In this paper, the recursive state estimation problem is investigated for an array of discrete time-varying coupled stochastic complex networks with missing measurements. A set of random variables satisfying certain probabilistic distributions is introduced to characterize the phenomenon of the missing measurements, where each sensor can have individual missing probability. The Taylor series expansion is employed to deal with the nonlinearities and the high-order terms of the linearization errors are estimated. The purpose of the addressed state estimation problem is to design a time-varying state estimator such that, in the presence of the missing measurements and the random disturbances, an upper bound of the estimation error covariance can be guaranteed and the explicit expression of the estimator parameters is given. By using the Riccatilike difference equations approach, the estimator parameter is characterized by the solutions to two Riccati-like difference equations. It is shown that the obtained upper bound is minimized by the designed estimator parameters and the proposed state estimation algorithm is of a recursive form suitable for online computation. Finally, an illustrative example is provided to demonstrate the feasibility and effectiveness of the developed state estimation scheme.
A neural radiance field (NeRF) is a scene model supporting high-quality view synthesis, optimized per scene. In this thesis, we explore enabling user editing of a category-level NeRF -also known as a conditional radiance field -trained on a shape category. Specifically, we introduce a method for propagating coarse 2D user scribbles to the 3D space, to modify the color or shape of a local region. First, we propose a conditional radiance field that incorporates new modular network components, including a shape branch that is shared across object instances. Observing multiple instances of the same category, our model learns underlying part semantics without any supervision, thereby allowing the propagation of coarse 2D user scribbles to the entire 3D region (e.g., chair seat). Next, we propose a hybrid network update strategy that targets specific network components, which balances efficiency and accuracy. During user interaction, we formulate an optimization problem that both satisfies the user's constraints and preserves the original object structure. We demonstrate our approach on various editing tasks over three shape datasets and show that it outperforms prior neural editing approaches. Finally, we edit the appearance and shape of a real photograph and show that the edit propagates to extrapolated novel views.
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