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

Calibration Curves: Correlation Coefficient01:10

Calibration Curves: Correlation Coefficient

In a linear calibration curve, there is a value called the calibration coefficient, denoted by 'r,' which measures the strength and the direction of association between two variables. The correlation coefficient value ranges from −1 to +1. A value of +1 indicates a perfect positive linear correlation, −1 denotes a perfect negative correlation, and 0 implies no correlation between the two variables. A positive correlation value establishes that as one variable increases, the other increases, and...
Correlation and Regression00:53

Correlation and Regression

In statistics, correlation describes the degree of association between two variables. In the subfield of linear regression, correlation is mathematically expressed by the correlation coefficient, which describes the strength and direction of the relationship between two variables. The coefficient is symbolically represented by 'r' and ranges from -1 to +1. A positive value indicates a positive correlation where the two variables move in the same direction. A negative value suggests a negative...
2D NMR: Overview of Heteronuclear Correlation Techniques01:18

2D NMR: Overview of Heteronuclear Correlation Techniques

Heteronuclear correlation spectroscopy is an analytical technique that investigates the coupling between different types of nuclei, often a proton and an X-nucleus, such as carbon-13 or nitrogen-15. This method is commonly used in nuclear magnetic resonance (NMR) spectroscopy to gain insights into complex chemical compounds' structural and compositional aspects. A typical heteronuclear correlation spectrum displays X-nucleus chemical shifts on one axis and a proton spectrum on the other axis.
Applications of Integration to Probability Density Functions01:27

Applications of Integration to Probability Density Functions

Continuous probability distributions are used to model random variables that can take on any real value within a specified range. These variables do not take on isolated or countable values but rather exist on a continuum. For example, the height of an individual can be measured with increasing precision—such as 163.5 or 165.25 centimeters—demonstrating that height is a continuous random variable.The behavior of such variables is described using a probability density function (PDF), which...
Constraints and Statical Determinacy01:26

Constraints and Statical Determinacy

In structural engineering, the equilibrium of a system is not only determined by its equations of equilibrium but also with the help of constraints. Constraints refer to restrictions on the motion of a system. The proper combinations of constraints can minimize the total number of constraints needed to maintain a system in mechanical equilibrium. When this happens, the system is said to be statically determinate. For such systems, the unknown reaction supports can be estimated using equilibrium...
Coefficient of Correlation01:12

Coefficient of Correlation

The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable x and the dependent variable y.
If you suspect a linear relationship between x and y, then r can measure how strong the linear relationship is.
What the VALUE of r tells us:
The value of r is always between –1 and +1: –1 ≤ r ≤ 1.
The size of the correlation r indicates the strength of the linear...

You might also read

Related Articles

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

Sort by
Same journal

UniNDM: A Unified Noise-driven Detection and Mitigation Framework Against Sexual Content in Text-to-Image Generation.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

Prototype-Anchored Generalized Manifold Regression for Unknown-Domain Object Detection.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

STPP: Efficient and Progressive Structured Pruning Via Enhanced Sparsification Paradigm.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

Incomplete Multimodal Probability Flow Recovery for Emotion Recognition.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

MIDAS: Mutual Information Disentanglement With Uncertainty-Aware Fusion for Incomplete Multimodal Sentiment Analysis.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

How Relation Enrichment Improves Clustering Ensemble Performance: A Second Order Induced Relation View.

IEEE transactions on pattern analysis and machine intelligence·2026

Related Experiment Video

Updated: May 29, 2026

Multimodal Cross-Device and Marker-Free Co-Registration of Preclinical Imaging Modalities
07:13

Multimodal Cross-Device and Marker-Free Co-Registration of Preclinical Imaging Modalities

Published on: October 27, 2023

Bounds on (deterministic) correlation functions with application to registration.

V N Dvornychenko1

  • 1Ford Aerospace and Communications Corporation, Newport Beach, CA 92660; Electro-Mechanical Division, Northrop Corporation, Anaheim, CA 92801.

IEEE Transactions on Pattern Analysis and Machine Intelligence
|August 27, 2011
PubMed
Summary

This study reveals bounds on L2 function correlations, showing deterministic autocorrelations exhibit cosine-like behavior with specific discontinuities. These findings enhance image registration algorithms.

More Related Videos

Four-Dimensional CT Analysis Using Sequential 3D-3D Registration
05:05

Four-Dimensional CT Analysis Using Sequential 3D-3D Registration

Published on: November 23, 2019

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

Related Experiment Videos

Last Updated: May 29, 2026

Multimodal Cross-Device and Marker-Free Co-Registration of Preclinical Imaging Modalities
07:13

Multimodal Cross-Device and Marker-Free Co-Registration of Preclinical Imaging Modalities

Published on: October 27, 2023

Four-Dimensional CT Analysis Using Sequential 3D-3D Registration
05:05

Four-Dimensional CT Analysis Using Sequential 3D-3D Registration

Published on: November 23, 2019

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

Area of Science:

  • Signal Processing
  • Image Analysis
  • Mathematical Analysis

Background:

  • Correlation functions are crucial for image registration.
  • Existing methods often rely on L2 functions, whose correlation properties are not fully exploited.
  • Understanding the behavior of deterministic correlations is key to improving registration accuracy.

Purpose of the Study:

  • To investigate the bounds and behavior of auto/cross-correlations for L2 functions.
  • To demonstrate the practical advantages of these bounds in correlation-based applications.
  • To develop improved registration algorithms based on novel correlation insights.

Main Methods:

  • Analysis of L2 function auto/cross-correlations.
  • Derivation of bounds for deterministic correlation functions.
  • Characterization of autocorrelation envelopes and their discontinuities.
  • Development of new inequalities based on these findings.

Main Results:

  • Established bounds for L2 function correlations, applicable to deterministic registration functions.
  • Demonstrated that deterministic autocorrelation envelopes exhibit cosine-like behavior.
  • Identified jump discontinuities in autocorrelations at specific normalized relative displacements (reciprocal of integers).
  • Derived several extending inequalities.

Conclusions:

  • The identified bounds and behaviors of deterministic correlations offer significant advantages for registration.
  • The cosine-like behavior with discontinuities provides a new framework for understanding correlation properties.
  • The derived inequalities can be directly applied to create more accurate and efficient image registration algorithms.