HydraMarker: Efficient, Flexible, and Multifold Marker Field Generation.

An n-order marker field is a special binary matrix whose n×n subregions are all distinct from each other in four orientations. It is commonly used to guide the composing process of position-sensing markers, which can be detected and identified in a camera image with very limited scope or severe visibility problems. Despite the advantages, position-sensing markers are rare and overlooked because generating marker fields is difficult. In this article, we broaden the definition of marker field, making it more powerful and flexible. Then, we propose bWFC (binary wave function collapse) and its high-speed version, fast-bWFC, to solve the generation problem. The methods are packaged into an open-sourced toolkit named HydraMarker, with which, users not only can generate marker fields on laptops within a short period of time, but also can highly customize them: preset values; fields and subregions in any shape; multifold local uniqueness. Comparative results indicate that the proposed method has superior efficiency, quality, and capability. It makes marker field generation accessible to common marker designers, opening up more possibilities for fiducial markers.