Abstract
Feature extraction in noisy image datasets presents many challenges in model reliability. In this paper, we use the discrete Fourier transform in conjunction with persistent homology analysis to extract specific frequencies that correspond with certain topological features of an image. This method allows the image to be compressed and reformed while ensuring that meaningful data can be differentiated. Our experimental results show a level of compression comparable to that of using JPEG using six different metrics. The end goal of persistent homology-guided frequency filtration is its potential to improve performance in binary classification tasks (when augmenting a Convolutional Neural Network) compared to traditional feature extraction and compression methods. These findings highlight a useful end result: enhancing the reliability of image compression under noisy conditions.
Abstract (translated)
在嘈杂的图像数据集中提取特征给模型可靠性带来了许多挑战。本文中，我们使用离散傅里叶变换与持久同调分析相结合的方法来提取特定频率，这些频率对应于图像中的某些拓扑特征。这种方法允许图像被压缩和重组，并确保有意义的数据可以被区分出来。我们的实验结果显示，在使用六种不同指标的情况下，这种压缩水平可媲美JPEG的性能。 持久同调引导下的频谱过滤最终目标在于提高二分类任务中的表现（在增强卷积神经网络时），相较于传统的特征提取与压缩方法有潜在的优势。这些发现突显了一个有用的最终结果：即在嘈杂条件下提升图像压缩的可靠性。
URL
https://arxiv.org/abs/2512.07065
