# Feature-Centered First Order Structure Tensor Scale-Space in 2D and 3D

arXiv: https://arxiv.org/abs/2409.13389 · HTML: https://mlsanity.com/paper/2409.13389/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 42 references that are in the map.
- First posted on arXiv 20 Sep 2024.

## Builds on (most cited first, 3 of 3)

- [Deep Scale-spaces: Equivariance Over Scale](https://mlsanity.com/paper/1905.11697/) (2019)
- [Scale-covariant and scale-invariant Gaussian derivative networks](https://mlsanity.com/paper/2011.14759/) (2020)
- [Dense scale selection over space, time and space-time](https://mlsanity.com/paper/1709.08603/) (2017)

## Built on by (most cited first, 1 of 1)

- [MozzaVID: Mozzarella Volumetric Image Dataset](https://mlsanity.com/paper/2412.04880/) (2024)

## Abstract (arXiv)

The structure tensor method is often used for 2D and 3D analysis of imaged structures, but its results are in many cases very dependent on the user's choice of method parameters. We simplify this parameter choice in first order structure tensor scale-space by directly connecting the width of the derivative filter to the size of image features. By introducing a ring-filter step, we substitute the Gaussian integration/smoothing with a method that more accurately shifts the derivative filter response from feature edges to their center. We further demonstrate how extracted structural measures can be used to correct known inaccuracies in the scale map, resulting in a reliable representation of the feature sizes both in 2D and 3D. Compared to the traditional first order structure tensor, or previous structure tensor scale-space approaches, our solution is much more accurate and can serve as an out-of-the-box method for extracting a wide range of structural parameters with minimal user input.