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Mesh parameterization is one of the fundamental operations in computer graphics (CG) and computeraided design (CAD). In this paper, we propose a novel local/global parameterization approach, ARAP++, for singleand multi-boundary triangular meshes. It is an extension of the as-rigid-as-possible (ARAP) approach, which stitches together 1-ring patches instead of individual triangles. To optimize the spring energy, we introduce a linear iterative scheme which employs convex combination weights and a fitting Jacobian matrix corresponding to a prescribed family of transformations. Our algorithm is simple, efficient, and robust. The geometric properties (angle and area) of the original model can also be preserved by appropriately prescribing the singular values of the fitting matrix. To reduce the area and stretch distortions for high-curvature models, a stretch operator is introduced. Numerical results demonstrate that ARAP++ outperforms several state-of-the-art methods in terms of controlling the distortions of angle, area, and stretch. Furthermore, it achieves a better visualization performance for several applications, such as texture mapping and surface remeshing.

Joint analysis of spatial and spectral features has always been an important method for change detection in hyperspectral images. However, many existing methods cannot extract effective spatial features from the data itself. Moreover, when combining spatial and spectral features, a rough uniform global combination ratio is usually required. To address these problems, in this paper, we propose a novel attention-based spatial and spectral network with PCA-guided self-supervised feature extraction mechanism to detect changes in hyperspectral images. The whole framework is divided into two steps. First, a self-supervised mapping from each patch of the difference map to the principal components of the central pixel of each patch is established. By using the multi-layer convolutional neural network, the main spatial features of differences can be extracted. In the second step, the attention mechanism is introduced. Specifically, the weighting factor between the spatial and spectral features of each pixel is adaptively calculated from the concatenated spatial and spectral features. Then, the calculated factor is applied proportionally to the corresponding features. Finally, by the joint analysis of the weighted spatial and spectral features, the change status of pixels in different positions can be obtained. Experimental results on several real hyperspectral change detection data sets show the effectiveness and advancement of the proposed method.

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