Horn–Schunck Optical Flow (Serial + OpenMP, OpenCV)

Overview

This project implements the Horn–Schunck (HS) dense optical flow algorithm:

• Serial version (single-threaded)
• Parallel version using OpenMP (Jacobi double buffering)

Given two consecutive grayscale frames, HS estimates a per-pixel motion vector field (u, v).

Algorithm (intuitive)

HS assumes two things:

1. Brightness constancy: the same point keeps the same intensity between frames.
2. Smooth flow: neighboring pixels move similarly.

It balances these by minimizing an energy made of:

• A data term (enforces brightness constancy using image derivatives Ix, Iy, It)
• A smoothness term (enforces spatial smoothness, controlled by α)

Iterative update:

• Compute spatial derivatives Ix, Iy and temporal derivative It.
• At each iteration, average neighbors of u and v (smoothing), then correct using Ix, Iy, It.
• Repeat for a fixed number of iterations.

Update schemes:

• Serial uses in-place Gauss–Seidel (faster per iteration).
• Parallel uses Jacobi double buffering (u_next/v_next from previous u/v, then swap) to avoid races and be deterministic.

Requirements

• C++17
• CMake 3.16+
• OpenCV (core, imgproc, highgui)
• OpenMP (for the parallel build)

Run

• Ensure you have two images in data directory, e.g., data/rm1.jpg and data/rm2.jpg

•   chmod +x run.sh
    ./run.sh

The program will:

• Print serial and parallel timing
• Save visualizations to:
  • output/flow_serial.png
  • output/flow_parallel.png
• Open windows showing both flows (requires a GUI/X11 session)

Headless tip: If imshow fails on a server, comment out the imshow/waitKey lines or run with a virtual display.

Tuning

• alpha (regularization): higher = smoother flow, lower = more detail but noisier.
  • Typical range: 0.1 to 1.5 (default here: 0.5)
• iterations: more = better convergence but slower.
  • Typical range: 50–500 (default here: 100)

Matching results:

• If you want the serial and parallel outputs to be identical, use Jacobi in serial as well (double buffering). Gauss–Seidel may converge faster per iteration but will differ slightly.

Performance tips

• Set OMP_NUM_THREADS to control threads, e.g.:
  • export OMP_NUM_THREADS=$(nproc)
• Build Release for speed.
• For very large images, consider 8-neighbor averaging or a separable blur for the smoothing step.

Files

• main.cpp: I/O, timing, visualization
• include/opt_flow_serial.hpp, include/opt_flow_parallel.hpp: APIs
• src/opt_flow_serial.cpp: serial HS
• src/opt_flow_parallel.cpp: OpenMP HS (Jacobi double buffering)

Reference

• B. K. P. Horn and B. G. Schunck, “Determining Optical