Automatic label placement

Abstract: A major factor affecting the clarity of graphical displays that include text labels is the degree to which labels obscure display features (including other labels) as a result of spatial overlap. Point-feature label placement (PFLP) is the problem of placing text labels adjacent to point features on a map or diagram so as to maximize legibility. This problem occurs frequently in the production of many types of informational graphics, though it arises most often in automated cartography. In this paper we present a comprehensive treatment of the PFLP problem, viewed as a type of combinatorial optimization problem. Complexity analysis reveals that the basic PFLP problem and most interesting variants of it are NP-hard. These negative results help inform a survey of previously reported algorithms for PFLP; not surprisingly, all such algorithms either have exponential time complexity or are incomplete. To solve the PFLP problem in practice, then, we must rely on good heuristic methods. We propose two new methods, one based on a discrete form of gradient descent, the other on simulated annealing, and report on a series of empirical tests comparing these and the other known algorithms for the problem. Based on this study, the first to be conducted, we identify the best approaches as a function of available computation time.

Abstract: We examine the computational complexity of cartographic label placement, a problem derived from the cartographer's task of placing text labels adjacent to map features in such a way as to minimize overlaps with other labels and map features. Cartographic label placement is one of the most time-consuming tasks in the production of maps. Consequently, several attempts have been made to automate the label-placement task for some or all classes of cartographic features (punctual, linear, or areal features), but all previously published algorithms for the most basic task|point-feature-label placement| either exhibit worst-case exponential time complexity, or incorporate incomplete heuristics that may fail to nd an admissible labeling even when one exists. The computational complexity of label placement is therefore a matter of practical signi cance in automated cartography. We show that admissible label placement is NP-complete, even for very simple versions of the problem. Thus, no polynomial time algorithm exists unless P = NP . Similarly, we show that optimal label placement can be solved in polynomial time if and only if P = NP , and this result holds even if we require only approximately optimal placements. The results are especially interesting because cartographic label placement is one of the few combinatorial problems that remains NP-hard even under a geometric (Euclidean) interpretation. The results are of broader practical signi cance, as they also apply to point-feature labeling in non-cartographic displays, e.g., the labeling of points in a scatter plot.

Abstract: View management, a relatively new area of research in Augmented Reality (AR) applications, is about the spatial layout of 2D virtual annotations in the view plane. This paper represents the first study in an actual AR application of a specific view management task: evaluating the placement of 2D virtual labels that identify information about real counterparts. Here, we objectively evaluated four different placement algorithms, including a novel algorithm for placement based on identifying existing clusters. The evaluation included both a statistical analysis of traditional metrics (e.g. counting overlaps) and an empirical user study guided by principles from human cognition. The numerical analysis of the three real-time algorithms revealed that our new cluster-based method recorded the best average placement accuracy while requiring only relatively moderate computation time. Measures of objective readability from the user study demonstrated that in practice, human subjects were able to read labels fastest with the algorithms that most quickly prevented overlap, even if placement wasn't ideal.

Abstract: Partial label learning aims to learn from training examples each associated with a set of candidate labels, among which only one label is valid for the training example. The basic strategy to learn from partial label examples is disambiguation, i.e. by trying to recover the ground-truth labeling information from the candidate label set. As one of the popular machine learning paradigms, maximum margin techniques have been employed to solve the partial label learning problem. Existing attempts perform disambiguation by optimizing the margin between the maximum modeling output from candidate labels and that from non-candidate ones. Nonetheless, this formulation ignores considering the margin between the ground-truth label and other candidate labels. In this paper, a new maximum margin formulation for partial label learning is proposed which directly optimizes the margin between the ground-truth label and all other labels. Specifically, the predictive model is learned via an alternating optimization procedure which coordinates the task of ground-truth label identification and margin maximization iteratively. Extensive experiments on artificial as well as real-world datasets show that the proposed approach is highly competitive to other well-established partial label learning approaches.