Motion segmentation in moving camera videos is a very challenging task because of the motion dependence between the camera and moving objects. Camera motion compensation is recognized as an effective approach. However...Motion segmentation in moving camera videos is a very challenging task because of the motion dependence between the camera and moving objects. Camera motion compensation is recognized as an effective approach. However, existing work depends on prior-knowledge on the camera motion and scene structure for model selection. This is not always available in practice. Moreover, the image plane motion suffers from depth variations, which leads to depth-dependent motion segmentation in 3D scenes. To solve these problems, this paper develops a prior-free dependent motion segmentation algorithm by introducing a modified Helmholtz-Hodge decomposition （HHD） based object-motion oriented map （OOM）. By decomposing the image motion （optical flow） into a curl-free and a divergence-free component, all kinds of camera-induced image motions can be represented by these two components in an invariant way. HHD identifies the camera-induced image motion as one segment irrespective of depth variations with the help of OOM. To segment object motions from the scene, we deploy a novel spatio-temporal constrained quadtree labeling. Extensive experimental results on benchmarks demonstrate that our method improves the performance of the state-of-the-art by 10%-20% even over challenging scenes with complex background.展开更多
The covariant derivative is a generalization of differentiating vectors.The Euclidean derivative is a special case of the covariant derivative in Euclidean space.The covariant derivative gathers broad attention,partic...The covariant derivative is a generalization of differentiating vectors.The Euclidean derivative is a special case of the covariant derivative in Euclidean space.The covariant derivative gathers broad attention,particularly when computing vector derivatives on curved surfaces and volumes in various applications.Covariant derivatives have been computed using the metric tensor from the analytically known curved axes.However,deriving the global axis for the domain has been mathematically and computationally challenging for an arbitrary two-dimensional(2D)surface.Consequently,computing the covariant derivative has been difficult or even impossible.A novel high-order numerical scheme is proposed for computing the covariant derivative on any 2D curved surface.A set of orthonormal vectors,known as moving frames,expand vectors to compute accurately covariant derivatives on 2D curved surfaces.The proposed scheme does not require the construction of curved axes for the metric tensor or the Christoffel symbols.The connectivity given by the Christoffel symbols is equivalently provided by the attitude matrix of orthonormal moving frames.Consequently,the proposed scheme can be extended to the general 2D curved surface.As an application,the Helmholtz‐Hodge decomposition is considered for a realistic atrium and a bunny.展开更多
基金This work is supported by the National Natural Science Foundation of China under Grant No. 61503277.
文摘Motion segmentation in moving camera videos is a very challenging task because of the motion dependence between the camera and moving objects. Camera motion compensation is recognized as an effective approach. However, existing work depends on prior-knowledge on the camera motion and scene structure for model selection. This is not always available in practice. Moreover, the image plane motion suffers from depth variations, which leads to depth-dependent motion segmentation in 3D scenes. To solve these problems, this paper develops a prior-free dependent motion segmentation algorithm by introducing a modified Helmholtz-Hodge decomposition （HHD） based object-motion oriented map （OOM）. By decomposing the image motion （optical flow） into a curl-free and a divergence-free component, all kinds of camera-induced image motions can be represented by these two components in an invariant way. HHD identifies the camera-induced image motion as one segment irrespective of depth variations with the help of OOM. To segment object motions from the scene, we deploy a novel spatio-temporal constrained quadtree labeling. Extensive experimental results on benchmarks demonstrate that our method improves the performance of the state-of-the-art by 10%-20% even over challenging scenes with complex background.
基金the National Research Foundation of Korea(NRF-2021R1A2C109297811).
文摘The covariant derivative is a generalization of differentiating vectors.The Euclidean derivative is a special case of the covariant derivative in Euclidean space.The covariant derivative gathers broad attention,particularly when computing vector derivatives on curved surfaces and volumes in various applications.Covariant derivatives have been computed using the metric tensor from the analytically known curved axes.However,deriving the global axis for the domain has been mathematically and computationally challenging for an arbitrary two-dimensional(2D)surface.Consequently,computing the covariant derivative has been difficult or even impossible.A novel high-order numerical scheme is proposed for computing the covariant derivative on any 2D curved surface.A set of orthonormal vectors,known as moving frames,expand vectors to compute accurately covariant derivatives on 2D curved surfaces.The proposed scheme does not require the construction of curved axes for the metric tensor or the Christoffel symbols.The connectivity given by the Christoffel symbols is equivalently provided by the attitude matrix of orthonormal moving frames.Consequently,the proposed scheme can be extended to the general 2D curved surface.As an application,the Helmholtz‐Hodge decomposition is considered for a realistic atrium and a bunny.
