用几何不变量提取轮廓特征，高效且可解释。
Varifold Moment Invariants for Sustainable and Explainable Contour Feature Extraction
- 基于变流形矩构建轮廓不变特征，融合区域与边界信息。
- 在多个数据集上达高精度，仅需少量几何可解释特征。
- 计算轻量，适合部署在低功耗设备上。
我们提出变流形矩不变量（VMI）作为多种已有矩不变量的统一框架。该方法与平移旋转不变的轮廓特征密切相关，如扩展高斯图像、椭圆傅里叶描述符或形状分布。变流形方法的优势在于能结合区域几何、边界形状及切线线族信息，生成大量具有强区分能力且几何意义明确的不变特征。将VMI特征提取与随机森林或多层感知机等轻量分类器结合，在轮廓类任务上超越现有最优方法，同时大幅降低计算开销，使算法可在资源受限设备上运行。我们在多个广泛使用的异构数据集（叶片、物体、细胞）上验证了该方法，仅使用少量几何可解释特征即实现了高分类准确率。
原文摘要 · Abstract (English)
We introduce Varifold Moments Invariants (VMI) as a unifying framework for many previously introduced Moment Invariants. These invariants are deeply related to other contour features that are invariant under translations and rotations, like Extended Gaussian Image, Elliptic Fourier Descriptors or Shape Distributions. The advantage of the varifold approach to moments consists in being able to combine the geometry of the region, its boundary, and the family of lines tangent to it, in order to create a substantial number of invariant features with high discriminating power and clear geometric meaning. By coupling our VMI feature extraction with the light feature classifiers Random Forest or Multi-Layer-Perceptron, we outperform state-of-the-art approaches based on contours, while decreasing drastically the computational cost to the point of allowing our algorithm to run on light devices. We tested our approach on classification tasks on a large number of widely-used datasets of various types (leaves, objects, cells) and achieved high accuracy with a low number of geometrically interpretable features.
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