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Everything about Convolution
Integral expressing the amount of overlap of one function as it is shifted over another
In mathematics, convolution is a mathematical operation on two functions and that produces a third function, as the integral of the product of the two functions after one is reflected about the y-axis and shifted. The term convolution refers to both the resulting function and to the process of computing it. The integral is evaluated for all values of shift, producing the convolution function. The choice of which function is reflected and shifted before the integral does not change the integral result. Graphically, it expresses how the 'shape' of one function is modified by the other. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: ConvolutionA 5-minute orientation
- Skim a recent paper: UniFormer: Unifying Convolution and Self-Attention for Visual RecognitionInfluential work since 2022
- Pick up a classic book: Generalized gamma convolutions and related classes of distributions and densitiesThe most-reprinted book on the subject
- Read the landmark paper: DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFsCited 18,996 times
- Go sideways: Convolution theoremA closely related topic
- Go sideways: Fourier transformA closely related topic
📖 Definitions
Noun A twist or fold.
Noun Any of the folds on the surface of the brain.
Noun The shape of something rotating; a vortex.
Noun The state or condition of being convoluted.
🏆 Landmark papers (most cited)
DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs
Cubic convolution interpolation for digital image processing
Remaining useful life estimation in prognostics using deep convolution neural networks
Invariant Scattering Convolution Networks
Improving the full spectrum fitting method: accurate convolution with Gauss–Hermite functions
DEA-Net: Single Image Dehazing Based on Detail-Enhanced Convolution and Content-Guided Attention
Selection of a convolution function for Fourier inversion using gridding (computerised tomography application)
Hierarchical adaptive deep convolution neural network and its application to bearing fault diagnosis
🆕 Influential since 2022
UniFormer: Unifying Convolution and Self-Attention for Visual Recognition
LiConvFormer: A lightweight fault diagnosis framework using separable multiscale convolution and broadcast self-attention
ConvUNeXt: An efficient convolution neural network for medical image segmentation
Intelligent Mechanical Fault Diagnosis Using Multisensor Fusion and Convolution Neural Network
CTformer: convolution-free Token2Token dilated vision transformer for low-dose CT denoising
📚 Books worth reading
- 📕Generalized gamma convolutions and related classes of distributions and densitiesLennart Bondesson · 1992
The convolution transformI. I. Hirschman · 1955
Convolution and Fourier transforms for communications engineersR. D. A. Maurice · 1976- 📕The convolution productW. Kecs · 1899
- 📕Convolutional representations of commutants and multipliersNikolai Bozhinov · 1988
- 📕Recent advances in visualizing 3D flow with LICVictoria L. Interrante · 1998
Rankin-Selberg convolutions for SO2l+1 x GLnDavid Soudry · 1993
Convolutional codesPh Piret · 1988
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Convolution theorem In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution of two functions (or signals) is the…
- Fourier transform In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input and outputs another function that describes the extent…
- Distribution (mathematical analysis) In mathematical analysis, distributions are a type of generalized function that makes it possible to differentiate functions whose derivatives do not exist…
- Cross-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…
- Dirac delta function In mathematical analysis, the Dirac delta function (or 𝜹 distribution), also known as the unit impulse, is a generalized function on the real numbers…
- Poisson summation formula In mathematics, the Poisson summation formula is an equation that relates the Fourier series coefficients of the periodic summation of a function to values…
- Hilbert transform In mathematics and signal processing, the Hilbert transform is a specific singular integral that takes a function, u(t) of a real variable and produces…
- Fourier series A Fourier series (/ˈfʊrieɪ, -iər/) is a series expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example…