Legged robots need to make contact with irregular surfaces, when operating in unstructured natural terrains. Representing and perceiving these areas to reason about potential contact between a robot and its surrounding environment, is still largely an open problem. This paper introduces a new framework to model and map local rough terrain surfaces, for tasks such as bipedal robot foot placement. The system operates in real-time, on data from an RGB-D and an IMU sensor. We introduce a set of parametrized patch models and an algorithm to fit them in the environment. Potential contacts are identified as bounded curved patches of approximately the same size as the robot's foot sole. This includes sparse seed point sampling, point cloud neighborhood search, and patch fitting and validation. We also present a mapping and tracking system, where patches are maintained in a local spatial map around the robot as it moves. A bio-inspired sampling algorithm is introduced for finding salient contacts. We include a dense volumetric fusion layer for spatiotemporally tracking, using multiple depth data to reconstruct a local point cloud. We present experimental results on a mini-biped robot that performs foot placements on rocks, implementing a 3D foothold perception system, that uses the developed patch mapping and tracking framework.Index Terms-irregular surface modeling, foothold contact modeling, bounded curved patch modeling, curved patch fitting and tracking, 3D perception for bipedal robots, bipedal robot foot placement, rough terrain stepping, legged robot locomotion ! • Dimitrios Kanoulas and Nikos G. Tsagarakis are with the Humanoids and