This paper analyzes the problem of shape modeling using the principle of active geometric deformable models. While the basic modeling technique already exists in the literature, we highlight many of its drawbacks and discuss their source and steps to overcome them. We propose a new stopping criterion to address the stopping problem. We also propose to apply a level set algorithm to implement th...

In this work we solve inverse problems coming from the area of Computed Tomography by means of regularization methods based on conjugate gradient iterations. We develop a stopping criterion which is eecient for the computation of a regularized solution for the least{squares normal equations. The stopping rule can be suitably applied also to the Tikhonov regularization method. We report computat...

Two natural and efficient stopping criteria are derived for conjugate gradient (CG) methods, based on iteration parameters. The derivation makes use of the inner product matrix B defining the CG method. In particular, the relationship between the eigenvalues and B-norm of a matrix is investigated, and it is shown that the ratio of largest to smallest eigenvalues defines the B-condition number o...

Decomposition and Monte Carlo sampling-based algorithms hold much promise for solving stochastic programs with many scenarios. A critical component of such algorithms is a stopping criterion to ensure the quality of the solution. In this paper, we develop a stopping rule theory for a class of algorithms that estimate bounds on the optimal objective function value by sampling. We provide rules f...

In this paper we study a Monte Carlo simulation–based approach to stochastic discrete optimization problems. The basic idea of such methods is that a random sample is generated and the expected value function is approximated by the corresponding sample average function. The obtained sample average optimization problem is solved, and the procedure is repeated several times until a stopping crite...

Validation can be used to detect when overrtting starts during supervised training of a neural network; training is then stopped before convergence to avoid the overrtting (\early stopping"). The exact criterion used for validation-based early stopping, however, is usually chosen in an ad-hoc fashion or training is stopped interactively. This trick describes how to select a stopping criterion i...

Parallel simulation methods can be used to reduce the execution time of the simulations of complex systems. In this context, we apply the method of the replications in parallel in order to reduce the execution time of the models. The particular technique consists of starting a fixed number of replications that are maintained in execution until a stop criterion is achieved. Different stopping cr...

Diffusion MRI tractography is often used to estimate structural connections between brain areas and there is a fast-growing interest in quantifying these connections based on their position, shape, size and length. However, a portion of the connections reconstructed with tractography is biased by their position, shape, size and length. Thus, connections reconstructed are not equally distributed...