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A Recursive Pyramidal Algorithm for Solving the Image Registration Problem

Stefan Dirnstorfer

TL;DR

The paper reframes image registration as estimating a displacement field $d$ that aligns two images by minimizing $\| f_1 - T(f_2, d) \|$ with $T(f,d)(x)=f(x-d(x))$ under a velocity bound $M$ and a continuity bound $\lambda$. It introduces a recursive, multi-scale scheme that first computes a coarse disparity on downsampled images and then refines it with a CNN-predicted residual, summing the two components to obtain the final $d$; recursion ends when images are too small, maintaining the slope bound. The approach is demonstrated on stereopsis with a single CNN operating on $19\times15$ windows and about $5.5\times 10^5$ parameters, trained on only 74 Middlebury pairs, achieving competitive performance on continuous regions while highlighting limitations near occlusions. The contribution emphasizes simplicity, data efficiency, and a lightweight implementation that can serve as a foundation for broader image-registration tasks and multi-sensor extensions, especially where data, time, or code constraints are critical.

Abstract

The problem of image registration is finding a transformation that aligns two images, such that the corresponding points are in the same location. This paper introduces a simple, end-to-end trainable algorithm that is implementable in a few lines of Python code. The approach is shown to work with very little training data and training time, while achieving accurate results in some settings. An example application to stereo vision was trained from 74 images on a 19x15 input window. With just a dozen lines of Python code this algorithm excels in brevity and may serve as a good start in related scenarios with limitations to training data, training time or code complexity.

A Recursive Pyramidal Algorithm for Solving the Image Registration Problem

TL;DR

The paper reframes image registration as estimating a displacement field that aligns two images by minimizing with under a velocity bound and a continuity bound . It introduces a recursive, multi-scale scheme that first computes a coarse disparity on downsampled images and then refines it with a CNN-predicted residual, summing the two components to obtain the final ; recursion ends when images are too small, maintaining the slope bound. The approach is demonstrated on stereopsis with a single CNN operating on windows and about parameters, trained on only 74 Middlebury pairs, achieving competitive performance on continuous regions while highlighting limitations near occlusions. The contribution emphasizes simplicity, data efficiency, and a lightweight implementation that can serve as a foundation for broader image-registration tasks and multi-sensor extensions, especially where data, time, or code constraints are critical.

Abstract

The problem of image registration is finding a transformation that aligns two images, such that the corresponding points are in the same location. This paper introduces a simple, end-to-end trainable algorithm that is implementable in a few lines of Python code. The approach is shown to work with very little training data and training time, while achieving accurate results in some settings. An example application to stereo vision was trained from 74 images on a 19x15 input window. With just a dozen lines of Python code this algorithm excels in brevity and may serve as a good start in related scenarios with limitations to training data, training time or code complexity.

Paper Structure

This paper contains 15 sections, 10 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Problem statement
  3. Objective
  4. Constraints
  5. The algorithm
  6. Schematic view of the algorithm
  7. Accuracy Considerations
  8. Implementation for Image Data
  9. Helper Functions
  10. Training
  11. Application to Stereopsis
  12. The CNN Model
  13. Validation Data
  14. Test Data
  15. Conclusion

Figures (3)

  • Figure 1: Data flow in the recursive scheme. The algorithm works on scaled down versions of the input images and then corrects the result.
  • Figure 2: Left and right camera view on two scenes. The ground truth was not used during training. Results in column four.
  • Figure 3: Left and right camera view, followed by the inferred disparity. The algorithm measures the disparities of extended landmarks precisely, but performs poorly on discontinuous geometries where monocular inference is required.