Matlab programmed method for the optical flow estimation based on the integral image

Abstract

The Optical Flow computation is the estimation of the apparent displacement of the object on an image sequence (actual image and next image). There are different methods for Optical Flow estimation, standing out exhaustive methods and differential methods. Differential Methods propose a model that considers the error in the Optical flow estimation. This model is minimized solving the Euler-Lagrange equations of linearized versions of the functional terms like in the differential model developed by Horn & Schunck. The exhaustive methods take a point and his environment in the actual image and search for the more similar in the next image like in the Steinbücker model of Exhaustive Search. In this paper is presented the implementation of the differential methods of Horn & Schunck and the Steinbücker's exhaustive “variational” method. Additionally it is posed a new method that combines the differential method and the exhaustive one. With the use of the integral image and a cost volume it manages to obtain a processing time reduction of the exhaustive methods close to a 98% in comparison to a similar implementation in Matlab. Through the implementation of the combined methods it is possible to reach below 15 degrees in average angular error (AAE).

The Optical Flow computation is the estimation of the apparent displacement of the object on an image sequence (actual image and next image). There are different methods for Optical Flow estimation, standing out exhaustive methods and differential methods. Differential Methods propose a model that considers the error in the Optical flow estimation. This model is minimized solving the Euler-Lagrange equations of linearized versions of the functional terms like in the differential model developed by Horn & Schunck. The exhaustive methods take a point and his environment in the actual image and search for the more similar in the next image like in the Steinbücker model of Exhaustive Search. In this paper is presented the implementation of the differential methods of Horn & Schunck and the Steinbücker's exhaustive “variational” method. Additionally it is posed a new method that combines the differential method and the exhaustive one. With the use of the integral image and a cost volume it manages to obtain a processing time reduction of the exhaustive methods close to a 98% in comparison to a similar implementation in Matlab. Through the implementation of the combined methods it is possible to reach below 15 degrees in average angular error (AAE).