Abstract : Graphs change over time, and typically variations on the small multiples or animation pattern is used to convey this dynamism visually. However, both of these classical techniques have significant drawbacks, so a new approach, Storyline Visualization of Events on a Network (SVEN) is proposed. SVEN builds on storyline techniques, conveying nodes as contiguous lines over time. SVEN encodes time in a natural manner, along the horizontal axis, and optimizes the vertical placement of storylines to decrease clutter (line crossings, straightness, and bends) in the drawing. This paper demonstrates SVEN on several different flavors of real-world dynamic data, and outlines the remaining near-term future work.
Visibility representations, which have existed since the mid 1980s, are also visually similar to storylines @cite_3 . These are representations of planar graphs where nodes are drawn as horizontal lines, and edges are drawn as vertical lines connecting their endpoints. Node-edge crossings are not allowed, so non-planar graphs do not have visibility representations. Due to this constraint, it is not apparent how visibility representations can be used as a general purpose solution for the dynamic graph visualization problem. Nor is it apparent how to overload the horizontal axis in a visibility representation to also encode time.
@cite_3
2039512408 1970022459 2416791088 2039204626
We studyvisibility representations of graphs, which are constructed by mapping vertices to horizontal segments, and edges to vertical segments that intersect only adjacent vertex-segments. Every graph that admits this representation must be planar. We consider three types of visibility representations, and we give complete characterizations of the classes of graphs that admit them. Furthermore, we present linear time algorithms for testing the existence of and constructing visibility representations of planar graphs. Many applications of our results can be found in VLSI layout. It has been known for some time that larger graphs can be interpreted if laid out in 3D and displayed with stereo and or motion depth cues to support spatial perception. However, prior studies were carried out using displays that provided a level of detail far short of what the human visual system is capable of resolving. Therefore, we undertook a graph comprehension study using a very high resolution stereoscopic display. In our first experiment, we examined the effect of stereoscopic display, kinetic depth, and using 3D tubes versus lines to display the links. The results showed a much greater benefit for 3D viewing than previous studies. For example, with both motion and stereoscopic depth cues, unskilled observers could see paths between nodes in 333 node graphs with less than a 10p error rate. Skilled observers could see up to a 1000-node graph with less than a 10p error rate. This represented an order of magnitude increase over 2D display. In our second experiment, we varied both nodes and links to understand the constraints on the number of links and the size of graph that can be reliably traced. We found the difference between number of links and number of nodes to best account for error rates and suggest that this is evidence for a “perceptual phase transition.” These findings are discussed in terms of their implications for information display. In this paper, we explore various aspects of fusing LIDAR and color imagery for pedestrian detection in the context of convolutional neural networks (CNNs), which have recently become state-of-art for many vision problems. We incorporate LIDAR by up-sampling the point cloud to a dense depth map and then extracting three features representing different aspects of the 3D scene. We then use those features as extra image channels. Specifically, we leverage recent work on HHA [9] (horizontal disparity, height above ground, and angle) representations, adapting the code to work on up-sampled LIDAR rather than Microsoft Kinect depth maps. We show, for the first time, that such a representation is applicable to up-sampled LIDAR data, despite its sparsity. Since CNNs learn a deep hierarchy of feature representations, we then explore the question: At what level of representation should we fuse this additional information with the original RGB image channels? We use the KITTI pedestrian detection dataset for our exploration. We first replicate the finding that region-CNNs (R-CNNs) [8] can outperform the original proposal mechanism using only RGB images, but only if fine-tuning is employed. Then, we show that: 1) using HHA features and RGB images performs better than RGB-only, even without any fine-tuning using large RGB web data, 2) fusing RGB and HHA achieves the strongest results if done late, but, under a parameter or computational budget, is best done at the early to middle layers of the hierarchical representation, which tend to represent midlevel features rather than low (e.g. edges) or high (e.g. object class decision) level features, 3) some of the less successful methods have the most parameters, indicating that increased classification accuracy is not simply a function of increased capacity in the neural network. Let S be a set of n non-intersecting line segments in the plane. The visibility graph G S of S is the graph that has the endpoints of the segments in S as nodes and in which two nodes are adjacent whenever they can “see” each other (i.e., the open line segment joining them is disjoint from all segments or is contained in a segment). Two new methods are presented to construct G S . Both methods are very simple to implement. The first method is based on a new solution to the following problem: given a set of points, for each point sort the other points around it by angle. It runs in time O( n 2 ). The second method uses the fact that visibility graphs often are sparse and runs in time O( m log n ) where m is the number of edges in G S . Both methods use only Ogr;( n ) storage.