Vector graphics provide continuous and often even smooth geometric representations of images. While recent approaches to automatically vectorize images lead to relatively good results, they typically leave ample room for improvement: the geometry and color of the vector graphics primitives can be further (automatically) optimized. We propose a novel method that generates high-quality vectorizations based on optimizing input curved triangle meshes (optionally with mesh colors). To overcome the key challenge of establishing a differentiable mapping between the input parameters, i.e., geometry and (mesh) colors of the gradient mesh, and the difference between the vectorized and input image, we treat the input image as a continuous bilinear interpolatory spline and employ Monte Carlo integration. We test our algorithm on various images and show that it can effectively and efficiently improve the quality of an initial vectorization. • We introduce a differentiable error function to drive optimization. • We derive an explicit gradient from the error function using the Monte Carlo method. • We illustrate the effectiveness of the method on various examples.

Abstract We present HyperFLINT (Hypernetwork‐based FLow estimation and temporal INTerpolation), a novel deep learning‐based approach for estimating flow fields, temporally interpolating scalar fields, and facilitating parameter space exploration in spatio‐temporal scientific ensemble data. This work addresses the critical need to explicitly incorporate ensemble parameters into the learning process, as traditional methods often neglect these, limiting their ability to adapt to diverse simulation settings and provide meaningful insights into the data dynamics. HyperFLINT introduces a hypernetwork to account for simulation parameters, enabling it to generate accurate interpolations and flow fields for each timestep by dynamically adapting to varying conditions, thereby outperforming existing parameter‐agnostic approaches. The architecture features modular neural blocks with convolutional and deconvolutional layers, supported by a hypernetwork that generates weights for the main network, allowing the model to better capture intricate simulation dynamics. A series of experiments demonstrates HyperFLINT's significantly improved performance in flow field estimation and temporal interpolation, as well as its potential in enabling parameter space exploration, offering valuable insights into complex scientific ensembles.

A component tree is a graph representation that encodes the connected components of the upper or lower level sets of a grayscale image . Consequently, the nodes of a component tree represent binary images of the encoded connected components. There exist various algorithms that efficiently extract information and attributes of nodes of a component tree by incrementally exploiting the subset relation encoding in the tree. However, to the best of our knowledge, there is no such incremental approach to extract the contours of the nodes. In this paper, we propose an efficient incremental method to compute the contours of the nodes of a component tree by counting the edges (sides) of contour pixels. In addition, we discuss our method’s time complexity. We also experimentally show that our proposed method is faster than the standard approach based on node reconstruction.

We present FLINT (learning-based FLow estimation and temporal INTerpolation), a novel deep learning-based approach to estimate flow fields for 2D+time and 3D+time scientific ensemble data. FLINT can flexibly handle different types of scenarios with (1) a flow field being partially available for some members (e.g., omitted due to space constraints) or (2) no flow field being available at all (e.g., because it could not be acquired during an experiment). The design of our architecture allows to flexibly cater to both cases simply by adapting our modular loss functions, effectively treating the different scenarios as flow-supervised and flow-unsupervised problems, respectively (with respect to the presence or absence of ground-truth flow). To the best of our knowledge, FLINT is the first approach to perform flow estimation from scientific ensembles, generating a corresponding flow field for each discrete timestep, even in the absence of original flow information. Additionally, FLINT produces high-quality temporal interpolants between scalar fields. FLINT employs several neural blocks, each featuring several convolutional and deconvolutional layers. We demonstrate performance and accuracy for different usage scenarios with scientific ensembles from both simulations and experiments.

Mesh-based image vectorization techniques have been studied for a long time, mostly owing to their compactness and flexibility in capturing image features. However, existing methods often lead to relatively dense meshes, especially when applied to images with high-frequency details or textures. We present a novel method that automatically vectorizes an image into a sparse collection of Coons patches whose size adapts to image features. To balance the number of patches and the accuracy of feature alignment, we generate the layout based on a harmonic cross field constrained by image features. We support T-junctions, which keeps the number of patches low and ensures local adaptation to feature density, naturally complemented by varying mesh-color resolution over the patches. Our experimental results demonstrate the utility, accuracy, and sparsity of our method.

The ability to edit an image using intuitive commands and primitives is a desired feature for any image editing software. In this paper, we combine recent results in medial axes with the well-established morphological tree representations to develop an interactive image editing tool that provides global and local image manipulation using high-level primitives. We propose a new way to render interactive morphological trees using icicle plots and introduce different ways of manipulating spline-based medial axis transforms for grayscale and colored image editing. Different applications of the tool, such as watermark removal, image deformation, dataset augmentation for machine learning, artistic illumination manipulation, image rearrangement, and clothing design, are described and showcased on examples.

