This paper presents a novel surface registration technique using the spectrum of the shapes, which can facilitate accurate localization and visualization of non-isometric deformations of the surfaces. In order to register two surfaces, we map both eigenvalues and eigenvectors of the Laplace-Beltrami of the shapes through optimizing an energy function. The function is defined by the integration of a smoothness term to align the eigenvalues and a distance term between the eigenvectors at feature points to align the eigenvectors. The feature points are generated using the static points of certain eigenvectors of the surfaces. By using both the eigenvalues and the eigenvectors on these feature points, the computational efficiency is improved considerably without losing the accuracy in comparison to the approaches that use the eigenvectors for all vertices. In our technique, the variation of the shape is expressed using a scale function defined at each vertex. Consequently, the total energy function to align the two given surfaces can be defined using the linear interpolation of the scale function derivatives. Through the optimization of the energy function, the scale function can be solved and the alignment is achieved. After the alignment, the eigenvectors can be employed to calculate the point-to-point correspondence of the surfaces. Therefore, the proposed method can accurately define the displacement of the vertices. We evaluate our method by conducting experiments on synthetic and real data using hippocampus, heart, and hand models. We also compare our method with non-rigid Iterative Closest Point (ICP) and a similar spectrum-based methods. These experiments demonstrate the advantages and accuracy of our method.

This paper presents a novel approach based on spectral geometry to quantify and visualize non-isometric deformations of 3D surfaces by mapping two manifolds. The proposed method can determine multi-scale, non-isometric deformations through the variation of Laplace-Beltrami spectrum of two shapes. Given two triangle meshes, the spectra can be varied from one to another with a scale function defined on each vertex. The variation is expressed as a linear interpolation of eigenvalues of the two shapes. In each iteration step, a quadratic programming problem is constructed, based on our derived spectrum variation theorem and smoothness energy constraint, to compute the spectrum variation. The derivation of the scale function is the solution of such a problem. Therefore, the final scale function can be solved by integral of the derivation from each step, which, in turn, quantitatively describes non-isometric deformations between two shapes. To evaluate the method, we conduct extensive experiments on synthetic and real data. We employ real epilepsy patient imaging data to quantify the shape variation between the left and right hippocampi in epileptic brains. In addition, we use longitudinal Alzheimer data to compare the shape deformation of diseased and healthy hippocampus. In order to show the accuracy and effectiveness of the proposed method, we also compare it with spatial registration-based methods, e.g., non-rigid Iterative Closest Point (ICP) and voxel-based method. These experiments demonstrate the advantages of our method.

This paper presents a registration-free method based on geometry spectrum for mapping two shapes. Our method can quantify and visualize the surface deformation by the variation of Laplace-Beltrami spectrum of the object. In order to examine our method, we employ synthetic data that has non-isometric deformation. We have also applied our method to quantifying the shape variation between the left and right hippocampus in epileptic human brains. The results on both synthetic and real patient data demonstrate the effectiveness and accuracy of our method.

In this paper, we present a web-based medical image processing scientific workflow system called DATAVIEW. This platform is implemented to satisfy the need of physicians to process their data by computer scientists and therefore, overcome the problem of delay for communicating between these two groups and speed up the processing which is very important in emergency conditions. For employing this workflow system, clinicians do not require to install any software tools and can create, save, share, reuse, and run their workflows only using a web browser without knowing the implementation details of the service. For employing the DATAVIEW workflow system for the medical image processing purpose, we extend this workflow system by integrating medical image software tools to this platform which is one of the challenges of this research. Also, in order to provide processing the data in parallel, we integrate high-end computing resource like grids to the system to speed up the processing, which is another challenge for this work. This is very important in medical imaging field because some software tools are very time consuming and in the urgent time, the physicians need to process multiple patients in parallel and get the results fast. As a case study, we choose epilepsy, which is one of the most common brain disorders.

This paper presents finite element computation of brain deformation during craniotomy. Two mechanical models are compared for this purpose: linear solid-mechanic model and linear elastic model. Both models assume finite deformation of the brain after opening the skull. We use a test sphere as a model of the brain, tetrahedral finite element mesh, and function optimization that optimizes the modelspsila parameters by minimizing the distance between the resulting deformation and the supposed deformation. Based on the final value of the objective function, we conclude that the accuracy of the solid mechanic model is higher than that of the elastic model. Applications of the methods to the MR images of the brain confirm this finding.