Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Gradient Vectors and Their Applications01:19

Gradient Vectors and Their Applications

Every point on a topographical map corresponds to a particular elevation, so the landscape can be modeled as a surface whose height depends on horizontal position. From any given location, a hiker may face infinitely many directions, but only one direction produces the fastest possible increase in elevation. This unique route is called the direction of steepest ascent, and in multivariable calculus, it is represented by the gradient vector of the elevation function.The gradient vector points...
Significance of the Gradient Vector01:27

Significance of the Gradient Vector

A surface defined by a function of two variables can be understood by examining how it changes along specific directions. When one variable is held constant, the surface reduces to a curve that reflects variation in the other variable. For example, fixing one variable and moving parallel to a coordinate axis produces a cross-sectional curve. The slope of this curve at a given point represents how the function changes in that particular direction, providing a measure of local steepness.By...
Gradient Fields01:27

Gradient Fields

A gradient field is a vector field derived from a scalar field. A scalar field assigns a single numerical value to every point in space, such as temperature, pressure, or electric potential. The gradient field describes how that value changes from point to point. It gives both the direction of the fastest increase and the rate of change in that direction.For a scalar field f(x, y), the gradient is written as\begin{equation*}\nabla f=\left\langle \jfrac{\partial f}{\partial x},\jfrac{\partial...
Fast Fourier Transform01:10

Fast Fourier Transform

The Fast Fourier Transform (FFT) is a computational algorithm designed to compute the Discrete Fourier Transform (DFT) efficiently. By breaking down the calculations into smaller, manageable sections, the FFT significantly reduces the computational complexity involved. Direct computation of an N-point DFT requires N2 complex multiplications, whereas the FFT algorithm needs only (N/2)log⁡2N multiplications, offering a much faster performance.
The computational efficiency of the FFT becomes...
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Latent alignment in deep learning models for EEG decoding.

Journal of neural engineering·2025
Same author

Introducing SPINE: A Holistic Approach to Synthetic Pulmonary Imaging Evaluation Through End-to-End Data and Model Management.

IEEE open journal of engineering in medicine and biology·2024
Same author

EEGminer: discovering interpretable features of brain activity with learnable filters.

Journal of neural engineering·2024
Same author

A causal perspective on brainwave modeling for brain-computer interfaces.

Journal of neural engineering·2024
Same author

Inverse Image Frequency for Long-Tailed Image Recognition.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2023
Same author

BrainWave-Scattering Net: a lightweight network for EEG-based motor imagery recognition.

Journal of neural engineering·2023

Related Experiment Video

Updated: Jun 13, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Robust FFT-based scale-invariant image registration with image gradients.

Georgios Tzimiropoulos1, Vasileios Argyriou, Stefanos Zafeiriou

  • 1Department of Electrical and Electronic Engineering, Imperial College London, London SW7 2AZ, UK. gt204@imperial.ac.uk

IEEE Transactions on Pattern Analysis and Machine Intelligence
|May 19, 2010
PubMed
Summary

This study introduces a robust FFT-based image registration method. It accurately estimates scale, rotation, and translation for improved image analysis.

More Related Videos

Analyzing Dendritic Morphology in Columns and Layers
08:41

Analyzing Dendritic Morphology in Columns and Layers

Published on: March 23, 2017

Related Experiment Videos

Last Updated: Jun 13, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Analyzing Dendritic Morphology in Columns and Layers
08:41

Analyzing Dendritic Morphology in Columns and Layers

Published on: March 23, 2017

Area of Science:

  • Computer Vision
  • Image Processing
  • Signal Processing

Background:

  • Image registration is crucial for aligning images from different sources or times.
  • Existing FFT-based methods lack robustness and accuracy, especially with image variations.
  • Scale and rotation invariance are key challenges in image registration.

Purpose of the Study:

  • To develop a robust and accurate FFT-based image registration technique.
  • To overcome limitations of previous scale-invariant registration methods.
  • To enable reliable estimation of scale, rotation, and translation in images.

Main Methods:

  • Utilizes Fast Fourier Transform (FFT)-based correlation in log-polar Fourier domain for scale and rotation estimation.
  • Employs normalized gradient correlation in the spatial domain for precise translation recovery.
  • Introduces complex gray-level edge maps for efficient log-polar Fourier representations.

Main Results:

  • The proposed method demonstrates enhanced robustness and accuracy compared to existing techniques.
  • Successfully estimates translations, arbitrary rotations, and scale factors up to 6.
  • Mitigates issues like low-pass characteristics, interpolation errors, border effects, and aliasing.

Conclusions:

  • The novel FFT-based approach provides a robust solution for scale-invariant image registration.
  • The use of complex gray-level edge maps and normalized gradient correlation significantly improves performance.
  • This method offers a reliable tool for various image analysis applications requiring precise registration.