In this paper, we introduce a novel approach to mesh editing with the Poisson equation as the theoretical foundation. The most distinctive feature of this approach is that it modifies the original mesh geometry implicitly through gradient field manipulation. Our approach can produce desirable and pleasing results for both global and local editing operations, such as deformation, object merging, and smoothing. With the help from a few novel interactive tools, these operations can be performed conveniently with a small amount of user interaction. Our technique has three key components, a basic mesh solver based on the Poisson equation, a gradient field manipulation scheme using local transforms, and a generalized boundary condition representation based on local frames. Experimental results indicate that our framework can outperform previous related mesh editing techniques.

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Sparse-view computed tomography (CT) holds great promise for speeding up data acquisition and reducing radiation dose in CT scans. Recent advances in reconstruction algorithms for sparse-view CT, such as iterative reconstruction algorithms, obtained high-quality image while requiring advanced computing power. Lately, deep learning (DL) has been widely used in various applications and has obtained many remarkable outcomes. In this paper, we propose a new method for sparse-view CT reconstruction based on the DL approach. The method can be divided into two steps. First, filter backprojection (FBP) was used to reconstruct the CT image from sparsely sampled sinogram. Then, the FBP results were fed to a DL neural network, which is a DenseNet and deconvolution-based network (DD-Net). The DD-Net combines the advantages of DenseNet and deconvolution and applies shortcut connections to concatenate DenseNet and deconvolution to accelerate the training speed of the network; all of those operations can greatly increase the depth of network while enhancing the expression ability of the network. After the training, the proposed DD-Net achieved a competitive performance relative to the state-of-the-art methods in terms of streaking artifacts removal and structure preservation. Compared with the other state-of-the-art reconstruction methods, the DD-Net method can increase the structure similarity by up to 18% and reduce the root mean square error by up to 42%. These results indicate that DD-Net has great potential for sparse-view CT image reconstruction.

In this paper, we propose a novel shape interpolation approach based on Poisson equation. We formulate the trajectory problem of shape interpolation as solving Poisson equations defined on a domain mesh. A non-linear gradient field interpolation method is proposed to take both vertex coordinates and surface orientation into account. With proper boundary conditions, the in-between shapes are reconstructed implicitly from the interpolated gradient fields, while traditional methods usually manipulate vertex coordinates directly. Besides of global shape interpolation, our method is also applicable to local shape interpolation, and can be further enhanced by incorporating with deformation. Our approach can generate visual pleasing and physical plausible morphing sequences with stable area and volume changes. Experimental results demonstrate that our technique can avoid the shrinkage problem appeared in linear shape interpolation.

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