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Many techniques exist for adapting videos to satisfy heterogeneous resource conditions or user preferences. However, selections of appropriate adaptations among various choices are often ad hoc. To provide a systematic solution, we present a general conceptual framework to model video entity, adaptation, resource, utility, and relations among them. The framework extends the conventional rate-distortion model in terms of flexibility and generality. It allows for formulations of various adaptation problems as resource-constrained utility maximization. It also facilitates new approaches to predicting critical information about resource-utility relations. We apply the framework to a practical case in dynamic bit rate adaptation. Furthermore, we present a description tool, which has been accepted as a part of the MPEG-21 digital item adaptation (DIA), to support utility-based adaptation.