Abstract Electroencephalography (EEG) coherence networks represent functional brain connectivity, and are constructed by calculating the coherence between pairs of electrode signals as a function of frequency. Visualization of such networks can provide insight into unexpected patterns of cognitive processing and help neuroscientists to understand brain mechanisms. However, visualizing dynamic EEG coherence networks is a challenge for the analysis of brain connectivity, especially when the spatial structure of the network needs to be taken into account. In this paper, we present a design and implementation of a visualization framework for such dynamic networks. First, requirements for supporting typical tasks in the context of dynamic functional connectivity network analysis were collected from neuroscience researchers. In our design, we consider groups of network nodes and their corresponding spatial location for visualizing the evolution of the dynamic coherence network. We introduce an augmented timeline‐based representation to provide an overview of the evolution of functional units (FUs) and their spatial location over time. This representation can help the viewer to identify relations between functional connectivity and brain regions, as well as to identify persistent or transient functional connectivity patterns across the whole time window. In addition, we introduce the time‐annotated FU map representation to facilitate comparison of the behaviour of nodes between consecutive FU maps. A colour coding is designed that helps to distinguish distinct dynamic FUs. Our implementation also supports interactive exploration. The usefulness of our visualization design was evaluated by an informal user study. The feedback we received shows that our design supports exploratory analysis tasks well. The method can serve as a first step before a complete analysis of dynamic EEG coherence networks.

Small to medium enterprises (SMEs), particularly those whose business is focused on developing innovative produces, are limited by a major bottleneck in the speed of computation in many applications. The recent developments in GPUs have been the marked increase in their versatility in many computational areas. But due to the lack of specialist GPUprogramming skills, the explosion of GPU power has not been fully utilized in general SME applications by inexperienced users. Also, the existing automatic CPU-to-GPU code translators are mainly designed for research purposes with poor user interface design and are hard to use. Little attentions have been paid to the applicability, usability, and learnability of these tools for normal users. In this paper, we present an online automated CPU-to-GPU source translation system (GPSME) for inexperienced users to utilize the GPU capability in accelerating general SME applications. This system designs and implements a directive programming model with a new kernel generation scheme and memory management hierarchy to optimize its performance. A web service interface is designed for inexperienced users to easily and flexibly invoke the automatic resource translator. Our experiments with nonexpert GPU users in four SMEs reflect that a GPSME system can efficiently accelerate real-world applications with at least 4× and have a better applicability, usability, and learnability than the existing automatic CPU-to-GPU source translators.

The papers in this special issue were presented at IEEE VIS 2016, held during October 23-28, 2016 in Baltimore, MD. VIS contains three conferences, held concurrently: the IEEE Visual Analytics Science and Technology Conference (IEEE VAST 2016), the IEEE Information Visualization Conference (IEEE InfoVis 2016), and the IEEE Scientific Visualization Conference (IEEE SciVis2016).

The assessment of the quality of body movements in real-time is of utmost importance in exergames, that is digital games controlled by body movements, that are designed for the elderly population. In consideration of the fact that among elderly people the number of injuries and fatalities (caused by fall incidences) is increasing, the ultimate goal of exergames is not only to provide fun, entertainment and exercise but also to improve postural control and balance. It is known that improving balance can reduce the number of falls among the elderly population. Real-time assessment of body movements during exergaming could be used to adapt the difficulty of the game as a function of the quality of the movements of the player, as well as to provide immediate feedback. This in turn could increase motivation to play and therefore increase the effectiveness of exergames as tools to improve balance. In a previous study we identified curvature and speed of motion trajectories as promising metrics for balance quantification using bi-dimensional force plate data [Soancatl et al. 2016]. The main aims of this study are (1) to investigate whether curvature and speed could be used to quantify balance using three-dimensional trajectories derived from whole body movements as recorded by Kinect, and (2) to identify which body parts provide the most insight into balance. We consider measures to be suitable for balance quantification if they can differentiate between two groups (older and younger participants). This categorization can provide insight into balance control, as in general it is known that younger adults (here: younger than 60 years) have better postural control than older adults.

Summary The support vector machine (SVM) is a supervised learning algorithm used for recognizing patterns in data. It is a very popular technique in machine learning and has been successfully used in applications such as image classification, protein classification, and handwriting recognition. However, the computational complexity of the kernelized version of the algorithm grows quadratically with the number of training examples. To tackle this high computational complexity, we have developed a directive‐based approach that converts a gradient‐ascent based training algorithm for the CPU to an efficient graphics processing unit (GPU) implementation. We compare our GPU‐based SVM training algorithm to the standard LibSVM CPU implementation, a highly optimized GPU‐LibSVM implementation, as well as to a directive‐based OpenACC implementation. The results on different handwritten digit classification datasets demonstrate an important speed‐up for the current approach when compared to the CPU and OpenACC versions. Furthermore, our solution is almost as fast and sometimes even faster than the highly optimized CUBLAS‐based GPU‐LibSVM implementation, without sacrificing the algorithm's accuracy. Copyright © 2014 John Wiley & Sons, Ltd.

Magnetic resonance diffusion tensor imaging (DTI) measures diffusion of water molecules and is used to characterize orientation of white matter fibers and connectivity of neurological structures. Segmentation and visualization of DT images is challenging, because of low data quality and complexity of anatomical structures. In this paper, we propose an interactive segmentation approach, based on a hierarchical representation of the input DT image through a tree structure. The tree is obtained by successively merging watershed regions, based on the morphological waterfall approach, hence the name watershed tree. Region merging is done according to a combined similarity and homogeneity criterion. We introduce filters that work on the proposed tree representation, and that enable region-based attribute filtering of DTI data. Linked views between the visualizations of the simplified DT image and the tree enable a user to visually explore both data and tree at interactive rates. The coupling of filtering, semiautomatic segmentation by labeling nodes in the tree, and various interaction mechanisms support the segmentation task. Our method is robust against noise, which we demonstrate on synthetic and real DTI data.

