Hsiang-Yun Wu

Optimized Topological Surgery for Unfolding 3D Meshes

Constructing a 3D papercraft model from its unfolding has been fun for both children and adults since we can reproduce virtual 3D models in the real world. However, facilitating the papercraft construction process is still a challenging problem, especially when the shape of the input model is complex in the sense that it has large variation in its surface curvature. This paper presents a new heuristic approach to unfolding 3D triangular meshes without any shape distortions, so that we can construct the 3D papercraft models through simple atomic operations for gluing boundary edges around the 2D unfoldings. Our approach is inspired by the concept of topological surgery, where the appearance of boundary edges of the unfolded closed surface can be encoded using a symbolic representation. To fully simplify the papercraft construction process, we developed a genetic‐based algorithm for unfolding the 3D mesh into a single connected patch in general, while optimizing the usage of the paper sheet and balance in the shape of that patch. Several examples together with user studies are included to demonstrate that the proposed approach works well for a broad range of 3D triangular meshes.

A zone-based approach for placing annotation labels on metro maps

Hand-drawn metro map illustrations often employ both internal and external labels in a way that they can assign enough information such as textual and image annotations to each landmark. Nonetheless, automatically tailoring the aesthetic layout of both textual and image labels together is still a challenging task, due to the complicated shape of the labeling space available around the metro network. In this paper, we present a zone-based approach for placing such annotation labels so that we can fully enhance the aesthetic criteria of the label arrangement. Our algorithm begins by decomposing the map domain into three different zones where we can limit the position of each label according to its type. The optimal positions of labels of each type are evaluated by referring to the zone segmentation over the map. Finally, a new genetic-based approach is introduced to compute the optimal layout of such annotation labels, where the order in which the labels are embedded into the map is improved through the evolutional computation algorithm. We also equipped a semantic zoom functionality, so that we can freely change the position and scale of the metro map.

Spatially efficient design of annotated metro maps

Annotating metro maps with thumbnail photographs is a commonly used technique for guiding travelers. However, conventional methods usually suffer from small labeling space around the metro stations especially when they are interchange stations served by two or more metro lines. This paper presents an approach for aesthetically designing schematic metro maps while ensuring effective placement of large annotation labels that are sufficiently close to their corresponding stations. Our idea is to distribute such labels in a well‐balanced manner to labeling regions around the metro network first and then adjust the lengths of metro line and leader line segments, which allows us to fully maximize the space coverage of the entire annotated map. This is accomplished by incorporating additional constraints into the conventional mixed‐integer programming formulation, while we devised a three‐step algorithm for accelerating the overall optimization process. We include several design examples to demonstrate the spatial efficiency of the map layout generated using the proposed approach through minimal user intervention.

Travel-Route-Centered Metro Map Layout and Annotation

When providing travel guides for a specific route in a metro network, we often place the route around the center of the map and annotate stations on the route with thumbnail photographs. Nonetheless, existing methods do not offer an effective means of customizing the network layout in order to accommodate such large annotation labels while preserving its planar embedding. This paper presents a new approach for designing the metro map layout in order to annotate stations on a specific travel route with large annotation labels. Our idea is to elongate the travel route to be straight along the centerline of the map so that we can systematically annotate such stations with external labels. This is accomplished by extending the conventional mixed‐integer programming technique for computing octilinear layouts where orientations inherent to the metro line segments are plausibly rearranged. The stations are then connected with external labels through leaders while minimizing intersections with metro lines for enhancing visual clarity. We present several design examples of metro maps and user studies to demonstrate that the proposed aesthetic criteria successfully direct viewers’ attention to specific travel routes.

Spectral-Based Contractible Parallel Coordinates

Parallel coordinates is well-known as a popular tool for visualizing the underlying relationships among variables in high-dimension datasets. However, this representation still suffers from visual clutter arising from intersections among poly line plots especially when the number of data samples and their associated dimension become high. This paper presents a method of alleviating such visual clutter by contracting multiple axes through the analysis of correlation between every pair of variables. In this method, we first construct a graph by connecting axis nodes with an edge weighted by data correlation between the corresponding pair of dimensions, and then reorder the multiple axes by projecting the nodes onto the primary axis obtained through the spectral graph analysis. This allows us to compose a dendrogram tree by recursively merging a pair of the closest axes one by one. Our visualization platform helps the visual interpretation of such axis contraction by plotting the principal component of each data sample along the composite axis. Smooth animation of the associated axis contraction and expansion has also been implemented to enhance the visual readability of behavior inherent in the given high-dimensional datasets.

