Geofences have attracted significant attention in the design of spatial and virtual regions for managing and engaging spatiotemporal events. By using geofences to monitor human activity across their boundaries, content providers can create spatially triggered events that include notifications about points of interest within a geofence by pushing spatial information to the devices of users. Traditionally, geofences were hand-crafted by providers. In addition to the hand-crafted approach, recent advances in collecting human mobility data through mobile devices can accelerate the automatic and data-driven design of geofences, also known as the geofence design problem. Previous approaches assume circular shapes; thus, their flexibility is insufficient, and they can only handle geofence-based applications for large areas with coarse resolutions. A challenge with using circular geofences in urban and high-resolution areas is that they often overlap and fail to align with political district boundaries and road segments, such as one-way streets and median barriers. In this study, we address the problem of extracting arbitrary shapes as geofences from human mobility data to mitigate this problem. In our formulation, we cast the existing optimization problems for circular geofences to 0-1 integer programming problems to represent arbitrary shapes. Although 0-1 integer programming problems are computationally hard, formulating them as quadratic (unconstrained) binary optimization problems enables efficient approximation of optimal solutions, because this allows the use of specialized quadratic solvers, such as the quantum annealing, and other state-of-the-art algorithms. We then develop and compare different formulation methods to extract discrete geofences. We confirmed that our new modeling approach enables flexible geofence design.