Extended Dynamic Programming and Fast Multidimensional Search Algorithm for Energy Minization in Stereo and Motion

TL;DR

This paper introduces an extended dynamic programming method with a recursive search strategy that significantly accelerates energy minimization for stereo and motion correspondence problems, especially in high-dimensional disparity spaces.

Contribution

The paper proposes a novel extended dynamic programming approach combined with a recursive minimum search that improves speed and accuracy in energy minimization for stereo and motion analysis.

Findings

Achieves faster energy minimization using RMS in high-dimensional disparity spaces.

Provides a lower energy bound than graph cuts on stereo and motion problems.

Enables parallel implementation on GPU platforms.

Abstract

This paper presents a novel extended dynamic programming approach for energy minimization (EDP) to solve the correspondence problem for stereo and motion. A significant speedup is achieved using a recursive minimum search strategy (RMS). The mentioned speedup is particularly important if the disparity space is 2D as well as 3D. The proposed RMS can also be applied in the well-known dynamic programming (DP) approach for stereo and motion. In this case, the general 2D problem of the global discrete energy minimization is reduced to several mutually independent sub-problems of the one-dimensional minimization. The EDP method is used when the approximation of the general 2D discrete energy minimization problem is considered. Then the RMS algorithm is an essential part of the EDP method. Using the EDP algorithm we obtain a lower energy bound than the graph cuts (GC) expansion technique on stereo and motion problems. The proposed calculation scheme possesses natural parallelism and can be realized on graphics processing unit (GPU) platforms, and can be potentially restricted further by the number of scanlines in the image plane. Furthermore, the RMS and EDP methods can be used in any optimization problem where the objective function meets specific conditions in the smoothness term.