Boudewijn P. F. Lelieveldt

Alexander Vieth, Boudewijn Lelieveldt, Elmar Eisemann et al.

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.

Alexander Vieth, Anna Vilanova, Boudewijn Lelieveldt et al.

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.

Zixia Zhou, Yuanyuan Wang, Boudewijn P. F. Lelieveldt et al.

t-distributed stochastic neighbor embedding (t-SNE) is a well-established visualization method for complex high-dimensional data. However, the original t-SNE method is nonparametric, stochastic, and often cannot well prevserve the global structure of data as it emphasizes local neighborhood. With t-SNE as a reference, we propose to combine the deep neural network (DNN) with the mathematical-grounded embedding rules for high-dimensional data embedding. We first introduce a deep embedding network (DEN) framework, which can learn a parametric mapping from high-dimensional space to low-dimensional embedding. DEN has a flexible architecture that can accommodate different input data (vector, image, or tensor) and loss functions. To improve the embedding performance, a recursive training strategy is proposed to make use of the latent representations extracted by DEN. Finally, we propose a two-stage loss function combining the advantages of two popular embedding methods, namely, t-SNE and uniform manifold approximation and projection (UMAP), for optimal visualization effect. We name the proposed method Deep Recursive Embedding (DRE), which optimizes DEN with a recursive training strategy and two-stage losse. Our experiments demonstrated the excellent performance of the proposed DRE method on high-dimensional data embedding, across a variety of public databases. Remarkably, our comparative results suggested that our proposed DRE could lead to improved global structure preservation.

Antonios Somarakis, Marieke E. Ijsselsteijn, Sietse J. Luk et al.

Spatially-resolved omics-data enable researchers to precisely distinguish cell types in tissue and explore their spatial interactions, enabling deep understanding of tissue functionality. To understand what causes or deteriorates a disease and identify related biomarkers, clinical researchers regularly perform large-scale cohort studies, requiring the comparison of such data at cellular level. In such studies, with little a-priori knowledge of what to expect in the data, explorative data analysis is a necessity. Here, we present an interactive visual analysis workflow for the comparison of cohorts of spatially-resolved omics-data. Our workflow allows the comparative analysis of two cohorts based on multiple levels-of-detail, from simple abundance of contained cell types over complex co-localization patterns to individual comparison of complete tissue images. As a result, the workflow enables the identification of cohort-differentiating features, as well as outlier samples at any stage of the workflow. During the development of the workflow, we continuously consulted with domain experts. To show the effectiveness of the workflow we conducted multiple case studies with domain experts from different application areas and with different data modalities.

Nicola Pezzotti, Sahar Yousefi, Mohamed S. Elmahdy et al.

Adaptive intelligence aims at empowering machine learning techniques with the additional use of domain knowledge. In this work, we present the application of adaptive intelligence to accelerate MR acquisition. Starting from undersampled k-space data, an iterative learning-based reconstruction scheme inspired by compressed sensing theory is used to reconstruct the images. We adopt deep neural networks to refine and correct prior reconstruction assumptions given the training data. The network was trained and tested on a knee MRI dataset from the 2019 fastMRI challenge organized by Facebook AI Research and NYU Langone Health. All submissions to the challenge were initially ranked based on similarity with a known groundtruth, after which the top 4 submissions were evaluated radiologically. Our method was evaluated by the fastMRI organizers on an independent challenge dataset. It ranked #1, shared #1, and #3 on respectively the 8x accelerated multi-coil, the 4x multi-coil, and the 4x single-coil track. This demonstrates the superior performance and wide applicability of the method.

Kirsten Koolstra, Peter Börnert, Boudewijn Lelieveldt et al.

In Magnetic Resonance Fingerprinting (MRF) the quality of the estimated parameter maps depends on the encoding capability of the variable flip angle train. In this work we show how the dimensionality reduction technique Hierarchical Stochastic Neighbor Embedding (HSNE) can be used to obtain insight into the encoding capability of different MRF sequences. Embedding high-dimensional MRF dictionaries into a lower-dimensional space and visualizing them with colors, being a surrogate for location in low-dimensional space, provides a comprehensive overview of particular dictionaries and, in addition, enables comparison of different sequences. Dictionaries for various sequences and sequence lengths were compared to each other, and the effect of transmit field variations on the encoding capability was assessed. Clear differences in encoding capability were observed between different sequences, and HSNE results accurately reflect those obtained from an MRF matching simulation.

