# Learning Task-Aware Sampling with Shared Saliency through Density-Equalizing Mappings

arXiv: https://arxiv.org/abs/2606.12869 · HTML: https://mlsanity.com/paper/2606.12869/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 39 references that are in the map.
- First posted on arXiv 11 Jun 2026.

## Builds on (most cited first, 21 of 21)

- [Deformable Convolutional Networks](https://mlsanity.com/paper/1703.06211/) (2017)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [Deformable ConvNets v2: More Deformable, Better Results](https://mlsanity.com/paper/1811.11168/) (2018)
- [Understanding the Effective Receptive Field in Deep Convolutional Neural Networks](https://mlsanity.com/paper/1701.04128/) (2017)
- [Learning shape correspondence with anisotropic convolutional neural networks](https://mlsanity.com/paper/1605.06437/) (2016)
- [Neural 3D Morphable Models: Spiral Convolutional Networks for 3D Shape Representation Learning and Generation](https://mlsanity.com/paper/1905.02876/) (2019)
- [SpiralNet++: A Fast and Highly Efficient Mesh Convolution Operator](https://mlsanity.com/paper/1911.05856/) (2019)
- [Active Convolution: Learning the Shape of Convolution for Image Classification](https://mlsanity.com/paper/1703.09076/) (2017)
- [Landmark and Intensity Based Registration with Large Deformations via Quasi-conformal Maps](https://mlsanity.com/paper/1310.1710/) (2013)
- [TEMPO: Feature-Endowed Teichm"uller Extremal Mappings of Point Clouds](https://mlsanity.com/paper/1511.06624/) (2015)
- [Fast Disk Conformal Parameterization of Simply-connected Open Surfaces](https://mlsanity.com/paper/1408.6974/) (2014)
- [A Learning-based Framework for Topology-Preserving Segmentation using Quasiconformal Mappings](https://mlsanity.com/paper/2210.03299/) (2022)
- [Spherical Density-Equalizing Map for Genus-0 Closed Surfaces](https://mlsanity.com/paper/2401.11795/) (2024)
- [Deformation-Invariant Neural Network and Its Applications in Distorted Image Restoration and Analysis](https://mlsanity.com/paper/2310.02641/) (2023)
- [Density-equalizing maps for simply-connected open surfaces](https://mlsanity.com/paper/1704.02525/) (2017)
- [Bijective Density-Equalizing Quasiconformal Map for Multiply-Connected Open Surfaces](https://mlsanity.com/paper/2308.05579/) (2023)
- [Area-preserving mapping of 3D ultrasound carotid artery images using density-equalizing reference map](https://mlsanity.com/paper/1812.03434/) (2018)
- [Volumetric density-equalizing reference map with applications](https://mlsanity.com/paper/2003.09725/) (2020)
- [QIS : Interactive Segmentation via Quasi-Conformal Mappings](https://mlsanity.com/paper/2402.14695/) (2024)
- [Toroidal density-equalizing map for genus-one surfaces](https://mlsanity.com/paper/2410.16833/) (2024)
- [Learning-based density-equalizing map](https://mlsanity.com/paper/2506.10027/) (2025)

## Abstract (arXiv)

In image and surface-based learning tasks, convolutional features are typically extracted using receptive fields that are sampled uniformly across the entire domain. However, informative structures are rarely distributed uniformly in practice and are often concentrated in localized regions. Such phenomena are particularly common in medical imaging, where pathological changes are spatially confined. Consequently, uniform convolution allocates equal computational effort to both informative and uninformative regions, resulting in inefficient feature extraction and suboptimal utilization of model capacity. To address this issue, we propose a framework for task-adaptive sampling that dynamically redistributes computational attention according to the spatial importance of the data. Specifically, we introduce the Density-Equalizing Convolutional Neural Network (DECNN), which employs density-equalizing mappings to guide convolution through a learned density function. The density function encodes the relative importance of different regions and induces a transformation that enlarges informative areas while compressing less relevant ones. As a result, convolutional receptive fields are redistributed non-uniformly over the domain, enabling denser sampling in task-relevant regions. By coupling this importance-driven transformation with convolution, DECNN performs adaptive feature extraction that focuses computational resources on informative structures. This leads to more efficient use of model capacity, yielding a lightweight yet expressive architecture while simultaneously producing an interpretable saliency map. Experiments on image classification and craniofacial surface analysis demonstrate that DECNN achieves competitive or superior performance with fewer parameters, accurately identifies task-relevant regions, and remains robust under complex geometric variations.