[论文解读] Manifold-Preserving Superpixel Hierarchies and Embeddings for the Exploration of High-Dimensional Images

Alexander Vieth, Boudewijn P. F. Lelieveldt+3 more|arXiv (Cornell University)|Feb 27, 2026

Advanced Image and Video Retrieval Techniques被引用 0

一句话总结

论文提出一个耦合图像布局与高维属性流形的超像素层次结构，并使用基于随机游走的相似度在多个抽象层次上构建保持流形的嵌入。

ABSTRACT

High-dimensional images, or images with a high-dimensional attribute vector per pixel, are commonly explored with coordinated views of a low-dimensional embedding of the attribute space and a conventional image representation. Nowadays, such images can easily contain several million pixels. For such large datasets, hierarchical embedding techniques are better suited to represent the high-dimensional attribute space than flat dimensionality reduction methods. However, available hierarchical dimensionality reduction methods construct the hierarchy purely based on the attribute information and ignore the spatial layout of pixels in the images. This impedes the exploration of regions of interest in the image space, since there is no congruence between a region of interest in image space and the associated attribute abstractions in the hierarchy. In this paper, we present a superpixel hierarchy for high-dimensional images that takes the high-dimensional attribute manifold into account during construction. Through this, our method enables consistent exploration of high-dimensional images in both image and attribute space. We show the effectiveness of this new image-guided hierarchy in the context of embedding exploration by comparing it with classical hierarchical embedding-based image exploration in two use cases.

研究动机与目标

• 通过将图像结构与属性空间流形整合，激发对非常大尺寸高维图像的研究.
• 提出一种在图像空间聚合期间保持流形几何的超像素层次结构。
• 开发基于随机游走的相似度度量，驱动层次结构构建与分层嵌入。
• demonstrate 该方法能够产生简洁、具有空间含义的嵌入并具备竞争力的层次质量。
• 提供来自高光谱与高度多路复用成像的工具与证据来验证方法。

提出的方法

• 通过连通的k近邻图在像素属性上构建邻接图，以近似数据流形。
• 在属性图上计算基于随机游走的转移概率，以描述局部邻域。
• 使用类Borůvka迭代，依据随机游走特征分布之间的Bhattacharyya系数相似性来合并超像素。
• 在某一层次表示每个超像素，通过合并相应的节点并相应更新转移矩阵。
• 通过用从随机游走特征导出的Bhattacharyya基距离替代t-SNE/UMAP距离，在每个层级计算嵌入。
• 通过切分嵌入概率以聚焦于选定的超像素并在需要时用相似性阈值扩大子集，实现子集嵌入的细化。

Figure 1 : Image Hierarchies: Classical image-space-based hierarchies, like image pyramids, progressively blur and subsample the image (a). Attribute-space-based hierarchies, as used in hierarchical DR methods (b), ignore the image space entirely and only aim to preserve manifold structure of the at

实验结果

研究问题

• RQ1 如何在尊重图像空间与高维属性数据的流形结构的前提下构建超像素层次结构？
• RQ2 基于随机游走的相似度能否为层次结构构建和嵌入提供鲁棒的流形保持距离？
• RQ3 以图像引导的层次结构是否比传统的图像无关的层次DR方法产生更简洁、空间更一致的嵌入？
• RQ4 该方法是否能够扩展到大尺寸高维图像，并通过对嵌入的细化实现交互式探索？

主要发现

• 提出的保持流形的超像素层次结构的嵌入在空间一致性和简洁性方面优于像HSNE等无关_baseline。
• 基于Bhattacharyya的相似性（由属性图上的随机游走特征构建）有效指导超像素合并与邻域嵌入。
• 该方法在实现竞争力的层次质量的同时，支持对高维图像数据进行“先概览、后细节”的探索。
• 在更高抽象层次的嵌入可以用更少的关键点表示空间区域，相较于基线的分层DR方法。
• 该方法支持子集细化，能够进行有针对性的交互式放大而不丢失层次上下文。

Figure 2 : Graph structures : 4-connected image graph $\mathcal{I}$ (left) and attribute-based graph $\mathcal{G}$ (right). Different neighborhoods of the same node 1 are highlighted in grey.