 February 2014 / Revised: 22 March 2015 / Accepted: 12 April 2015 © Springer-Verlag London 2015 Abstract Optical flow approaches for motion estimation calculate vector fields which determine the apparent veloc- ities of objects in time-varying image sequences. Image motion estimation is a fundamental issue in low-level vision and is used in many applications in image sequence process- ing, such as robot navigation, object tracking, image coding and structure reconstruction. The accuracy of optical flow estimation algorithms has been improving steadily as evi- denced by results on the Middlebury optical flow benchmark. Actually, several methods are used to estimate the optical flow, but a good compromise between computational cost and accuracy is hard to achieve. This work presents a combined local–global total variation approach with structure–texture image decomposition. The combination is used to control the propagation phenomena and to gain robustness against illumination changes, influence of noise on the results and sensitivity to outliers. The resulted method is able to com- pute larger displacements in a reasonable time. Keywords Motion estimation · Structure–texture image decomposition · Optical flow · Local–global total variation approach B I. Bellamine insafbellamine20@gmail.com H. Tairi htairi@yahoo.fr 1 LIIAN, Department of Computer Science, Faculty of Science Dhar El Mahraz, University Sidi Mohamed Ben Abdellah, BP 1796, Fez, Morocco 1 Introduction Optical flow is the displacement of each image pixels in an image sequence. Motion estimation plays an important role in computer vision applications, such as video surveillance, traffic monitoring, recognition of gestures, analysis of sport events, mobile robotics and study of the objects’ behavior (people, animals, vehicles, etc ...). In the literature, the differential methods belong to the most widely used techniques for optic flow estimation in image sequences. They are based on the computation of spatial and temporal image derivatives. Differential tech- niques can be classified into global strategies which attempt to minimize global energy functional, and local methods that may optimize some local energy-like expression. Examples of the first category comprise the classic method of Horn and Schunck [1] and discontinuity-preserving variants such as [2]. Local methods include the Lucas–Kanade method [3], the structure tensor approach of Bigün et al. [4] and its space- variant version by Nagel and Gehrke [5], but also techniques using second-order derivatives such as [6]. Global methods yield flow fields with 100% density, but are experimentally known to be more sensitive to noise [7, 8]. Local methods, on the other hand, may offer relatively high robustness under noise, but do not give dense flow fields. In [9], a variational approach results after combining the method of Lucas–Kanade (LK) and Horn and Schunck (HS): E CLG =    λ ·   region w · r (u ,v) 2   ‖∇u ‖ 2 +‖∇v‖ 2   (1) (CLG = Combined local–global) E CLG is the functional error to be minimized, w represents the weighting factor, λ is data fidelity factor,  refers to the 123