## 1 Introduction  
A honeybee (_Apis mellifera_) colony consists of female worker bees, male bees (drones), and a single queen [1]. The number of worker bees varies with the season from 10,000 to 40,000. The number of drones also depends on the season and ranges from zero to several hundred. Each colony has a structured division of labor [2]. The queen is the only reproductive female in the colony. Her main duty is to propagate the species by laying eggs. When the queen is several days old, she takes flight to mate in the air with drones from other hives. When she returns to the hive, she remains fertilized for three to four years. A prolific queen may lay up to 3000 eggs per day [1]. The drones are male bees. They have no sting and no means of gathering nectar, secreting wax, or bringing water. Their sole role is to mate with queens on their bridal trip and instantly die in the act of copulation. Only one in a thousand gets a chance to mate [1]. All day-to-day colony work is done by the female worker bees. When workers emerge from their cells, they start cleaning cells in the brood nest. After a week, they feed and nurse larvae. The nursing assignment lasts one or two weeks and is followed by other duties such as cell construction, receiving nectar from foragers, and guarding the hive's entrance. In their third or fourth week, the female bees become foragers. There are three kinds of foragers: nectar foragers, pollen foragers, and water foragers. Page [3] argued that pollen foraging is a function of the number of cells without pollen encountered on the boundary cells and the pollen cells. Thus, if a forager encounters more empty pollen cells than some value representative of her response threshold, she leaves the hive for another pollen load. If, on the other hand, she encounters fewer empty cells, she stops foraging for pollen and engages in nectar or water foraging. The foragers live 5-6 weeks and do not perform their previous duties within the hive. The well-being of a honeybee colony in a hive critically depends on robust forager traffic. Repeated discrepancies or disruptions in forager traffic indicate that the hive may not be healthy. Thus, accurate measurement of honeybee traffic in the vicinity of the hive is fundamental for electronic beehive monitoring (EBM) systems that continuously monitor honeybee colonies to detect and report deviations from the norm. Our EBM research (e.g., [4; 5; 6]), during which we watched hundreds of field-captured honeybee traffic videos of three different bee races (Carniolan, Italian, and Buckfast), leads us to the conclusion that honeybee traffic in the vicinity of a [PERSON] hive [7] can be divided into three distinct classes: _incoming_, _outgoing_, and _lateral_. Incoming traffic consists of bees entering the hive either through the landing pad or holes drilled in supers. Outgoing traffic consists of bees leaving the hive either from the landing pad or from holes drilled in supers. Lateral traffic consists of bees flying more or less in parallel to the front side of the hive (i.e., the side with the landing pad). We refer to these three types of traffic as _directional_ traffic and juxtapose it with _omnidirectional_ traffic [6] where bee motions are detected regardless of direction. In this investigation, we contribute to the body of research on insect and animal flight by presenting a bee motion estimation algorithm based on digital particle image velocimetry (DPIV) [8] to measure levels of directional honeybee traffic in the vicinity of a Langstroh hive. The algorithm does not compute honeybee flight paths or trajectories, which, as our longitudinal field deployment convinced us [4; 6], is feasible only at very low levels of honeybee traffic. Rather, the proposed method uses DPIV to compute motion vectors, analytically classifies them as incoming, outgoing, or lateral, and uses the classified vector counts to measure directional honeybee traffic. The remainder of our article is organized as follows.