Modern embedded systems consist of heterogeneous computing resources with diverse energy and performance trade-offs. This is because these resources exercise the application tasks differently, generating varying workloads and energy consumption. As a result, minimizing energy consumption in these systems is challenging as continuous adaptation between application task mapping (i.e. allocating tasks among the computing resources) and dynamic voltage/frequency scaling (DVFS) is required. Existing approaches have limitations due to lack of such adaptation with practical validation (Table I). This paper addresses such limitation and proposes a novel adaptive energy minimization approach for embedded heterogeneous systems. Fundamental to this approach is a runtime model, generated through regression-based learning of energy/performance trade-offs between different computing resources in the system. Using this model, an application task is suitably mapped on a computing resource during runtime, ensuring minimum energy consumption for a given application performance requirement. Such mapping is also coupled with a DVFS control to adapt to performance and workload variations. The proposed approach is designed, engineered and validated on a Zynq-ZC702 platform, consisting of CPU, DSP and FPGA cores. Using several image processing applications as case studies, it was demonstrated that our proposed approach can achieve significant energy savings (>70%), when compared to the existing approaches.