Analyzing high-dimensional images is a complex task. Unlike regular color images, they are not straightforward to visualize. Their additional information content increases the complexity of interpretation, both in terms of computational processing and human comprehension. Visual analytics - the combination of visualization, interaction, and automated analysis methods - has proven useful to gain insights into such large, difficult-to-handle data. For example, non-linear dimensionality reduction is a commonly employed technique in visual analytics for exposing interesting patterns through lower-dimensional representations of high-dimensional data.

In this thesis, we investigate non-linear dimensionality-reduction methods for the exploration of high-dimensional images. Specifically, we address the problem that current dimensionality-reduction methods are image-agnostic: they treat spatially resolved data without considering their spatial layout. We present algorithmic solutions that yield image-informed embeddings and interactions techniques that connect images and embedding representations. To a large extend, we utilize hierarchical approaches to handle the image data. We show how these techniques enable more insightful exploration of high-dimensional images.

Further, we present an open-source visual analytics software framework for rapid prototyping and extensible workflow development for high-dimensional data analysis. All algorithms and techniques described in this thesis are made available in or fully implemented as plugins for this framework.

Exploration and analysis of high-dimensional data are important tasks in many fields that produce large and complex data, like the financial sector, systems biology, or cultural heritage. Tailor-made visual analytics software is developed for each specific application, limiting their applicability in other fields. However, as diverse as these fields are, their characteristics and requirements for data analysis are conceptually similar. Many applications share abstract tasks and data types and are often constructed with similar building blocks. Developing such applications, even when based mostly on existing building blocks, requires significant engineering efforts. We developed ManiVault, a flexible and extensible open-source visual analytics framework for analyzing high-dimensional data. The primary objective of ManiVault is to facilitate rapid prototyping of visual analytics workflows for visualization software developers and practitioners alike. ManiVault is built using a plugin-based architecture that offers easy extensibility. While our architecture deliberately keeps plugins self-contained, to guarantee maximum flexibility and re-usability, we have designed and implemented a messaging API for tight integration and linking of modules to support common visual analytics design patterns. We provide several visualization and analytics plugins, and ManiVault's API makes the integration of new plugins easy for developers. ManiVault facilitates the distribution of visualization and analysis pipelines and results for practitioners through saving and reproducing complete application states. As such, ManiVault can be used as a communication tool among researchers to discuss workflows and results. A copy of this paper and all supplemental material is available at osf.io/9k6jw, and source code at github.com/ManiVaultStudio.

High-dimensional images (i.e., with many attributes per pixel) are commonly acquired in many domains, such as geosciences or systems biology. The spatial and attribute information of such data are typically explored separately, e.g., by using coordinated views of an image representation and a low-dimensional embedding of the high-dimensional attribute data. Facing ever growing image data sets, hierarchical dimensionality reduction techniques lend themselves to overcome scalability issues. However, current embedding methods do not provide suitable interactions to reflect image space exploration. Specifically, it is not possible to adjust the level of detail in the embedding hierarchy to reflect changing level of detail in image space stemming from navigation such as zooming and panning. In this paper, we propose such a mapping from image navigation interactions to embedding space adjustments. We show how our mapping applies the "overview first, details-on-demand" characteristic inherent to image exploration in the high-dimensional attribute space. We compare our strategy with regular hierarchical embedding technique interactions and demonstrate the advantages of linking image and embedding interactions through a representative use case.

High-dimensional imaging is becoming increasingly relevant in many fields from astronomy and cultural heritage to systems biology. Visual exploration of such high-dimensional data is commonly facilitated by dimensionality reduction. However, common dimensionality reduction methods do not include spatial information present in images, such as local texture features, into the construction of low-dimensional embeddings. Consequently, exploration of such data is typically split into a step focusing on the attribute space followed by a step focusing on spatial information, or vice versa. In this paper, we present a method for incorporating spatial neighborhood information into distance-based dimensionality reduction methods, such as t-Distributed Stochastic Neighbor Embedding (t-SNE). We achieve this by modifying the distance measure between high-dimensional attribute vectors associated with each pixel such that it takes the pixel's spatial neighborhood into account. Based on a classification of different methods for comparing image patches, we explore a number of different approaches. We compare these approaches from a theoretical and experimental point of view. Finally, we illustrate the value of the proposed methods by qualitative and quantitative evaluation on synthetic data and two real-world use cases.