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

2026-06-10

AI Summary

This work proposes Density-Equilibrated Convolutional Neural Networks (DECNN), a novel architecture that addresses the limitations of conventional convolution—namely, its reliance on uniform sampling, which fails to adapt to the locally concentrated information in images and curved surfaces, leading to computational redundancy and restricted representational capacity. DECNN introduces, for the first time, a density-equilibration mechanism into convolutional design by learning a task-aware spatial importance density function that dynamically generates non-uniform sampling patterns, enabling denser sampling in critical regions to enhance feature extraction efficiency. The method simultaneously produces interpretable saliency maps and supports multi-task saliency sharing. Experiments demonstrate that DECNN achieves comparable or superior performance to existing approaches in both image classification and craniofacial surface analysis with fewer parameters, accurately focusing on task-relevant regions while exhibiting robustness to complex geometric variations.

Abstract

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.

Problem

• non-uniform sampling
• task-aware attention
• density-equalizing mapping
• informative region localization
• computational efficiency

Innovation

• task-aware sampling
• density-equalizing mapping
• adaptive convolution
• saliency learning
• non-uniform feature extraction