Constrained optimization for disoccluding geographic landmarks in 3D urban maps

In composing hand-drawn 3D urban maps, the most common design problem is to avoid overlaps between geographic features such as roads and buildings by displacing them consistently over the map domain. Nonetheless, automating this map design process is still a challenging task because we have to maximally retain the 3D depth perception inherent in pairs of parallel lines embedded in the original layout of such geographic features. This paper presents a novel approach to disoccluding important geographic features when creating 3D urban maps for enhancing their visual readability. This is accomplished by formulating the design criteria as a constrained optimization problem based on the linear programming approach. Our mathematical formulation allows us to systematically eliminate occlusions of landmark roads and buildings, and further controls the degree of local 3D map deformation by devising an objective function to be minimized. Various design examples together with a user study are presented to demonstrate the robustness and feasibility of the proposed approach.

Manipulating Bilevel Feature Space for Category-Aware Image Exploration

The demand for interactively designing the image feature space has been increasing due to the ongoing need for image retrieval, recognition, and labeling. Although conventional methods provide an interface for locally rearranging such a feature space, category-level global manipulation is still missing and thus manually rearranging the overall image categorization usually requires a time-consuming task. This paper presents a novel approach to exploring images in the database through the manipulation of bi-level feature space representations, where the upper-and lower-level representations characterize the global categories and local features of the images, respectively. In this approach, the upper-level space describes similarity relationship among the underlying categories extracted from the bag-of-features model, while the lower-level space encodes the closeness between a pair of images within the same category. The key idea behind this approach is to associate the relationship between the two feature spaces with a two-layered graph representation and project it onto 2D screen space using pivot MDS for user manipulation. Experimental results are provided to demonstrate that our approach allows users to understand the entire structure of the given image dataset and reorganize the layout according to their preference both locally and globally.

Visualizing Multivariate Data Using Singularity Theory

This is a survey article on recent developments in visualization of large data, especially that of multivariate volume data. We present two essential ingredients. The first one is the mathematical background, especially the singularity theory of differentiable mappings, which enables us to capture topological features of given multivariate data in a mathematically rigorous way. The second one is a new development in computer science, called the joint contour net, which can encode topological structures of a given set of multivariate data in an efficient and robust way. Some applications to real data analysis are also presented.

Voronoi-Based Label Placement for Metro Maps

Metro maps with thumbnail photographs serve as common travel guides for providing sufficient information to meet the requirements of travelers in the cities. However, conventional methods attempt to minimize the total distance between stations and labels while maximizing the number of the labels rather than further taking into account the overall balance of the spatial distribution of labels. This paper presents an entropy-based approach for effectively annotating large annotation labels sufficiently close to the metro stations. Our idea is to decompose the entire labeling space intro regions bounded by the metro lines, and then further partition each region into Voronoi cells, each of which is reserved for a station to be annotated. This is accomplished by incorporating a new genetic-based optimization, while the fitness of the decomposition is evaluated by the entropy of the relative coverage ratios of such Voronoi cells. We also include several design examples to demonstrate that the proposed approach successfully distributes large labels around the metro network with minimal user intervention.

Interactively Uncluttering Node Overlaps for Network Visualization

Visual interaction with networks have been promising in the sense that we can successfully elucidate underlying relationships hidden behind complicated mutual relationships such as co-authorship networks, product co purchasing networks, and scale-free social networks. However, it is still burdensome to alleviate visual clutter arising from overlaps among node labels especially in such interactive environments as the networks become dense in terms of the topological connectivity. This paper presents a novel approach for dynamically rearranging the network layouts by incorporating centroidal Voronoi tessellation for better readability of node labels. Our idea is to smoothly transform the network layouts obtained through the conventional force-directed algorithm to that produced by the centroidal Voronoi tessellation to seek a plausible compromise between them. We also incorporated the Chebyshev distance metric into the centroidal Voronoi tessellation while adaptively adjusting the aspect ratios of the Voronoi cells so that we can place rectangular labels compactly over the network nodes. Finally, we applied the proposed approach to relatively large networks to demonstrate the feasibility of our formulation especially in interactive environments.