Non-convex methods play a critical role in low-rank tensor completion for their approximation to tensor rank is tighter than that of convex methods.But they usually cost much more time for calculating singular values ...Non-convex methods play a critical role in low-rank tensor completion for their approximation to tensor rank is tighter than that of convex methods.But they usually cost much more time for calculating singular values of large tensors.In this paper,we propose a double transformed tubal nuclear norm(DTTNN)to replace the rank norm penalty in low rank tensor completion(LRTC)tasks.DTTNN turns the original non-convex penalty of a large tensor into two convex penalties of much smaller tensors,and it is shown to be an equivalent transformation.Therefore,DTTNN could take advantage of non-convex envelopes while saving time.Experimental results on color image and video inpainting tasks verify the effectiveness of DTTNN compared with state-of-the-art methods.展开更多
In freeform surface modelling, developable surfaces have much application value. But, in 3D space, there is not always a regular developable surface which interpolates the given boundary of an arbitrary piecewise smoo...In freeform surface modelling, developable surfaces have much application value. But, in 3D space, there is not always a regular developable surface which interpolates the given boundary of an arbitrary piecewise smooth closed curve. In this paper, tensor product Bézier surfaces interpolating the closed curves are determined and the resulting surface is a minimum of the functional defined by the L2-integral norm of the Gaussian curvature. The Gaussian curvature of the surfaces is minimized by the method of solving nonlinear optimization problems. An improved approach trust-region form method is proposed. A simple application example is also given.展开更多
基金financially supported by the National Nautral Science Foundation of China(No.61703206)
文摘Non-convex methods play a critical role in low-rank tensor completion for their approximation to tensor rank is tighter than that of convex methods.But they usually cost much more time for calculating singular values of large tensors.In this paper,we propose a double transformed tubal nuclear norm(DTTNN)to replace the rank norm penalty in low rank tensor completion(LRTC)tasks.DTTNN turns the original non-convex penalty of a large tensor into two convex penalties of much smaller tensors,and it is shown to be an equivalent transformation.Therefore,DTTNN could take advantage of non-convex envelopes while saving time.Experimental results on color image and video inpainting tasks verify the effectiveness of DTTNN compared with state-of-the-art methods.
文摘In freeform surface modelling, developable surfaces have much application value. But, in 3D space, there is not always a regular developable surface which interpolates the given boundary of an arbitrary piecewise smooth closed curve. In this paper, tensor product Bézier surfaces interpolating the closed curves are determined and the resulting surface is a minimum of the functional defined by the L2-integral norm of the Gaussian curvature. The Gaussian curvature of the surfaces is minimized by the method of solving nonlinear optimization problems. An improved approach trust-region form method is proposed. A simple application example is also given.
