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Everything about Cross-correlation
Covariance and correlation
In signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recognition, single particle analysis, electron tomography, averaging, cryptanalysis, and neurophysiology. The cross-correlation is similar in nature to the convolution of two functions. In an autocorrelation, which is the cross-correlation of a signal with itself, there will always be a peak at a lag of zero, and its size will be the signal energy. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Cross-correlationA 5-minute orientation
- Skim a recent paper: Generalizable Heterogeneous Federated Cross-Correlation and Instance Similarity LearningInfluential work since 2022
- Pick up a classic book: Spatial cross-correlation of Antarctic Sea ice and seabed topographyThe most-reprinted book on the subject
- Read the landmark paper: Symmetric diffeomorphic image registration with cross-correlation: Evaluating automated labeling of elderly and neurodegenerative brainCited 5,928 times
- Go sideways: Cross-covarianceA closely related topic
- Go sideways: AutocovarianceA closely related topic
📖 Definitions
Noun A notion used across various fields of scientific study that shows the relation between members of two or more groups of data.
🏆 Landmark papers (most cited)
Symmetric diffeomorphic image registration with cross-correlation: Evaluating automated labeling of elderly and neurodegenerative brain
DCCA cross-correlation coefficient: Quantifying level of cross-correlation
Fast Normalized Cross-Correlation
A critique of cross-lagged correlation.
Two‐photon image correlation spectroscopy and image cross‐correlation spectroscopy
Cross-correlation and maximum-likelihood analysis: a new approach to combining cross-correlation functions
Noise cross-correlation sensitivity kernels
Correlation in instruments: cross correlation flowmeters
🆕 Influential since 2022
Generalizable Heterogeneous Federated Cross-Correlation and Instance Similarity Learning
Temporal Cross-Layer Correlation Mining for Action Recognition
Spin cross-correlation experiments in an electron entangler
Self-Supervised Correlation Learning for Cross-Modal Retrieval
The Curious Case of the Cross-Sectional Correlation
📚 Books worth reading
- 📕Spatial cross-correlation of Antarctic Sea ice and seabed topographyRichard D. De Veaux · 1990
- 📕The electromagnetic scattering of broad bandwidth random signals by a discrete targetJohn K. Schindler · 1967
- 📕Optimizing the Zel'dovich approximationAdrian Melott · 1995
- 📕Stability, reliability, and cross-mode correlations of tests in a recommended 8-minute performance assessment batteryR. L. Wilkes · 1986
- 📕Fuzzy interference enhanced information recovery from digital PIV using cross-correlation combined with particle trackingMark P. Wernet · 1995
- 📕El ano nuevo en Costa RicaJennie Frazier · 1995
- 📕Reduction and analysis of seasons 15 and 16 (1991-1992), Pioneer Venus radio occultation data and correlative studies with observations of the near infra-red emission of VenusJon M. Jenkins · 1995
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Cross-covariance In probability and statistics, given two stochastic processes {Xt} and {Yt}, the cross-covariance is a function that gives the covariance of one process…
- Autocovariance In probability theory and statistics, given a stochastic process, the autocovariance is a function that gives the covariance of the process with itself…
- Autocorrelation Autocorrelation, sometimes known as serial correlation in the discrete time case, measures the correlation of a signal with a delayed copy of itself. Essentiall…
- Stationary process In mathematics and statistics, a stationary process (also called a strict/strictly stationary process or strong/strongly stationary process) is a stochastic…
- Feynman–Kac formula The Feynman–Kac formula, named after Richard Feynman and Mark Kac, establishes a link between parabolic partial differential equations and stochastic processes…
- Covariance matrix In probability theory and statistics, a covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance…
- Convolution In mathematics (in particular, functional analysis), convolution is a mathematical operation on two functions f and g that produces a third function f∗g…
- Wigner distribution function The Wigner distribution function (WDF) is used in signal processing as a transform in time-frequency analysis. The WDF was first proposed in physics to…