We present a visualization technique for brain fiber tracts from DTI data that provides insight into the structure of white matter through visual abstraction. We achieve this abstraction by analyzing the local similarity of tract segment directions at different scales using a stepwise increase of the search range. Next, locally similar tract segments are moved toward each other in an iterative process, resulting in a local contraction of tracts perpendicular to the local tract direction at a given scale. This not only leads to the abstraction of the global structure of the white matter as represented by the tracts, but also creates volumetric voids. This increase of empty space decreases the mutual occlusion of tracts and, consequently, results in a better understanding of the brain's three-dimensional fiber tract structure. Our implementation supports an interactive and continuous transition between the original and the abstracted representations via various scale levels of similarity. We also support the selection of groups of tracts, which are highlighted and rendered with the abstracted visualization as context.

Mathematical morphology is a very popular framework for processing binary or grayscale images. One of the key problems in applying this framework to color images is the notorious false color problem. We discuss the nature of this problem and its origins. In doing so, it becomes apparent that the lack of invariance of operators to certain transformations (forming a group) plays an important role. The main culprits are the basic join and meet operations, and the associated lattice structure that forms the theoretical basis for mathematical morphology. We show how a lattice that is not group invariant can be related to another lattice that is. When all transformations in a group are linear, these lattices can be related to one another via the theory of frames. This provides all the machinery to let us transform any (grayscale or color) morphological filter into a group-invariant filter on grayscale or color images. We then demonstrate the potential for both subjective and objective improvement in selected tasks.

The level-set method is one of the most popular techniques for capturing and tracking deformable interfaces. Although level sets have demonstrated great potential in visualization and computer graphics applications, such as surface editing and physically based modeling, their use for interactive simulations has been limited due to the high computational demands involved. In this paper, we address this computational challenge by leveraging the increased computing power of graphics processors, to achieve fast simulations based on level sets. Our efficient, sparse GPU level-set method is substantially faster than other state-of-the-art, parallel approaches on both CPU and GPU hardware. We further investigate its performance through a method for surface reconstruction, based on GPU level sets. Our novel multiresolution method for surface reconstruction from unorganized point clouds compares favorably with recent, existing techniques and other parallel implementations. Finally, we point out that both level-set computations and rendering of level-set surfaces can be performed at interactive rates, even on large volumetric grids. Therefore, many applications based on level sets can benefit from our sparse level-set method.

This Supplement to BMC Bioinformatics contains a collection of extended articles providing highlights from the 1st IEEE Symposium on Biological Data Visualization (BioVis 2011, http://www.biovis.net) held on October 23-24, 2011, in conjunction with IEEE Visweek in Providence, RI. The rapidly expanding field of biology creates enormous challenges for computational visualization techniques for enabling researchers to gain insight from large and highly complex data sets. The goal of the BioVis 2011 symposium was to create the premier international and interdisciplinary event for all aspects of visualization in biology. The symposium brought together researchers from the visualization, bioinformatics, and biology communities with the purpose of educating, inspiring, and engaging visualization researchers in problems in biological data visualization, as well as bioinformatics and biology researchers in state-of-the-art visualization research. The symposium also served as a platform for researchers in biology and bioinformatics to share pressing visualization challenges and potential solutions in their fields, to initiate interdisciplinary collaborations and to provide an outlet and training ground for young and freshly minted visualization researchers with a keen interest in problems of biology. For the BioVis 2011 Symposium, a new data visualization/analysis contest was inaugurated. The main goals of the contest were: the development of a better-informed visualization community, provided with deeper domain-specific intuition into the actual issues of interest to the biology and bioinformatics communities; a better-tooled biological community, provided with enhanced application software specifically adjusted to meet their analysis needs; and, finally, a mechanism to strongly promote fundable peer collaborations between visualization and bioinformatics/biology researchers. This contest was focused on specific biological problem domains, based on realistic domain data and domain questions. For BioVis 2011, the contest involved the analysis of expression Quantitative Trait Locus (eQTL) data. Judging for the contest entries was conducted by a panel of experts, including members from both the bioinformatics/biology and the visualization communities. The procedure for selecting the articles for this Supplement was as follows. A first selection of best papers from the twenty paper contributions to BioVis 2011 was made by the paper chairs, based on the reviewer scores and recommendations and the authors were requested to submit an extended version of their paper with at least 30% additional, unpublished, material. In addition, one paper was invited to discuss the BioVis 2011 contest, summarizing the problem and the contest submissions and discussing the lessons learned, for example, what worked, what didn't, and what seemed to be the biggest challenges in coming to a solution. These papers went through a new reviewing round with two independent reviewers. In agreement with the BMC peer review guidelines, the supplement editors did not review or make acceptance decisions about any manuscript to which they had contributed. Following the reviewing process papers were either accepted after taking into account the recommendations by the reviewers or rejected. As a result, seven papers have been accepted for this Supplement. The articles in this Supplement cover a wide spectrum of challenging problems in biological data visualization and their solutions. Heinrich et al. describe the interactive Hierarchical Aggregation Table (iHAT), which facilitates the visualization of multiple sequence alignments, associated metadata, and hierarchical clusterings. Smith et al. present RuleBender, a novel visualization system for the integrated visualization, modeling and simulation of rule-based intracellular biochemistry. In the same spirit, Strobelt et al. present HiTSEE (High-Throughput Screening Exploration Environment), a visualization tool for the analysis of large chemical screens used to examine biochemical processes. Paterson et al. describe VIPER (Visual Pedigree Explorer), a software tool for pedigree visualization that integrates an inheritance-checking algorithm with a novel space-efficient pedigree visualization. Livengood et al. present a system that enables interactive comparative visualization and analytics of metabolomics data obtained by two-dimensional gas chromatography-mass spectrometry. Mayerich et al. present NetMets, a method for quantifying and visualizing errors in biological network segmentation. Finally, Bartlett et al. present and discuss the eQTL biological data visualization challenge conducted as the BioVis 2011 contest. This is a tremendously important biological grand challenge domain with no extant solutions. The authors provide a thought-provoking perspective on the complex relations between the biology, bioinformatics, and visualization domains. They discuss the contest entries submitted to BioVis 2011, present the lessons learned, and conclude with open questions for the future. We hope that the collection of papers in this Supplement will enlighten the reader about the intense activity in the challenging field of biological data visualization, and will encourage and stimulate the interaction and collaboration between researchers from the biology, bioinformatics, and visualization communities.

