We present a new variational method for multi-view stereovision and non-rigid three-dimensional motion estimation from multiple video sequences. Our method minimizes the prediction error of the shape ...and motion estimates. Both problems then translate into a generic image registration task. The latter is entrusted to a global measure of image similarity, chosen depending on imaging conditions and scene properties. Rather than integrating a matching measure computed independently at each surface point, our approach computes a global image-based matching score between the input images and the predicted images. The matching process fully handles projective distortion and partial occlusions. Neighborhood as well as global intensity information can be exploited to improve the robustness to appearance changes due to non-Lambertian materials and illumination changes, without any approximation of shape, motion or visibility. Moreover, our approach results in a simpler, more flexible, and more efficient implementation than in existing methods. The computation time on large datasets does not exceed thirty minutes on a standard workstation. Finally, our method is compliant with a hardware implementation with graphics processor units. Our stereovision algorithm yields very good results on a variety of datasets including specularities and translucency. We have successfully tested our motion estimation algorithm on a very challenging multi-view video sequence of a non-rigid scene.PUBLICATION ABSTRACT
We give three conditions on initial data for the blowing up of the corresponding solutions to some system of Klein-Gordon equations on the three dimensional Euclidean space. We first use Levine's ...concavity argument to show that the negativeness of energy leads to the blowing up of local solutions in finite time. For the data of positive energy, we give a sufficient condition so that the corresponding solution blows up in finite time. This condition embodies datum with arbitrarily large energy. At last we use Payne-Sattinger's potential well argument to classify the datum with energy not so large (to be exact, below the ground states) into two parts: one part consists of datum leading to blowing-up solutions in finite time, while the other part consists of datum that leads to the global solutions.
In this paper, we investigate a nonlocal and nonlinear elliptic problem,(P){−a(∫Ω|∇u|2dx)Δu=λu+up in Ω,u=0 on ∂Ω, where N≤3, Ω⊂RN is a bounded domain with smooth boundary ∂Ω, a is a nondegenerate ...continuous function, p>1 and λ∈R. We show several effects of the nonlocal coefficient a on the structure of the solution set of (P). We first introduce a scaling observation and describe the solution set by using that of an associated semilinear problem. This allows us to get unbounded continua of solutions (λ,u) of (P). A rich variety of new bifurcation and multiplicity results are observed. We also prove that the nonlocal coefficient can induce up to uncountably many solutions in a convenient way. Lastly, we give some remarks from the variational point of view.
The propagation of electromagnetic waves in the plasma sheath is investigated theoretically and numerically using the variational method, which handles the inhomogeneity of the plasma sheath. We ...derive the variation of the action integral, which can be numerically represented by expanding the velocity and electromagnetic fields to the piecewise polynomial function space. We analyze the transmissivity of electromagnetic waves propagating through the plasma sheath with the barrier and the barrier-parabolic electron number density profile. We give the frequency-dependent transmissivity of electromagnetic wave propagation in different inhomogeneous plasma sheaths. The electromagnetic energy density derived from the Lagrangian density is also given, and the result shows that the collision between electrons and neutral particles can be used to enhance the transmission of electromagnetic waves in the plasma sheath.
In this article, we deal with the following fractional $ p $-Kirchhoff type equation
<disp-formula> <tex-math id="FE1"> \begin{document}$ \begin{equation*} \begin{cases} M\left( ...\int_{\mathbb{R}^{N}}\int_{\mathbb{R}^{N}}\frac{|u(x)-u(y)|^p}{|x-y|^{N+ps}}dxdy\right)(-\Delta)_p^su=\frac{|u|^{p_\alpha^*-2}u}{|x|^\alpha}+\frac{\lambda}{|x|^\beta} , &\rm \mathrm{in}\ \ \Omega, \\ u>0, &\rm \mathrm{in}\ \ \Omega, \\ u=0, &\rm \mathrm{in}\ \ \mathbb{R}^N\backslash \Omega, \end{cases} \end{equation*} $\end{document} </tex-math> </disp-formula>
where $ \Omega\subset \mathbb{R}^N $ is a smooth bounded domain containing $ 0 $, $ (-\Delta)_p^s $ denotes the fractional $ p $-Laplacian, $ M(t)=a+bt^{k-1} $ for $ t\geq0 $ and $ k>1 $, $ a, b>0 $, $ \lambda>0 $ is a parameter, $ 0<s<1 $, $ 0\leq\alpha<ps<N $, $ \frac{N(p-2)+ps}{p-1}<\beta<\frac{N(p_\alpha^*-1)+\alpha}{p_\alpha^*} $, $ 1<p<pk<p_\alpha^*=\frac{p(N-\alpha)}{N-ps} $ is the fractional critical Hardy-Sobolev exponent. With aid of the variational method and the concentration compactness principle, we prove the existence of two distinct positive solutions.
•Second-order differential form of even-parity SPN equations are derived.•New interface and boundary conditions are derived unlike traditional SPN.•Equivalence with GSPN for K = 0 is brought out.
...Simplified PN (SPN) equations are derived based on variational method using a modified version of ansatz originally proposed by Pomraning. New boundary and interface conditions are derived for the SPN equations using the corresponding angular flux expression. The equivalence of equations, thus derived, along with its interface and boundary conditions with those of a specific case of Generalized SPN (GSPN), put forward by Chao, is brought out.
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