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Image Processing for Motion Magnification

Nadaniela Egidi, Josephin Giacomini, Paolo Leonesi, Pierluigi Maponi, Federico Mearelli, Edin Trebovic

TL;DR

This work proposes a numerical technique using the Phase-Based Motion Magnification which analyses the video sequence in the Fourier Domain and rely on the Fourier Shifting Property and describes the mathematical foundation of this method and the corresponding implementation in a numerical algorithm.

Abstract

Motion Magnification (MM) is a collection of relative recent techniques within the realm of Image Processing. The main motivation of introducing these techniques in to support the human visual system to capture relevant displacements of an object of interest; these motions can be in object color and in object location. In fact, the goal is to opportunely process a video sequence to obtain as output a new video in which motions are magnified and visible to the viewer. We propose a numerical technique using the Phase-Based Motion Magnification which analyses the video sequence in the Fourier Domain and rely on the Fourier Shifting Property. We describe the mathematical foundation of this method and the corresponding implementation in a numerical algorithm. We present preliminary experiments, focusing on some basic test made up using synthetic images.

Image Processing for Motion Magnification

TL;DR

This work proposes a numerical technique using the Phase-Based Motion Magnification which analyses the video sequence in the Fourier Domain and rely on the Fourier Shifting Property and describes the mathematical foundation of this method and the corresponding implementation in a numerical algorithm.

Abstract

Motion Magnification (MM) is a collection of relative recent techniques within the realm of Image Processing. The main motivation of introducing these techniques in to support the human visual system to capture relevant displacements of an object of interest; these motions can be in object color and in object location. In fact, the goal is to opportunely process a video sequence to obtain as output a new video in which motions are magnified and visible to the viewer. We propose a numerical technique using the Phase-Based Motion Magnification which analyses the video sequence in the Fourier Domain and rely on the Fourier Shifting Property. We describe the mathematical foundation of this method and the corresponding implementation in a numerical algorithm. We present preliminary experiments, focusing on some basic test made up using synthetic images.

Paper Structure

This paper contains 13 sections, 3 theorems, 22 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Fourier Analysis and Motion Magnification
  3. Fourier Analysis
  4. Motion Magnification
  5. DFT and Motion Magnification
  6. Algorithm implementation
  7. MATLAB code listings
  8. Numerical Results
  9. Multi-frame
  10. Video Sequence
  11. Conclusion
  12. Declaration of interests
  13. Bibliography with BibTeX

Key Result

Theorem 2.1

Let $\mathbf{\delta} \in \mathbb{R}^d$, then:

Figures (6)

  • Figure 1: (a) Original Frame (b) Shifted Frame (c) Magnified Frame ($\alpha = 20$)
  • Figure 2: (a) Original Frame (b) Shifted Frame (c) Magnified Frame ($\alpha = 105$)
  • Figure 3: (a) Original Frame (b) Shifted Frame (c) Magnified Frame ($\alpha = 25$)
  • Figure 4: (a) Original Frame (b) Shifted Frame (c) Magnified Frame ($\alpha = 50$)
  • Figure 5: The figure shows a frame of the video sequence in which we point out the line of intensities pixels value in red, used to exhibit the effect of the amplification.
  • ...and 1 more figures

Theorems & Definitions (8)

  • Definition 2.1
  • Theorem 2.1: Fourier Shift Theorem
  • proof
  • Theorem 2.2
  • proof
  • Definition 3.1
  • Proposition 3.1
  • proof