Supervised Descent Method (SDM) is a highly efficient and accurate approach for facial landmark locating/face alignment. It learns a sequence of descent directions that minimize the difference between the estimated shape and the ground truth in HOG feature space during training, and utilize them in testing to predict shape increment iteratively. In this paper, we propose to modify SDM in three ...

A new IPM (Interior Point Method) for LPs has been discussed in [9, 10] based on a centering step that attempts to maximize the radius of the inscribed sphere with center on the current objective plane, and using descent directions derived without using matrix inversions. The method is a descent method and may be called the sphere method for LP. In contrast to all the existing IPMs which involv...

1. This note summarizes a paper [4] to appear in full elsewhere. It presents an algorithm for the minimization of a general (not necessarily differentiable) convex function. Its central idea is the construction of descent directions as projections of the origin onto the convex hull of previously calculated subgradients as long as satisfactory progress can be made. Using projection to obtain a d...

In this paper, we present iterative methods for finding optimal state-dependent routing strategies in single commodity networks. The key to our method is to show that there exists a family of optimization problems with convex cost and linear constraints that have solutions that can be converted into an optimal routing strategy by way of aflow relaxation transformation. These problems, when solv...

Intravascular ultrasound (IVUS) is a catheter-based medical imaging technique that produces cross-sectional images of blood vessels and is particularly useful for studying atherosclerosis. In this paper, we present a probabilistic approach for the semi-automatic segmentation of the luminal border on IVUS images. Specifically, we parameterize the lumen contour using a sum of Gaussian functions t...

The specification and design of coordinated control strategies for networked vehicles and systems is discussed. A strategy to find the local minimum of an oceanographic scalar field with networked autonomous underwater vehicles (AUV) is presented. The strategy consists in coordinating the motions of the AUVs to implement a modified version of the simplex optimization algorithm. In the original ...

The popular multiplicative algorithms in non-negative matrix factorization (NMF) are known to have slow convergence. Several algorithms have been proposed to improve the convergence of iterative algorithms in NMF, such as the projected gradient algorithms. However, these algorithms also suffer a common problem, that is, a previously exploited descent direction may be searched again in subsequen...

A normal quartic polynomial is a quartic polynomial whose fourth degree term coefficient tensor is positive definite. Its minimization problem is one of the simplest cases of nonconvex global optimization, and has engineering applications. We call a direction a global descent direction of a function at a point if there is another point with a lower function value along this direction. For a nor...

In this paper, we presented a theoretical result and then discussed possible applications of our result to SDR problems. In addition to providing insights into existing SDR methods when Y is univariate; our theorem also applies to multivariate responses, especially when the response takes the form of ðY ;W Þ, where Y is a continuous variable and W is categorical. r 2007 Elsevier B.V. All rights...

Sufficient dimension reduction aims at finding transformations of predictor X without losing any regression information of Y versus X . If we are only interested in the information contained in the mean function or the kth moment function of Y given X , estimation of the central mean space or the central kth moment space becomes our focus. However, existing estimators for the central mean space...