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Everything about Scale space implementation

In the areas of computer vision, image analysis and signal processing, the notion of scale-space representation is used for processing measurement data at multiple scales, and specifically enhance or suppress image features over different ranges of scale. A special type of scale-space representation is provided by the Gaussian scale space, where the image data in N dimensions is subjected to smoothing by Gaussian convolution. Most of the theory for Gaussian scale space deals with continuous images, whereas one when implementing this theory will have to face the fact that most measurement data are discrete. Hence, the theoretical problem arises concerning how to discretize the continuous theory while either preserving or well approximating the desirable theoretical properties that lead to the choice of the Gaussian kernel. This article describes basic approaches for this that have been developed in the literature, see also for an in-depth treatment regarding the topic of approximating the Gaussian smoothing operation and the Gaussian derivative computations in scale-space theory, and for a complementary treatment regarding hybrid discretization methods. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Scale space implementationA 5-minute orientation
  2. Skim a recent paper: A two‐dimensional, reach‐scale implementation of space‐time image velocimetry (STIV) and comparison to particle image velocimetry (PIV)Influential work since 2022
  3. Pick up a classic book: Computer Engineering and TechnologyThe most-reprinted book on the subject
  4. Read the landmark paper: Real-time implementation of fast discriminative scale space tracking algorithmCited 18 times
  5. Go sideways: Multi-scale approachesA closely related topic
  6. Go sideways: Stochastic approximationA closely related topic

📖 Definitions

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🗂️ The subject at a glance

  1. Statement of the problem
  2. Separability
  3. The sampled Gaussian kernel
  4. The discrete Gaussian kernel
  5. Recursive filters
  6. Finite-impulse-response (FIR) smoothers
  7. Real-time implementation within pyramids and discrete approximation of scale-normalized derivatives
  8. Other multi-scale approaches

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics