Interventional cone-beam CT (CBCT) is used for 3D guidance in interventional radiology (IR) procedures in the abdomen, with extended presence in trans-arterial chemoembolization (TACE) interventions for liver cancer. Image quality in this scenario is challenged by complex motion of soft-tissue abdominal structures, and by long acquisition times. We propose an image-based approach to estimate complex deformable motion through a combination of locally rigid motion trajectories. Methods: Deformable motion is estimated by minimizing a multi-region autofocus cost function. Motion is considered locally rigid for each region of interest (ROI) and the deformable motion field is obtained through spatial spline-based interpolation of the local trajectories. The multi-component cost function includes two regularization terms; one to penalize abrupt temporal transitions, and another to penalize abrupt spatial changes in the trajectory. Performance of deformable motion compensation was assessed in simulation studies with a digital abdomen phantom featuring a motion-induced deformable liver in static surrounding anatomy. Spherical inserts (4 - 12 mm diameter, -100 - 100 HU contrast) were placed in the liver. Image quality was evaluated by structural similarity (SSIM) with the static image as reference. Results: Motion compensated liver images showed better delineation of structure boundaries and recovery of distorted spherical shapes compared to their motion-corrupted counterparts. Consistent increase in SSIM was observed after motion compensation for the range of motion amplitudes studied (4 mm to 10 mm), showing 11% and 26% greater SSIM for 4 mm and 10 mm motion, respectively. Conclusion: The results indicate feasibility of image-based deformable motion compensation in soft-tissue abdominal CBCT imaging.