Hessam Sokooti, Bob de Vos, Floris Berendsen et al.

We propose a supervised nonrigid image registration method, trained using artificial displacement vector fields (DVF), for which we propose and compare three network architectures. The artificial DVFs allow training in a fully supervised and voxel-wise dense manner, but without the cost usually associated with the creation of densely labeled data. We propose a scheme to artificially generate DVFs, and for chest CT registration augment these with simulated respiratory motion. The proposed architectures are embedded in a multi-stage approach, to increase the capture range of the proposed networks in order to more accurately predict larger displacements. The proposed method, RegNet, is evaluated on multiple databases of chest CT scans and achieved a target registration error of 2.32 $\pm$ 5.33 mm and 1.86 $\pm$ 2.12 mm on SPREAD and DIR-Lab-4DCT studies, respectively. The average inference time of RegNet with two stages is about 2.2 s.

Hessam Sokooti, Gorkem Saygili, Ben Glocker et al.

Predicting registration error can be useful for evaluation of registration procedures, which is important for the adoption of registration techniques in the clinic. In addition, quantitative error prediction can be helpful in improving the registration quality. The task of predicting registration error is demanding due to the lack of a ground truth in medical images. This paper proposes a new automatic method to predict the registration error in a quantitative manner, and is applied to chest CT scans. A random regression forest is utilized to predict the registration error locally. The forest is built with features related to the transformation model and features related to the dissimilarity after registration. The forest is trained and tested using manually annotated corresponding points between pairs of chest CT scans in two experiments: SPREAD (trained and tested on SPREAD) and inter-database (including three databases SPREAD, DIR-Lab-4DCT and DIR-Lab-COPDgene). The results show that the mean absolute errors of regression are 1.07 $\pm$ 1.86 and 1.76 $\pm$ 2.59 mm for the SPREAD and inter-database experiment, respectively. The overall accuracy of classification in three classes (correct, poor and wrong registration) is 90.7% and 75.4%, for SPREAD and inter-database respectively. The good performance of the proposed method enables important applications such as automatic quality control in large-scale image analysis.

Nicola Pezzotti, Julian Thijssen, Alexander Mordvintsev et al.

The t-distributed Stochastic Neighbor Embedding (tSNE) algorithm has become in recent years one of the most used and insightful techniques for the exploratory data analysis of high-dimensional data. tSNE reveals clusters of high-dimensional data points at different scales while it requires only minimal tuning of its parameters. Despite these advantages, the computational complexity of the algorithm limits its application to relatively small datasets. To address this problem, several evolutions of tSNE have been developed in recent years, mainly focusing on the scalability of the similarity computations between data points. However, these contributions are insufficient to achieve interactive rates when visualizing the evolution of the tSNE embedding for large datasets. In this work, we present a novel approach to the minimization of the tSNE objective function that heavily relies on modern graphics hardware and has linear computational complexity. Our technique does not only beat the state of the art, but can even be executed on the client side in a browser. We propose to approximate the repulsion forces between data points using adaptive-resolution textures that are drawn at every iteration with WebGL. This approximation allows us to reformulate the tSNE minimization problem as a series of tensor operation that are computed with TensorFlow.js, a JavaScript library for scalable tensor computations.

Nicola Pezzotti, Boudewijn P. F. Lelieveldt, Laurens van der Maaten et al.

Progressive Visual Analytics aims at improving the interactivity in existing analytics techniques by means of visualization as well as interaction with intermediate results. One key method for data analysis is dimensionality reduction, for example, to produce 2D embeddings that can be visualized and analyzed efficiently. t-Distributed Stochastic Neighbor Embedding (tSNE) is a well-suited technique for the visualization of several high-dimensional data. tSNE can create meaningful intermediate results but suffers from a slow initialization that constrains its application in Progressive Visual Analytics. We introduce a controllable tSNE approximation (A-tSNE), which trades off speed and accuracy, to enable interactive data exploration. We offer real-time visualization techniques, including a density-based solution and a Magic Lens to inspect the degree of approximation. With this feedback, the user can decide on local refinements and steer the approximation level during the analysis. We demonstrate our technique with several datasets, in a real-world research scenario and for the real-time analysis of high-dimensional streams to illustrate its effectiveness for interactive data analysis.