Abstract High‐dimensional data visualization is receiving increasing interest because of the growing abundance of high‐dimensional datasets. To understand such datasets, visualization of the structures present in the data, such as clusters, can be an invaluable tool. Structures may be present in the full high‐dimensional space, as well as in its subspaces. Two widely used methods to visualize high‐dimensional data are the scatter plot matrix (SPM) and the parallel coordinate plot (PCP). SPM allows a quick overview of the structures present in pairwise combinations of dimensions. On the other hand, PCP has the potential to visualize not only bi‐dimensional structures but also higher dimensional ones. A problem with SPM is that it suffers from crowding and clutter which makes interpretation hard. Approaches to reduce clutter are available in the literature, based on changing the order of the dimensions. However, usually this reordering has a high computational complexity. For effective visualization of high‐dimensional structures, also PCP requires a proper ordering of the dimensions. In this paper, we propose methods for reordering dimensions in PCP in such a way that high‐dimensional structures (if present) become easier to perceive. We also present a method for dimension reordering in SPM which yields results that are comparable to those of existing approaches, but at a much lower computational cost. Our approach is based on finding relevant subspaces for clustering using a quality criterion and cluster information. The quality computation and cluster detection are done in image space, using connected morphological operators. We demonstrate the potential of our approach for synthetic and astronomical datasets, and show that our method compares favorably with a number of existing approaches.

The Discrete Wavelet Transform (DWT) has a wide range of applications from signal processing to video and image compression. We show that this transform, by means of the lifting scheme, can be performed in a memory and computation-efficient way on modern, programmable GPUs, which can be regarded as massively parallel coprocessors through NVidia's CUDA compute paradigm. The three main hardware architectures for the 2D DWT (row-column, line-based, block-based) are shown to be unsuitable for a CUDA implementation. Our CUDA-specific design can be regarded as a hybrid method between the row-column and block-based methods. We achieve considerable speedups compared to an optimized CPU implementation and earlier non-CUDA-based GPU DWT methods, both for 2D images and 3D volume data. Additionally, memory usage can be reduced significantly compared to previous GPU DWT methods. The method is scalable and the fastest GPU implementation among the methods considered. A performance analysis shows that the results of our CUDA-specific design are in close agreement with our theoretical complexity analysis.

Abstract Summary: SpotXplore is a plugin for Cytoscape for extraction and visualization of differentially expressed subnetworks (hotspots) from gene networks. The hotspot-based visualization approach enables interactive exploration of regulatory interactions in differentially expressed gene sets, and it allows a researcher to explore gene expression in direct relation to the affected cellular gene network. The hotspots provide a view beyond the commonly used metabolic pathways and gene ontologies. Availability: http://www.win.tue.nl/∼mwestenb/spotxplore/ Contact: [email protected] Supplementary information: Example data and user manual are available at SpotXplore's web site.

An object in the peripheral visual field is more difficult to recognize when surrounded by other objects. This phenomenon is called "crowding". Crowding places a fundamental constraint on human vision that limits performance on numerous tasks. It has been suggested that crowding results from spatial feature integration necessary for object recognition. However, in the absence of convincing models, this theory has remained controversial. Here, we present a quantitative and physiologically plausible model for spatial integration of orientation signals, based on the principles of population coding. Using simulations, we demonstrate that this model coherently accounts for fundamental properties of crowding, including critical spacing, "compulsory averaging", and a foveal-peripheral anisotropy. Moreover, we show that the model predicts increased responses to correlated visual stimuli. Altogether, these results suggest that crowding has little immediate bearing on object recognition but is a by-product of a general, elementary integration mechanism in early vision aimed at improving signal quality.

The standard morphological operators are (i) defined on Euclidean space, (ii) based on structuring elements, and (iii) invariant with respect to translation. There are several ways to generalise this. One way is to make the operators adaptive by letting the size or shape of structuring elements depend on image location or on image features. Another one is to extend translation invariance to more general invariance groups, where the shape of the structuring element spatially adapts in such a way that global group invariance is maintained. We review group-invariant morphology, discuss the relations with adaptive morphology, point out some pitfalls, and show that there is no inherent incompatibility between a spatially adaptive structuring element and global translation invariance of the corresponding morphological operators.

