The integration of haptics into virtual environments has triggered a new era by allowing interaction with virtual objects through force feedback in a number of fields. Medicine has been the field with highest potential benefit through improved realism and immersion. Not only have virtual environments become superior to traditional medical training methods due to cost-efficiency, repeatability, and objective assessment but the idea of surgery rehearsal by using patient specific data has been raised as well.

Achieving sufficient realism in haptics has been a significant challenge due to performance requirements. In order to provide a stable and smooth feedback to the user, the update rates of force feedback need to be in the range of 1~kHz, which restricts the solution time for real-time interactive applications. Realism, on the other hand, demands advanced algorithms capable of simulating physical properties. These advanced algorithms have a high computational burden, taking significant amounts of time and their real-time use, therefore, mostly requires simplification of the virtual scene affecting realism.

During palpation, information is transferred to the hand from the local neighbourhood of contact. In deformation simulations, it is therefore common to use a multiresolution scheme, where the local region is modelled with a higher resolution than more distant regions, and at higher update rates. This approach saves computational power, however the less elaborate modelling in the more remote regions affects accuracy. This thesis presents a pipeline to analyse the error introduced by multiresolution techniques. The idea is to estimate how simulation parameters lead to different error magnitudes, as a preprocessing step. This information can subsequently be used for monitoring the error in real-time, or for adjusting simulation parameters to keep the error under a desired limit.

There is a trade-off between accuracy/error and computation time required. In an ideal situation, this error should be kept under perceivable levels. Levels of perception is a topic that has been surveyed in psychophysics among other aspects of touch. It has been shown that differences smaller than a ratio of a reference signal, such as force or stiffness, cannot be perceived. Evaluating the exact value of this ratio, however, is nontrivial since there are many secondary factors having a significant impact, such as the multimodal input. This thesis presents the analysis of some factors affecting the sense of touch that were shown to have such impact. Effects of exploratory procedures on stiffness perception were examined through user studies, followed by another study indicating the significant effects of stiffness gradient.

Medical data, such as MR and CT, has much higher resolution than is practically used for deformable meshes. It has been common practice to model deformation behaviour by a mesh with lower resolution than is used for visual representation. Lastly, this thesis presents an approach to introduce high-resolution information. The proposed algorithm allows for the detection of inhomogeneous structures beneath a surface. This can be applied in situations similar to the diagnosis of tumours by palpation. The approach is independent of mesh structure and resolution, and can be integrated into any proxybased haptic rendering algorithm. This makes the algorithm a complementary choice for deformation simulation.

Photo-realistic image synthesis in real-time is a key challenge in computer graphics. A number of techniques where the light transport in a scene is pre-computed, compressed and used for real-time image synthesis have been proposed. In this work, we extend this idea and present a technique where the radiance distribution in a scene, including arbitrarily complex materials and light sources, is pre-computed using photo-realistic rendering techniques and stored as surface light fields (SLF) at each surface. An SLF describes the full appearance of each surface in a scene as a 4D function over the spatial and angular domains. An SLF is a complex data set with a large memory footprint often in the order of several GB per object in the scene. The key contribution in this work is a novel approach for compression of surface light fields that enables real-time rendering of complex scenes. Our learning-based compression technique is based on exemplar orthogonal bases (EOB), and trains a compact dictionary of full-rank orthogonal basis pairs with sparse coefficients. Our results outperform the widely used CPCA method in terms of storage cost, visual quality and rendering speed. Compared to PRT techniques for real-time global illumination, our approach is limited to static scenes but can represent high frequency materials and any type of light source in a unified framework.