Question

Given an image and a set of labels attached to particular points on the image, I’m looking for an algorithm to lay out the labels to the sides of the image with certain constraints (roughly same number of labels on each side, labels roughly equidistant, lines connecting the labels to their respective points with no lines crossing).

Now, an approximate solution can typically be found quite naively by ordering the labels by Y coordinate (of the point they refer to), as in this example (proof of concept only, please ignore accuracy or otherwise of actual data!).

Now to satisfy the condition of no crossings, some ideas that occurred to me:

• use a genetic algorithm to find an ordering of labels with no crossovers;
• use another method (e.g. dynamic programming algorithm) to search for such an ordering;
• use one of the above algorithms, allowing for variations in the spacing as well as ordering, to find the solution that minimises number of crossings and variation from even spacing;
• maybe there are criteria I can use to brute search through every possible ordering of the labels within certain criteria (do not re-order two labels if their distance is greater than X);
• if all else fails, just try millions of random orderings/spacing offsets and take the one that gives the minimum crossings/spacing variation. (Advantage: straightforward to program and will probably find a good enough solution; slight disadvantage, though not a show-stopper: maybe can’t then run it on the fly during the application to allow user to change layout/size of the image.)

Before I embark on one of these, I would just welcome some other people’s input: has anybody else experience with a similar problem and have any information to report on the success/failure of any of the above methods, or if they have a better/simpler solution that isn’t occurring to me? Thanks for your input!

Answer 1

Lucas Bradsheet’s honours thesis Labelling Maps using Multi-Objective Evolutionary Algorithms has quite a good discussion of this.

First off, this paper creates usable metrics for a number of metrics of labelling quality.

For example, clarity (how obvious the mapping between sites and labels was): clarity(s)=r_s+r_s^1/r_t
where r_s is the distance between a site and its label and r_t is the distance between a site and there closest other label).

It also has useful metrics for the conflicts between labels, sites and borders, as well as for measuring the density and symmetry of labels. Bradsheet then uses a multiple objective genetic algorithm to generate a “Pareto frontier” of feasible solutions. It also includes information about how he mutated the individuals, and some notes on improving the speed of the algorithm.

There’s a lot of detail in it, and it should provide some good food for thought.