SUMMARY: Unraveling regulatory mechanisms (e.g. identification of motifs in cis-regulatory regions) remains a major challenge in the analysis of transcriptome experiments. Existing applications identify putative motifs from gene lists obtained at rather arbitrary cutoff and require additional manual processing steps. Our standalone application MOTIFATOR identifies the most optimal parameters for motif discovery and creates an interactive visualization of the results. Discovered putative motifs are functionally characterized, thereby providing valuable insight in the biological processes that could be controlled by the motif. AVAILABILITY: MOTIFATOR is freely available at http://www.motifator.nl.

A physically motivated method for surface reconstruction is proposed that can recover smooth surfaces from noisy and sparse data sets. No orientation information is required. By a new technique based on regularized-membrane potentials the input sample points are aggregated, leading to improved noise tolerability and outlier removal, without sacrificing much with respect to detail (feature) recovery. After aggregating the sample points on a volumetric grid, a novel, iterative algorithm is used to classify grid points as exterior or interior to the surface. This algorithm relies on intrinsic properties of the smooth scalar field on the grid which emerges after the aggregation step. Second, a mesh-smoothing paradigm based on a mass-spring system is introduced. By enhancing this system with a bending-energy minimizing term we ensure that the final triangulated surface is smoother than piecewise linear. In terms of speed and flexibility, the method compares favorably with respect to previous approaches. Most parts of the method are implemented on modern graphics processing units (GPUs). Results in a wide variety of settings are presented, ranging from surface reconstruction on noise-free point clouds to grayscale image segmentation.

We present a technique for the illustrative rendering of 3D line data at interactive frame rates. We create depth-dependent halos around lines to emphasize tight line bundles while less structured lines are de-emphasized. Moreover, the depth-dependent halos combined with depth cueing via line width attenuation increase depth perception, extending techniques from sparse line rendering to the illustrative visualization of dense line data. We demonstrate how the technique can be used, in particular, for illustrating DTI fiber tracts but also show examples from gas and fluid flow simulations and mathematics as well as describe how the technique extends to point data. We report on an informal evaluation of the illustrative DTI fiber tract visualizations with domain experts in neurosurgery and tractography who commented positively about the results and suggested a number of directions for future work.

BACKGROUND: A typical step in the analysis of gene expression data is the determination of clusters of genes that exhibit similar expression patterns. Researchers are confronted with the seemingly arbitrary choice between numerous algorithms to perform cluster analysis. RESULTS: We developed an exploratory application that benchmarks the results of clustering methods using functional annotations. In addition, a de novo DNA motif discovery algorithm is integrated in our program which identifies overrepresented DNA binding sites in the upstream DNA sequences of genes from the clusters that are indicative of sites of transcriptional control. The performance of our program was evaluated by comparing the original results of a time course experiment with the findings of our application. CONCLUSION: DISCLOSE assists researchers in the prokaryotic research community in systematically evaluating results of the application of a range of clustering algorithms to transcriptome data. Different performance measures allow to quickly and comprehensively determine the best suited clustering approach for a given dataset.

Abstract DNA microarrays are used to measure the expression levels of thousands of genes simultaneously. In a time series experiment, the gene expressions are measured as a function of time. We present an application for integrated visualization of genome expression and network dynamics in both regulatory networks and metabolic pathways. Integration of these two levels of cellular processes is necessary, since it provides the link between the measurements at the transcriptional level (gene expression levels approximated from microarray data) and the phenotype (the observable characteristics of an organism) at the functional and behavioral level. The integration requires visualization approaches besides traditional clustering and statistical analysis methods. Our application can (i) visualize the data from time series experiments in the context of a regulatory network and KEGG metabolic pathways; (ii) identify and visualize active regulatory subnetworks from the gene expression data; (iii) perform a statistical test to identify and subsequently visualize pathways that are affected by differentially expressed genes. We present a case study, which demonstrates that our approach and application both facilitates and speeds up data analysis tremendously in comparison to a more traditional approach that involves many manual, laborious, and error‐prone steps.

A general algorithm for computing Euclidean skeletons of 2D and 3D data sets in linear time is presented. These skeletons are defined in terms of a new concept, called the integer medial axis (IMA) transform. We prove a number of fundamental properties of the IMA skeleton, and compare these with properties of the CMD (centers of maximal disks) skeleton. Several pruning methods for IMA skeletons are introduced (constant, linear and square-root pruning) and their properties studied. The algorithm for computing the IMA skeleton is based upon the feature transform, using a modification of a linear-time algorithm for Euclidean distance transforms. The skeletonization algorithm has a time complexity which is linear in the number of input points, and can be easily parallelized. We present experimental results for several data sets, looking at skeleton quality, memory usage and computation time, both for 2D images and 3D volumes.

