The current protocol for image guidance in open abdominal liver tumor removal surgeries involves a rigid registration between the patient's operating room space and the pre-operative diagnostic image-space. Systematic studies have shown that the liver can deform up to 2 cm during surgeries in a non-rigid fashion thereby compromising the accuracy of these surgical navigation systems. Compensating for intra-operative deformations using mathematical models has shown promising results. In this work, we follow up the initial rigid registration with a computational approach that is geared towards minimizing the residual closest point distances between the un-deformed pre-operative surface and the rigidly registered intra-operative surface. We also use a surface Laplacian equation based filter that generates a realistic deformation field. Preliminary validation of the proposed computational framework was performed using phantom experiments and clinical trials. The proposed framework improved the rigid registration errors for the phantom experiments on average by 43%, and 74% using partial and full surface data, respectively. With respect to clinical data, it improved the closest point residual error associated with rigid registration by 54% on average for the clinical cases. These results are highly encouraging and suggest that computational models can be used to increase the accuracy of image-guided open abdominal liver tumor removal surgeries.