Manifold-Preserving Superpixel Hierarchies and Embeddings for the Exploration of High-Dimensional Images

2026-02-27

AI Summary

This work addresses a critical limitation in existing hierarchical embedding methods for high-dimensional image exploration: the neglect of pixel spatial layout, which leads to misalignment between image space and attribute space representations and hinders precise localization of regions of interest. To resolve this, the authors propose a novel superpixel-based hierarchical structure that, for the first time, simultaneously integrates the manifold geometry of high-dimensional attributes with spatial adjacency in the image domain during hierarchy construction. By aligning these two spaces throughout the hierarchical abstraction, the method combines manifold-preserving superpixel segmentation, hierarchical embedding, and dimensionality reduction for visualization. Evaluations on two case studies demonstrate significant improvements over conventional approaches, substantially enhancing the joint exploratory analysis of image and attribute spaces.

Technology Category

• Computer Vision: Representation Learning for Vision
• Machine Learning: Learning with Manifolds
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Web Mining and Content Analysis: Web data visualization

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.

Problem

• high-dimensional images
• hierarchical embedding
• spatial layout
• manifold preservation
• superpixel hierarchy

Innovation

• manifold-preserving
• superpixel hierarchy
• high-dimensional images
• hierarchical embedding
• spatial coherence