A common approach for visualizing data sets is to map them to images in which distinct data dimensions are mapped to distinct visual features, such as color, size and orientation. Here, we consider visualizations in which different data dimensions should receive equal weight and attention. Many of the end-user tasks performed on these images involve a form of visual search. Often, it is simply assumed that features can be judged independently of each other in such tasks. However, there is evidence for perceptual dependencies when simultaneously presenting multiple features. Such dependencies could potentially affect information visualizations that contain combinations of features for encoding information and, thereby, bias subjects into unequally weighting the relevance of different data dimensions. We experimentally assess (1) the presence of judgment dependencies in a visualization task (searching for a target node in a node-link diagram) and (2) how feature contrast relates to salience. From a visualization point of view, our most relevant findings are that (a) to equalize saliency (and thus bottom-up weighting) of size and color, color contrasts have to become very low. Moreover, orientation is less suitable for representing information that consists of a large range of data values, because it does not show a clear relationship between contrast and salience; (b) color and size are features that can be used independently to represent information, at least as far as the range of colors that were used in our study are concerned; (c) the concept of (static) feature salience hierarchies is wrong; how salient a feature is compared to another is not fixed, but a function of feature contrasts; (d) final decisions appear to be as good an indicator of perceptual performance as indicators based on measures obtained from individual fixations. Eye tracking, therefore, does not necessarily present a benefit for user studies that aim at evaluating performance in search tasks.

A typical data-driven visualization of electroencephalography (EEG) coherence is a graph layout, with vertices representing electrodes and edges representing significant coherences between electrode signals. A drawback of this layout is its visual clutter for multichannel EEG. To reduce clutter, we define a functional unit (FU) as a data-driven region of interest (ROI). An FU is a spatially connected set of electrodes recording pairwise significantly coherent signals, represented in the coherence graph by a spatially connected clique. Earlier we presented two methods to detect FUs: a maximal clique based (MCB) method (time complexity O(3n/3), with n being the number of vertices) and a more efficient watershed based (WB) method (time complexity O (n2 log n)). To reduce the potential over-segmentation of the WB method, we introduce here an improved WB (IWB) method (time complexity O(n2 log n)). The IWB method merges basins representing FUs during the segmentation if they are spatially connected and if their union is a clique. The WB and IWB methods are both up to a factor of 100,000 faster than the MCB method for a typical multichannel setting with 128 EEG channels, thus making interactive visualization of multichannel EEG coherence possible. Results show that considering the MCB method as the gold standard, the difference between IWB and MCB FU maps is smaller than between WB and MCB FU maps. We also introduce two novel group maps for data-driven group analysis as extensions of the IWB method. First, the group mean coherence map preserves dominant features from a collection of individual FU maps. Second, the group FU size map visualizes the average FU size per electrode across a collection of individual FU maps. Finally, we employ an extensive case study to evaluate the IWB FU map and the two new group maps for data-driven group analysis. Results, in accordance with the conventional findings, indicate differences in EEG coherence between younger and older adults. However, they also suggest that an initial selection of hypothesis-driven ROIs could be extended with additional data-driven ROIs.

Synchronous electrical activity in different brain regions is generally assumed to imply functional relationships between these regions. A measure for this synchrony is electroencephalography (EEG) coherence, computed between pairs of signals as a function of frequency. Existing high-density EEG coherence visualizations are generally either hypothesis-driven, or data-driven graph visualizations which are cluttered. In this paper, a new method is presented for data-driven visualization of high-density EEG coherence, which strongly reduces clutter and is referred to as functional unit (FU) map. Starting from an initial graph, with vertices representing electrodes and edges representing significant coherences between electrode signals, we define an FU as a set of electrodes represented by a clique consisting of spatially connected vertices. In an FU map, the spatial relationship between electrodes is preserved, and all electrodes in one FU are assigned an identical gray value. Adjacent FUs are visualized with different gray values and FUs are connected by a line if the average coherence between FUs exceeds a threshold. Results obtained with our visualization are in accordance with known electrophysiological findings. FU maps can be used as a preprocessing step for conventional analysis.

This paper is concerned with a multiresolution representation for maximum intensity projection (MIP) volume rendering based on morphological pyramids which allows progressive refinement. We consider two algorithms for progressive rendering from the morphological pyramid: one which projects detail coefficients level by level, and a second one, called streaming MIP, which resorts the detail coefficients of all levels simultaneously with respect to decreasing magnitude of a suitable error measure. The latter method outperforms the level-by-level method, both with respect to image quality with a fixed amount of detail data, and in terms of flexibility of controlling approximation error or computation time. We improve the streaming MIP algorithm, present a GPU implementation for both methods, and perform a comparison with existing CPU and GPU implementations.

Abstract Summary: FIVA (Function Information Viewer and Analyzer) aids researchers in the prokaryotic community to quickly identify relevant biological processes following transcriptome analysis. Our software assists in functional profiling of large sets of genes and generates a comprehensive overview of affected biological processes. Availability: http://bioinformatics.biol.rug.nl/standalone/fiva/ Contact: [email protected] Supplementary information: http://bioinformatics.biol.rug.nl/standalone/fiva/suppMaterials.php

In this paper, we describe a multiscale and multishape morphological method for pattern-based analysis and classification of gray-scale images using connected operators. Compared with existing methods, which use structuring elements, our method has three advantages. First, in our method, the time needed for computing pattern spectra does not depend on the number of scales or shapes used, i.e., the computation time is independent of the dimensions of the pattern spectrum. Second, size and strict shape attributes can be computed, which we use for the construction of joint 2D shape-size pattern spectra. Third, our method is significantly less sensitive to noise and is rotation-invariant. Although rotation invariance can also be approximated by methods using structuring elements at different angles, this tends to be computationally intensive. The classification performance of these methods is discussed using four image sets: Brodatz, COIL-20, COIL-100, and diatoms. The new method obtains better or equal classification performance to the best competitor with a 5 to 9-fold speed gain.

