Normalized cut (Ncut) is one of the popular image segmentation models in which the parametric similarity matrix should be given in advance. In this paper, we propose a normalized cut segmentation algorithm with an adaptive similarity measure and spatial regularization. The statistical Parzen-Rosenblatt window, expectation maximum (EM) method and the regularization technique in partial differential equation (PDE) are unified in a proposed variational framework. The introduced EM strategy makes our method can adaptively update the similarity matrix, and it can produce a better classification criterion than the existing Ncut based methods. While the regularization can guarantee the proposed algorithm has a robust performance under noise and it can also rectify the similarity measure with a priori spatial location. In addition, the existence theorem of the proposed model is given in the paper. Compared with some existing spectral clustering methods such as the traditional Ncut algorithm and the variational based Chan-Vese model, the numerical experiments show that our methods can provide promising segmentation results.
Assume the joint probability density function of @math is @math . Then given a parameter set @math , where @math is an iteration number, @math can be transformed @cite_46 as where
@cite_46
2144970857 1724455341 2098213935 2030450972
Let (U_ i ,V_ i ) _ i=1 ^ n be a source of independent identically distributed (i.i.d.) discrete random variables with joint probability mass function p(u,v) and common part w=f(u)=g(v) in the sense of Witsenhausen, Gacs, and Korner. It is shown that such a source can be sent with arbitrarily small probability of error over a multiple access channel (MAC) X_ 1 X_ 2 , Y,p(y|x_ 1 ,x_ 2 ) , with allowed codes x_ l (u), x_ 2 (v) if there exist probability mass functions p(s), p(x_ 1 |s,u),p(x_ 2 |s,v) , such that H(U|V) H(V|U ) H(U,V|W) H(U,V) where p(s,u,v,x_ 1 ,x_ 2 ,y), Xl, X2, y)=p(s)p(u,v)p(x_ 1 |u,s)p(x_ 2 |v,s)p(y|x_ 1 ,x_ 2 ). lifts region includes the multiple access channel region and the Slepian-Wolf data compression region as special cases. Let @math be an i.i.d. sequence of random variables in @math , @math . We show that, for any function @math , under regularity conditions, [n^ 1 2 (n^ -1 i=1 ^n (X_i) f ^(X_i) - (x) ,dx ) P 0, ] where @math is the classical kernel estimator of the density of @math . This result is striking because it speeds up traditional rates, in root @math , derived from the central limit theorem when @math . Although this paper highlights some applications, we mainly address theoretical issues related to the later result. We derive upper bounds for the rate of convergence in probability. These bounds depend on the regularity of the functions @math and @math , the dimension @math and the bandwidth of the kernel estimator @math . Moreover, they are shown to be accurate since they are used as renormalizing sequences in two central limit theorems each reflecting different degrees of smoothness of @math . As an application to regression modelling with random design, we provide the asymptotic normality of the estimation of the linear functionals of a regression function. As a consequence of the above result, the asymptotic variance does not depend on the regression function. Finally, we debate the choice of the bandwidth for integral approximation and we highlight the good behavior of our procedure through simulations. In this letter, the joint probability density function (PDF) for the eigenvalues of a complex Wishart matrix and a perturbed version of it are derived. The latter version can be used to model channel estimation errors and variations over time or frequency. As an example, the joint PDF is used to calculate the transition probabilities between modulation states in an adaptive MIMO system. This leads to a Markov model for the system. We then use the model to investigate the modulation state entering rates (MSER), the average stay duration (ASD), and the effects of feedback delay on the accuracy of modulation state selection in mobile radio systems. Other applications of this PDF are also discussed. The typical fraction of the space of interactions between each pair of N Ising spins which solve the problem of storing a given set of p random patterns as N-bit spin configurations is considered. The volume is calculated explicitly as a function of the storage ratio, alpha =p N, of the value kappa (>0) of the product of the spin and the magnetic field at each site and of the magnetisation, m. Here m may vary between 0 (no correlation) and 1 (completely correlated). The capacity increases with the correlation between patterns from alpha =2 for correlated patterns with kappa =0 and tends to infinity as m tends to 1. The calculations use a saddle-point method and the order parameters at the saddle point are assumed to be replica symmetric. This solution is shown to be locally stable. A local iterative learning algorithm for updating the interactions is given which will converge to a solution of given kappa provided such solutions exist.