We present a method for tracking regions defined by Merge trees in time-dependent scalar fields. We build upon a recently published method that computes a directed acyclic graph (DAG) from local tracking information such as overlap and similarity, and tracks a single region by solving a shortest path problem in the DAG. However, the existing method is only able to track one selected region. Tracking all regions is not straightforward: the naïve version, tracking regions one by one, is very slow. We present a fast method here that tracks all regions at once. We showcase speedups of up to two orders of magnitude.

Goal directed agent navigation in crowd simulations involves a complex decision making process. An agent must avoid all collisions with static or dynamic obstacles (such as other agents) and keep a trajectory faithful to its target at the same time. This seemingly global optimization problem can be broken down into smaller local optimization problems by looking at a concept of criticality. Our method resolves critical agents - agents that are likely to come within collision range of each other - in order of priority using a Particle Swarm Optimization scheme. The resolution involves altering the velocities of agents to avoid criticality. Results from our method show that the navigation problem can be solved in several important test cases with minimal number of collisions and minimal deviation to the target direction. We prove the efficiency and correctness of our method by comparing it to four other well-known algorithms, and performing evaluations on them based on various quality measures.

We provide an initial model and preliminary findings of a lookahead based local optimization scheme for collision resolution between agents in large goal-directed crowd simulations. Considering crowd simulation to be a global optimization problem, we break down this large problem into smaller problems where each potential collision resolution step is independently optimized in terms of a criticality measure. Agents resolved earlier in order of criticality, maintain the optimized velocity obtained, for the resolution of agents that come later in that order. Hence, the problem is converted to a low dimensional optimization problem of one or two agents where all other obstacles are static or deterministically dynamic. We illustrate the performance of our method on four well known test scenarios.

Mixed reality offers new potentials for social interaction experiences with virtual agents. In addition, it can be used to experiment with the design of physical robots. However, while previous studies have investigated comfortable social distances between humans and artificial agents in real and virtual environments, there is little data with regards to mixed reality environments. In this paper, we conducted an experiment in which participants were asked to walk up to an agent to ask a question, in order to investigate the social distances maintained, as well as the subject's experience of the interaction. We manipulated both the embodiment of the agent (robot vs. human and virtual vs. physical) as well as closed vs. open posture of the agent. The virtual agent was displayed using a mixed reality headset. Our experiment involved 35 participants in a within-subject design. We show that, in the context of social interactions, mixed reality fares well against physical environments, and robots fare well against humans, barring a few technical challenges.

Mixed reality, which seeks to better merge virtual objects and theirinteractions with the real environment, offers numerous potentialsfor the improved design of robots and our interactions with them. Inthis paper, we present our ongoing work towards the developmentof a mixed reality platform for designing social interactions withrobots through the use of virtual robots. We present a summaryour work thus far on the use of the platform for investigatingproxemics between humans and virtual robots, and also highlightfuture research directions. These include the consideration of moresophisticated interactions involving verbal behaviours, interactionwith small formations of virtual robots, better integration of virtualobjects into real environments and experiments comparing the realsystems with their virtual counterparts.

Pedestrian trajectory prediction is a challenging problem. One of the aspects that makes it so challenging is the fact that the future positions of an agent are not only determined by its previous positions, but also by the interaction of the agent with its neighbors. Previous methods, like Social Attention have considered the interactions with all agents as neighbors. However, this ends up assigning high attention weights to agents who are far away from the queried agent and/or moving in the opposite direction, even though, such agents might have little to no impact on the queried agent’s trajectory. Furthermore, trajectory prediction of a queried agent involving all agents in a large crowded scenario is not efficient. In this paper, we propose a novel approach for selecting neighbors of an agent by modeling its perception as a combination of a location and a locomotion model. We demonstrate the performance of our method by comparing it with the existing state-of-the-art method on publicly available data-sets. The results show that our neighbor selection model overall improves the accuracy of trajectory prediction and enables prediction in scenarios with large numbers of agents in which other methods do not scale well.

We present an algorithm for tracking regions in time-dependent scalar fields that uses global knowledge from all time steps for determining the tracks. The regions are defined using merge trees, thereby representing a hierarchical segmentation of the data in each time step. The similarity of regions of two consecutive time steps is measured using their volumetric overlap and a histogram difference. The main ingredient of our method is a directed acyclic graph that records all relevant similarity information as follows: the regions of all time steps are the nodes of the graph, the edges represent possible short feature tracks between consecutive time steps, and the edge weights are given by the similarity of the connected regions. We compute a feature track as the global solution of a shortest path problem in the graph. We use these results to steer the - to the best of our knowledge - first algorithm for spatio-temporal feature similarity estimation. Our algorithm works for 2D and 3D time-dependent scalar fields. We compare our results to previous work, showcase its robustness to noise, and exemplify its utility using several real-world data sets.

Similarity estimation in scalar fields using level set topology has attracted a lot of attention in the recent past. Most existing techniques match parts of contour or merge trees against each other by estimating a best overlap between them. Due to their combinatorial nature, these methods can be computationally expensive or prone to instabilities. In this paper, we use an inexpensive feature descriptor to compare subtrees of merge trees against each other. It is the data histogram of the voxels encompassed by a subtree. A small modification of the merge tree computation algorithm allows for obtaining these histograms very efficiently. Furthermore, the descriptor is robust against instabilities in the merge tree. The method is useful in an interactive environment, where a user can search for all structures similar to an interactively selected one. Our method is conservative in the sense that it finds all similar structures, with the rare occurrence of some false positives. We show with several examples the effectiveness, efficiency and accuracy of our method.

We present a method to find repeating topological structures in scalar data sets. More precisely, we compare all subtrees of two merge trees against each other - in an efficient manner exploiting redundancy. This provides pair-wise distances between the topological structures defined by sub/superlevel sets, which can be exploited in several applications such as finding similar structures in the same data set, assessing periodic behavior in time-dependent data, and comparing the topology of two different data sets. To do so, we introduce a novel data structure called the extended branch decomposition graph, which is composed of the branch decompositions of all subtrees of the merge tree. Based on dynamic programming, we provide two highly efficient algorithms for computing and comparing extended branch decomposition graphs. Several applications attest to the utility of our method and its robustness against noise.