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Investigating Optical Flow Computation: From Local Methods to a Multiresolution Horn-Schunck Implementation with Bilinear Interpolation

Haytham Ziani

TL;DR

An optical flow study balancing local and global cues under brightness constancy (via $I_x u + I_y v + I_t = 0$) introduces a multiresolution Horn–Schunck (MR-HS) framework that uses bilinear interpolation for flow prolongation and image warping to handle large displacements. The approach builds a Gaussian pyramid, upsampling flow with bilinear interpolation and warping images between levels, and refines the flow with Horn–Schunck iterations at each level. On the Sintel dataset, MR-HS reduces both Average Angular Error (AAE) and End-Point Error (EPE) relative to standard HS, demonstrating improved robustness in challenging scenes with large motions. The work highlights the synergy of local and global strategies and suggests avenues for future improvements via total variation regularization and hybrid methods for real-world motion analysis.

Abstract

This paper presents an applied analysis of local and global methods, with a focus on the Horn-Schunck algorithm for optical flow computation. We explore the theoretical and practical aspects of local approaches, such as the Lucas-Kanade method, and global techniques such as Horn-Schunck. Additionally, we implement a multiresolution version of the Horn-Schunck algorithm, using bilinear interpolation and prolongation to improve accuracy and convergence. The study investigates the effectiveness of these combined strategies in estimating motion between frames, particularly under varying image conditions.

Investigating Optical Flow Computation: From Local Methods to a Multiresolution Horn-Schunck Implementation with Bilinear Interpolation

TL;DR

An optical flow study balancing local and global cues under brightness constancy (via ) introduces a multiresolution Horn–Schunck (MR-HS) framework that uses bilinear interpolation for flow prolongation and image warping to handle large displacements. The approach builds a Gaussian pyramid, upsampling flow with bilinear interpolation and warping images between levels, and refines the flow with Horn–Schunck iterations at each level. On the Sintel dataset, MR-HS reduces both Average Angular Error (AAE) and End-Point Error (EPE) relative to standard HS, demonstrating improved robustness in challenging scenes with large motions. The work highlights the synergy of local and global strategies and suggests avenues for future improvements via total variation regularization and hybrid methods for real-world motion analysis.

Abstract

This paper presents an applied analysis of local and global methods, with a focus on the Horn-Schunck algorithm for optical flow computation. We explore the theoretical and practical aspects of local approaches, such as the Lucas-Kanade method, and global techniques such as Horn-Schunck. Additionally, we implement a multiresolution version of the Horn-Schunck algorithm, using bilinear interpolation and prolongation to improve accuracy and convergence. The study investigates the effectiveness of these combined strategies in estimating motion between frames, particularly under varying image conditions.

Paper Structure

This paper contains 10 sections, 13 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Sparse Methods
  3. Dense Methods
  4. Horn-Schunck Method
  5. Multiresolution Horn-Schunck
  6. Mathematical Formulation of Bilinear Interpolation
  7. Application in Flow Prolongation
  8. Application in Image Warping
  9. Experimental Results on the Sintel Dataset
  10. Conclusion

Figures (1)

  • Figure 1: Comparison of optical flow fields across four Sintel scenes (alley_1 (frames 1, 2), bamboo_2 (28, 29), market_2 (41, 42), and mountain_1(35, 36)) using input frames, ground truth, Horn-Schunck (HS), and multi-resolution Horn-Schunck (MR-HS).