Deformation Models

The computational modelling of deformations has been actively studied for the last thirty years. This is mainly due to its large range of applications that include computer animation, medical imaging, shape estimation, face deformation as well as other parts of the human body, and object tracking. In addition, these advances have been supported by the evolution of computer processing capabilities, enabling realism in a more sophisticated way. This book encompasses relevant works of expert researchers in the field of deformation models and their applications. The book is divided into two main parts. The first part presents recent object deformation techniques from the point of view of computer graphics and computer animation. The second part of this book presents six works that study deformations from a computer vision point of view with a common characteristic: deformations are applied in real world applications. The primary audience for this work are researchers from different multidisciplinary fields, such as those related with Computer Graphics, Computer Vision, Computer Imaging, Biomedicine, Bioengineering, Mathematics, Physics, Medical Imaging and Medicine.

In mathematical physics, one of the fascinating issues is the study of integrable systems. In particular, non-perturbative techniques that have been developed have triggered significant insight for real physics. There are basically two notions of integrability: classical integrability and quantum integrability. In this book, the focus is on the former, classical integrability. When the system has a finite number of degrees of freedom, it has been well captured by the Arnold–Liouville theorem. However, when the number of degrees of freedom is infinite, as in classical field theories, the integrable structure is enriched profoundly. In fact, the study of classically integrable field theories has a long history and various kinds of techniques, including the classical inverse scattering method, which have been developed so far. In previously published books, these techniques have been collected and well described and are easy to find in traditional, standard textbooks. One of the intriguing subjects in classically integrable systems is the investigation of deformations preserving integrability. Usually, it is not considered systematic to perform such a deformation, and one must study systems case by case and show the integrability of the deformed systems by constructing the associated Lax pair or action-angle variables. Recently, a new, systematic method to perform integrable deformations of 2D non-linear sigma models was developed. It was invented by C. Klimcik in 2002, and the integrability of the deformed sigma models was shown in 2008. The original work was done for 2D principal chiral models, but it has been generalized in various directions nowadays. In this book, the recent progress on this Yang–Baxter deformation is described in a pedagogical manner, including some simple examples. Applications of Yang–Baxter deformation to string theory are also described briefly.

Mass-spring systems are considered the simplest and most intuitive of all deformable models. They are computationally efficient, and can handle large deformations with ease. But they suffer several intrinsic limitations. In this book a modified mass-spring system for physically based deformation modeling that addresses the limitations and solves them elegantly is presented. Several implementations in modeling breast mechanics, heart mechanics and for elastic images registration are presented.

This book provides a real-time and knowledge-based fuzzy logic model for soft tissue deformation. The demand for surgical simulation continues to grow, as there is a major bottleneck in surgical simulation designation and every patient is unique. Deformable models, the core of surgical simulation, play a crucial role in surgical simulation designation. Accordingly, this book (1) presents an improved mass spring model to simulate soft tissue deformation for surgery simulation; (2) ensures the accuracy of simulation by redesigning the underlying Mass Spring Model (MSM) for liver deformation, using three different fuzzy knowledge-based approaches to determine the parameters of the MSM; (3) demonstrates how data in Central Processing Unit (CPU) memory can be structured to allow coalescing according to a set of Graphical Processing Unit (GPU)-dependent alignment rules; and (4) implements heterogeneous parallel programming for the distribution of grid threats for Computer Unified Device Architecture (CUDA)-based GPU computing.