In the event of natural or man-made disasters, providing rapid situational awareness through video/image data collected at salient incident scenes is often critical to the first responders. However, computer vision techniques that can process the media-rich and data-intensive content obtained from civilian smartphones or surveillance cameras require large amounts of computational resources or ancillary data sources that may not be available at the geographical location of the incident. In this paper, we propose an incident-supporting visual cloud computing solution by defining a collection, computation, and consumption (3C) architecture supporting fog computing at the network edge close to the collection/consumption sites, which is coupled with cloud offloading to a core computation, utilizing software-defined networking (SDN). We evaluate our 3C architecture and algorithms using realistic virtual environment test beds. We also describe our insights in preparing the cloud provisioning and thin-client desktop fogs to handle the elasticity and user mobility demands in a theater-scale application. In addition, we demonstrate the use of SDN for on-demand compute offload with congestion-avoiding traffic steering to enhance remote user quality of experience in a regional-scale application. The optimization between fogs computing at the network edge with core cloud computing for managing visual analytics reduces latency, congestion, and increases throughput.