In this letter, we propose an Edge-assisted adaptive heterogeneous resource allocation scheme based on atomic service chain (ASC) to jointly optimize adaptability for users, flexibility for networks, and profitability for providers. Particularly, we build an Edge-AI integrated computing power paradigm that integrates awareness, forwarding, storage, computing and processing capabilities. Moreover, we formulate the heterogeneous resource allocation problem into a non-linear non-convex integer optimization problem and propose an Edge-AI integrated ASC-based resource allocation approach for large-scale live video analytics to maximize average network utility with QoS support and minimize network congestion while considering the profitability. Experimental results demonstrate that the designed Edge-assisted ASC-based adaptive heterogeneous resource allocation approach outperforms the monolithic model-based scheme.