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Digital Image Correlation (DIC) has been widely used as a non-contact deformation measurement technique. Nevertheless, its accuracy is greatly affected by the speckle pattern on the specimen. To systematically evaluate how speckle deformability affects the precision of DIC algorithms. In this study, a test dataset of 2D speckle patterns with various prescribed deformation fields was numerically generated, containing two categories of speckles, i.e., the deformable and the non-deformable (rigid) ones. This dataset was used to evaluate the performance of inverse compositional Gauss-Newton (ICGN)-based DIC algorithms with two types of shape function (first-order and second-order), in the different scenarios of the deformation field. The results showed that imaging noise had a significant influence on the DIC algorithm. The first-order shape function (ICGN-1) performed better when tracking the simple linear deformation field. While the second-order shape function (ICGN-2) was proved to perform better on non-linear deformations. Moreover, the deformability of the speckle was found to have an obvious impact on the performance of the DIC algorithm. ICGN-2 could effectively reduce so-called speckle rigidity induced (SRI) error. Conclusively, ICGN-2 should be chosen as priority, because of its feasibility on non-linear deformation fields and speckle rigidity. While in the linear deformation scenarios, ICGN-1 was still a robust and efficient method.

Soft tissue modelling plays a significant role in surgery simulation as well as surgical procedure planning and training. However, it is a challenging research task to satisfy both physical realism and real-time simulation for soft tissue deformation. The finite element method (FEM) is a representative strategy for modelling of soft tissue deformation with highly physical realism. However, it suffers from expensive computations, unable to meet the requirement of real-time simulation. This paper proposes a novel method by combining FEM with the Kalman filter for real-time and accurate modelling of soft tissue deformation. The novelty of this method is that soft tissue deformation is formulated as a filtering identification process to online estimate soft tissue deformation from local measurement of displacement. To construct the discrete system state equation for filtering estimation, soft tissue deformation is discretised based on elastic theory in the space domain by FEM and is further discretised in the time domain by using the Wilson-θ implicit integration to solve the dynamic equilibrium equation of FEM deformation modelling. Subsequently, a Kalman filter is developed for online estimation and analysis of soft tissue deformation according to local measurement of displacement. Interactive tool-tissue interaction with haptic feedback is also achieved for surgery simulation. The presented method significantly improves the computational performance of the traditional FEM, but still maintains a similar level of accuracy. It not only achieves the real-time performance, but also exhibits the similar deformation behaviours as the traditional FEM and enables the use of large time steps to improve the simulation efficiency.