Manifold Learning for Hyperspectral Images

TL;DR

The paper tackles the difficulty of representing X-ray transmission hyperspectral images with traditional linear methods by leveraging topology-preserving non-linear embeddings. It introduces a Parametric UMAP pipeline to map data from $[H,W,C]$ to a lower-dimensional $[H,W,D]$ while retaining intrinsic structure, subsequently feeding embeddings into CNNs for segmentation, regression, and classification. Across Cigarettes, Stones, and Indian Pines experiments, UMAP-based representations consistently outperform PCA, NMF, and raw spectra, demonstrating improved feature separability, robustness, and efficiency. The work highlights the potential of topology-aware analysis in hyperspectral XRT data and advocates further exploration of topological data analysis to enhance practical performance in real-world imaging applications.

Abstract

Traditional feature extraction and projection techniques, such as Principal Component Analysis, struggle to adequately represent X-Ray Transmission (XRT) Multi-Energy (ME) images, limiting the performance of neural networks in decision-making processes. To address this issue, we propose a method that approximates the dataset topology by constructing adjacency graphs using the Uniform Manifold Approximation and Projection. This approach captures nonlinear correlations within the data, significantly improving the performance of machine learning algorithms, particularly in processing Hyperspectral Images (HSI) from X-ray transmission spectroscopy. This technique not only preserves the global structure of the data but also enhances feature separability, leading to more accurate and robust classification results.

Figures (13)

• Figure 1: Scheme of the experimental setting (left) view from aside. A top view of the detector is also given (right) to make the data collection process clearer to the reader.
• Figure 2: Pipeline of our proposed method.
• Figure 3: Comparison between raw spectral bands (top row) and UMAP-projected bands (bottom row).
• Figure 4: Illustration of the fusion process: normalized luggage and cigarette images are combined to generate synthetic data.
• Figure 5: The U-Net architecture consists of four downsampling blocks, each with a Double Convolution followed by Max Pooling (stride = 2), progressively increasing the number of filters from 8 to 64. The upsampling blocks include an Upsampling (scale = 2), concatenation with the corresponding output, and a Double Convolution to refine features. The final convolution reduces the output to a single prediction channel.