The Max-Tree designed for morphological attribute filtering in image processing, is a data structure in which the nodes represent connected components for all threshold levels in a data set. Attribute filters compute some attribute describing the shape or size of each connected component and then decide which components to keep or to discard. In this paper, we augment the basic Max-Tree data structure such that interactive volumetric filtering and visualization becomes possible. We introduce extensions that allow (1) direct, splatting-based, volume rendering; (2) representation of the Max-Tree on graphics hardware; and (3) fast active cell selection for isosurface generation. In all three cases, we can use the Max-Tree representation for visualization directly, without needing to reconstruct the volumetric data explicitly. We show that both filtering and visualization can be performed at interactive frame rates, ranging between 2.4 and 32 frames per seconds. In contrast, a standard texture-based volume visualization method manages only between 0.5 and 1.8 frames per second. For isovalue browsing, the experimental results show that the performance is comparable to the performance of an interval tree, where our method has the advantage that both filter threshold browsing and isolevel browsing are fast. It is shown that the methods using graphics hardware can be extended to other connected filters.

The field of visualization assists data interpretation in many areas, but does not manage all types of data equally well. This holds, in particular, for time-varying multichannel EEG data. No existing method can successfully visualize simultaneous information from all channels in use at all time steps. To address this problem, a new visualization method is presented based on the parallel coordinate method and making use of a tiled organization. This tiled organization employs a two-dimensional row-column representation, rather than a one-dimensional arrangement in columns as used for classical parallel coordinates. The usefulness of the new method, referred to as tiled parallel coordinates (TPC), is demonstrated by a particular type of EEG data. It can be applied to an arbitrary number of time steps, handling the maximum number of channels currently in use. An extensive user evaluation shows that, for a typical EEG assessment task, data evaluation by the TPC method is faster than by an existing clinical EEG visualization method, without loss of information. The generality of the TPC method makes it widely applicable to other time-varying multivariate data types.

We propose a novel, geometrically adaptive method for surface reconstruction from noisy and sparse point clouds, without orientation information. The method employs a fast convection algorithm to attract the evolving surface towards the data points. The force field in which the surface is convected is based on generalized Coulomb potentials evaluated on an adaptive grid (i.e., an octree) using a fast, hierarchical algorithm. Formulating reconstruction as a convection problem in a velocity field generated by Coulomb potentials offers a number of advantages. Unlike methods which compute the distance from the data set to the implicit surface, which are sensitive to noise due to the very reliance on the distance transform, our method is highly resilient to shot noise since global, generalized Coulomb potentials can be used to disregard the presence of outliers due to noise. Coulomb potentials represent long-range interactions that consider all data points at once, and thus they convey global information which is crucial in the fitting process. Both the spatial and temporal complexities of our spatially-adaptive method are proportional to the size of the reconstructed object, which makes our method compare favorably with respect to previous approaches in terms of speed and flexibility. Experiments with sparse as well as noisy data sets show that the method is capable of delivering crisp and detailed yet smooth surfaces.

We present a novel, physically-motivated method for surface reconstruction that can recover smooth surfaces from noisy and sparse data sets, without using orientation information. A new volumetric technique based on regularized-membrane potentials for aggregating the input sample points is introduced, which manages improved noise tolerability and outlier removal, without sacrificing much with respect to detail (feature) recovery. In this method, sample points are first aggregated on a volumetric grid. A labeling algorithm that relies on intrinsic properties of the smooth scalar field emerging after aggregation is used to classify grid points as exterior or interior to the surface. We also introduce a mesh-smoothing paradigm based on a mass-spring system, enhanced with a bending-energy minimizing term to ensure that the final triangulated surface is smoother than piecewise linear. The method compares favorably with respect to previous approaches in terms of speed and flexibility.

A multiscale, morphological method for the purpose of shape-based object recognition is presented. A connected operator similar to the morphological hat-transform is defined, and two scale-space representations are built, using the curvature function as the underlying one-dimensional signal. Each peak and valley of the curvature is extracted and described by its maximum and average heights and by its extent and represents an entry in the top or bottom hat-transform scale spaces. We demonstrate object recognition based on hat-transform scale spaces for three large data sets, a set of diatom contours, the set of silhouettes from the MPEG-7 database and the set of two-dimensional views of three-dimensional objects from the COIL-20 database. Our approach outperforms other methods for which comparative results exist.

The field of visualization assists data interpretation in many areas, but some types of data are not manageable by existing visualization techniques. This holds in particular for time-varying multichannel EEG data. No existing technique can simultaneously visualize information from all channels in use and all time steps. To address this problem, a new visualization technique is presented, based on the parallel coordinate method and making use of a tiled organization. This tiled organization employs a two-dimensional row-column representation, rather than a one-dimensional arrangement in columns as used for the classical parallel coordinates. The usefulness of the new method, referred to as tiled parallel coordinates, is demonstrated by one particular type of EEG data. It can be applied to an arbitrary number of time steps, for the maximum number of channels currently in use. The general setup of the method makes it widely applicable to other time-varying multivariate data types.

