We study projections onto a subspace and reflections with respect to a subspace in an arbitrary vector space with an inner product. We give necessary and sufficient conditions for two such transformations to commute. ...We study projections onto a subspace and reflections with respect to a subspace in an arbitrary vector space with an inner product. We give necessary and sufficient conditions for two such transformations to commute. We then generalize the result to affine subspaces and transformations.展开更多
Discriminative correlationfilters(DCF)with powerful feature descriptors have proven to be very effective for advanced visual object tracking approaches.However,due to thefixed capacity in achieving discriminative lear...Discriminative correlationfilters(DCF)with powerful feature descriptors have proven to be very effective for advanced visual object tracking approaches.However,due to thefixed capacity in achieving discriminative learning,existing DCF trackers perform thefilter training on a single template extracted by convolutional neural networks(CNN)or hand-crafted descriptors.Such single template learning cannot provide powerful discriminativefilters with guaranteed validity under appearance variation.To pinpoint the structural relevance of spatio-temporal appearance to thefiltering system,we propose a new tracking algorithm that incorporates the construction of the Grassmannian manifold learning in the DCF formulation.Our method constructs the model appearance within an online updated affine subspace.It enables joint discriminative learning in the origin and basis of the subspace,achieving enhanced discrimination and interpretability of the learnedfilters.In addition,to improve tracking efficiency,we adaptively integrate online incremental learning to update the obtained manifold.To this end,specific spatio-temporal appearance patterns are dynamically learned during tracking,highlighting relevant variations and alleviating the performance degrading impact of less discriminative representations from a single template.The experimental results obtained on several well-known datasets,i.e.,OTB2013,OTB2015,UAV123,and VOT2018,demonstrate the merits of the proposed method and its superiority over the state-of-the-art trackers.展开更多
文摘We study projections onto a subspace and reflections with respect to a subspace in an arbitrary vector space with an inner product. We give necessary and sufficient conditions for two such transformations to commute. We then generalize the result to affine subspaces and transformations.
基金supported in part by the National Natural Science Foundation of China(Grant Nos.U1836218,62106089).
文摘Discriminative correlationfilters(DCF)with powerful feature descriptors have proven to be very effective for advanced visual object tracking approaches.However,due to thefixed capacity in achieving discriminative learning,existing DCF trackers perform thefilter training on a single template extracted by convolutional neural networks(CNN)or hand-crafted descriptors.Such single template learning cannot provide powerful discriminativefilters with guaranteed validity under appearance variation.To pinpoint the structural relevance of spatio-temporal appearance to thefiltering system,we propose a new tracking algorithm that incorporates the construction of the Grassmannian manifold learning in the DCF formulation.Our method constructs the model appearance within an online updated affine subspace.It enables joint discriminative learning in the origin and basis of the subspace,achieving enhanced discrimination and interpretability of the learnedfilters.In addition,to improve tracking efficiency,we adaptively integrate online incremental learning to update the obtained manifold.To this end,specific spatio-temporal appearance patterns are dynamically learned during tracking,highlighting relevant variations and alleviating the performance degrading impact of less discriminative representations from a single template.The experimental results obtained on several well-known datasets,i.e.,OTB2013,OTB2015,UAV123,and VOT2018,demonstrate the merits of the proposed method and its superiority over the state-of-the-art trackers.
