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.

翻译：在图像与曲面学习任务中，卷积特征通常通过在全域均匀采样的感受野进行提取。然而，实际中具有信息量的结构极少均匀分布，往往集中在局部区域。这种现象在医学影像中尤为常见——病理改变具有空间局限性。均匀卷积对信息丰富与贫瘠区域分配相同计算量，导致特征提取效率低下及模型容量利用不充分。针对该问题，我们提出任务自适应采样框架，根据数据空间重要性动态重新分配计算注意力。具体而言，我们引入密度均衡卷积神经网络（DECNN），通过密度均衡映射引导卷积学习密度函数。该密度函数编码不同区域的相对重要性，通过变换放大信息丰富区域同时压缩无关区域，使卷积感受野在全域形成非均匀重分布，从而在任务相关区域实现密集采样。通过将这种重要性驱动的变换与卷积耦合，DECNN能将计算资源聚焦于信息结构进行自适应特征提取，既充分利用模型容量构建轻量高效架构，又能生成可解释的显著性图。在图像分类与颅面曲面分析实验表明，DECNN以更少参数达到同等或更优性能，精准识别任务相关区域，并在复杂几何形变下保持鲁棒性。