Although interventional x-ray angiography (XA) procedures involve relatively high radiation doses that can lead to deterministic tissue reactions in addition to stochastic effects, convenient and accurate estimation of absorbed organ doses has traditionally been out of reach. This has mainly been due to the absence of practical means to access dose-related data that describe the physical context of the numerous exposures during an XA procedure. The present work provides a comprehensive and general framework for the determination of absorbed organ dose, based on non-proprietary access to dose-related data by utilizing widely available DICOM radiation dose structured reports. The framework comprises a straightforward calculation workflow to determine the incident kerma and reconstruction of the geometrical relation between the projected x-ray beam and the patient's anatomy. The latter is difficult in practice, as the position of the patient on the table top is unknown. A novel patient-specific approach for reconstruction of the patient position on the table is presented. The proposed approach was evaluated for 150 patients by comparing the estimated position of the primary irradiated organs (the target organs) with their position in clinical DICOM images. The approach is shown to locate the target organ position with a mean (max) deviation of 1.3 (4.3), 1.8 (3.6) and 1.4 (2.9) cm for neurovascular, adult and paediatric cardiovascular procedures, respectively. To illustrate the utility of the framework for systematic and automated organ dose estimation in routine clinical practice, a prototype implementation of the framework with Monte Carlo simulations is included.