When robotic systems are deployed in the real world, they demand advanced mobility capabilities to operate in complex, three-dimensional environments designed for human use, e.g., multi-level buildings. Staircases have been an integral part of facilitating vertical movement in these three-dimensional environments. This work presents a novel method that enables mobile robots to locate and autonomously climb a range of different staircases. We develop a staircase detection algorithm that exploits viewpoints in a point cloud, making it possible to quickly detect staircases and estimate their physical parameters. Further, the algorithm can validate the number of traversable steps in the staircase by using a simple density metric to look for obstacles or damage. This staircase perception system runs on heterogeneous platforms in real-time that can each detect staircases and merge the detections. We present results wherein a wheeled robot works with a quadrupedal system to detect different staircases quickly. The performance of this staircase detection system is compared to the current state-of-the-art detection algorithm. We show that our approach significantly increases the speed of detections by two orders of magnitude without compromising the accuracy of parameter estimation.