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Laplacian Pyramid

introduced 1983 31 papers tagged archive 2025-07-28

archive 2025-07-28 Description, source and code snippet are the archive's method entry.

A Laplacian Pyramid is a linear invertible image representation consisting of a set of band-pass images spaced an octave apart, plus a low-frequency residual. Formally, let d(.) be a downsampling operation that blurs and decimates a j ×j image I so that d(I) is a new image of size j/2 ×j/2. Also, let u(.) be an upsampling operator which smooths and expands I to be twice the size, so u(I) is a new image of size 2j ×2j. We first build a Gaussian pyramid G(I) = [I₀, I₁, …, I_K], where I₀ = I and Iₖ is k repeated application of d(.) to I. K is the number of levels in the pyramid selected so that the final level has a minimal spatial extent (≤8 ×8 pixels).

The coefficients hₖ at each level k of the Laplacian pyramid L(I) are constructed by taking the difference between adjacent levels in the Gaussian pyramid, upsampling the smaller one with u(.) so that the sizes are compatible:

hₖ = ℒₖ(I) = Gₖ(I) − u(Gₖ₊₁(I)) = Iₖ − u(Iₖ₊₁)

Intuitively, each level captures the image structure present at a particular scale. The final level of the Laplacian pyramid h_K is not a difference image, but a low-frequency residual equal to the final Gaussian pyramid level, i.e. h_K = I_K. Reconstruction from a Laplacian pyramid coefficients [h₁, …, h_K] is performed using the backward recurrence:

Iₖ = u(Iₖ₊₁) + hₖ

which is started with I_K = h_K and the reconstructed image being I = Iₒ. In other words, starting at the coarsest level, we repeatedly upsample and add the difference image h at the next finer level until we return to the full-resolution image. Source: LAPGAN

Image : Design of FIR Filters for Fast Multiscale Directional Filter Banks

Papers archive 2025-07-28

30 shown of 31, newest first. Repository counts are the archive's code-links table. A Syntology line states what Syntology ran from that paper's harvested code; it is per sample and not a correctness claim.

Tasks archive 2025-07-28

20 shown of 59 tasks the archive attaches to papers tagged with this method, by distinct papers. A task without a page in the catalog is plain text.

TaskPapers
Image Generation5
Image-to-Image Translation3
Medical Image Analysis3
Translation3
Depth Estimation2
Image Registration2
Image Segmentation2
Semantic Segmentation2
Style Transfer2
Super-Resolution2
Vocal Bursts Intensity Prediction2
Action Classification1
Action Recognition1
Anomaly Segmentation1
Autonomous Navigation1
BIG-bench Machine Learning1
Computational Efficiency1
Decoder1
Deep Learning1
Denoising1

Usage over time archive 2025-07-28

Papers per year tagged with Laplacian Pyramid: 2015 to 2025, peak 9 9 0 2015: 1 paper 2015 2016: 0 papers 2016 2017: 0 papers 2017 2018: 2 papers 2018 2019: 3 papers 2019 2020: 6 papers 2020 2021: 3 papers 2021 2022: 1 paper 2022 2023: 0 papers 2023 2024: 6 papers 2024 2025: 9 papers 2025
Papers per year the archive tags with this method, by the paper's archive date (31 dated). Bars are counts, not a trend claim.

Components: the archive holds no method-to-method composition, so PwC's Components table cannot be rebuilt; the Papers list carries no Results column for the same reason (the archive does not join its leaderboard rows to method tags).

Categories archive 2025-07-28

Image Representations

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