A novel, physically motivated deformable model for shape recovery and segmentation is presented. The model, referred to as the charged-particle model (CPM), is inspired by classical electrodynamics and is based on a simulation of charged particles moving in an electrostatic field. The charges are attracted towards the contours of the objects of interest by an electrostatic field, whose sources are computed based on the gradient-magnitude image. The electric field plays the same role as the potential forces in the snake model, while internal interactions are modeled by repulsive Coulomb forces. We demonstrate the flexibility and potential of the model in a wide variety of settings: shape recovery using manual initialization, automatic segmentation, and skeleton computation. We perform a comparative analysis of the proposed model with the active contour model and show that specific problems of the latter are surmounted by our model. The model is easily extendable to 3D and copes well with noisy images.

We present a general wavelet-based denoising scheme for functional magnetic resonance imaging (fMRI) data and compare it to Gaussian smoothing, the traditional denoising method used in fMRI analysis. One-dimensional WaveLab thresholding routines were adapted to two-dimensional (2-D) images, and applied to 2-D wavelet coefficients. To test the effect of these methods on the signal-to-noise ratio (SNR), we compared the SNR of 2-D fMRI images before and after denoising, using both Gaussian smoothing and wavelet-based methods. We simulated a fMRI series with a time signal in an active spot, and tested the methods on noisy copies of it. The denoising methods were evaluated in two ways: by the average temporal SNR inside the original activated spot, and by the shape of the spot detected by thresholding the temporal SNR maps. Denoising methods that introduce much smoothness are better suited for low SNRs, but for images of reasonable quality they are not preferable, because they introduce heavy deformations. Wavelet-based denoising methods that introduce less smoothing preserve the sharpness of the images and retain the original shapes of active regions. We also performed statistical parametric mapping on the denoised simulated time series, as well as on a real fMRI data set. False discovery rate control was used to correct for multiple comparisons. The results show that the methods that produce smooth images introduce more false positives. The less smoothing wavelet-based methods, although generating more false negatives, produce a smaller total number of errors than Gaussian smoothing or wavelet-based methods with a large smoothing effect.

In this paper we present a multiscale morphological method for use in texture classification. A connected operator similar to the morphological hat-transform is defined, and two scale-space representations are built. The most important features are extracted from the scale spaces by unsupervised cluster analysis, and the resulting pattern vectors provide the input of a decision tree classifier. We obtain 93.5 % correct classification for the Brodatz texture database.

We describe a multiresolution extension to maximum intensity projection (MIP) volume rendering, allowing progressive refinement and perfect reconstruction. The method makes use of morphological adjunction pyramids. The pyramidal analysis and synthesis operators are composed of morphological 3-D erosion and dilation, combined with dyadic downsampling for analysis and dyadic upsampling for synthesis. In this case the MIP operator can be interchanged with the synthesis operator. This fact is the key to an efficient multiresolution MIP algorithm, because it allows the computation of the maxima along the line of sight on a coarse level, before applying a two-dimensional synthesis operator to perform reconstruction of the projection image to a finer level. For interpolation and resampling of volume data, which is required to deal with arbitrary view directions, morphological sampling is used, an interpolation method well adapted to the nonlinear character of MIP. The structure of the resulting multiresolution rendering algorithm is very similar to wavelet splatting, the main differences being that (i) linear summation of voxel values is replaced by maximum computation, and (ii) linear wavelet filters are replaced by nonlinear morphological filters.

This paper is concerned with X-ray volume visualization by means of wavelet splatting, a wavelet-based extension to splatting. Wavelet splatting allows multiresolution visualization of volume data. During user interaction, only low resolution images are computed. When interaction ceases, the image is refined incrementally. We discuss a particular implementation of wavelet splatting which was proposed previously, and show that certain rendering artefacts appear in the low resolution images, due to the particular ordering of the wavelet coefficients. We propose a new variant that uses a different ordering, and computes low resolution images based on the wavelet approximation coefficients only. This variant does not suffer from artefacts, and is faster by a factor of two to three.

A method for shape analysis of diatoms (single-cell algae with silica shells) based on extraction of features on the contour of the cells by multi-scale mathematical morphology is presented. After building a morphological contour curvature scale space, we present a method for extracting the most prominent features by unsupervised cluster analysis. The number of extracted features matches well with those found visually in 92% of the 350 diatom images examined.

The watershed transform is the method of choice for image segmentation in the field of mathematical morphology. We present a critical review of several definitions of the watershed transform and the associated sequential algorithms, and discuss vario

We describe a wavelet based X-ray rendering method in the frequency domain with a smaller time complexity than wavelet splatting. Standard Fourier volume rendering is summarized and interpolation and accuracy issues are briefly discussed. We review the implementation of the fast wavelet transform in the frequency domain. The wavelet X-ray transform is derived, and the corresponding Fourier-wavelet volume rendering algorithm (FWVR) is introduced, FWVR uses Haar or B-spline wavelets and linear or cubic spline interpolation. Various combinations are tested and compared with wavelet splatting (WS). We use medical MR and CT scan data, as well as a 3-D analytical phantom to assess the accuracy, time complexity, and memory cost of both FWVR and WS. The differences between both methods are enumerated.

In this paper we show how the classical morphological definitions for Euclidean space can be extended to the sphere, where the rotation group replaces the Euclidean translation group. The main problem to overcome is the non-commutativity of the rotation group. Some examples of morphological transformations on the sphere are given. To visualize the results we use a projection of the sphere onto a plane.