In the event of natural or man-made disasters, geospatial video analytics is valuable to provide situational awareness that can be extremely helpful for first responders. However, geospatial video analytics demands massive imagery/video data 'collection' from Internet-of-Things (IoT) and their seamless 'computation/consumption' within a geo-distributed (edge/core) cloud infrastructure in order to cater to user Quality of Experience (QoE) expectations. Thus, the edge computing needs to be designed with a reliable performance while interfacing with the core cloud to run computer vision algorithms. This is because infrastructure edges near locations generating imagery/video content are rarely equipped with high-performance computation capabilities. This thesis addresses challenges of interfacing edge and core cloud computing within the geo-distributed infrastructure as a novel 'function-centric computing' paradigm that brings new insights to computer vision, edge routing and network virtualization areas. Specifically, we detail the state-of-the-art techniques and illustrate our new/improved solution approaches based on function-centric computing for the two problems of: (i) high-throughput data collection from IoT devices at the wireless edge, and (ii) seamless data computation/consumption within the geo-distributed (edge/core) cloud infrastructure. To address (i), we present a novel deep learning-augmented geographic edge routing that relies on physical area knowledge obtained from satellite imagery. To address (ii), we describe a novel reliable service chain orchestration framework that builds upon microservices and utilizes a novel 'metapath composite variable' approach supported by a constrained-shortest path finder. Finally, we show both analytically and empirically, how our geographic routing, constrained shortest path finder and reliable service chain orchestration approaches that compose our function-centric computing framework are superior than many traditional and state-of-the-art techniques. As a result, we can significantly speedup (up to 4 times) data-intensive computing at infrastructure edges fostering effective disaster relief coordination to save lives.