face alignment by explicit shape regression we present a very efficient highly accurate explicit shape regression approach for face alignment unlike previous regression based approaches we directly learn a vectorial regression function to infer the whole facial shape a set of facial landmarks from the image and explicitly minimize the alignment errors over the training data the inherent shape constraint is naturally encoded into the regressor in a cascaded learning framework and applied from coarse to fine during the test without using a fixed parametric shape model as in most previous methods to make the regression more effective and efficient we design a two level boosted regression shape indexed features and a correlation based feature selection method this combination enables us to learn accurate models from large training data in a short time 20 min for 2 000 training images and run regression extremely fast in test 15 ms for a 87 landmarks shape experiments on challenging data show that our approach significantly outperforms the state of the art in terms of both accuracy and efficiency

stochastic variational inequalities on non convex domains abstract the objective of this work is to prove in a first step the existence and the uniqueness of a solution of the following multivalued deterministic differential equation d x t x t d t d m t t 0 x 0 x 0 where m r r d is a continuous function and is the frechet subdifferential of a semiconvex function the domain of can be non convex but some regularities of the boundary are required the continuity of the map m x c 0 t r d c 0 t r d associating to the input function m the solution x of the above equation as well as tightness criteria allows to pass from the above deterministic case to the following stochastic variational inequality driven by a multi dimensional brownian motion x t k t 0 t f s x s d s 0 t g s x s d b s t 0 d k t x t d t

preservation of prox regularity of sets with applications to constrained optimization in this paper we first provide counterexamples showing that sublevels of prox regular functions and levels of differentiable mappings with lipschitz derivatives may fail to be prox regular then we prove the uniform prox regularity of such sets under usual verifiable qualification conditions the preservation of uniform prox regularity of intersection and inverse image under usual qualification conditions is also established applications to constrained optimization problems are given

stochastic perturbation of sweeping process and a convergence result for an associated numerical scheme abstract here we present well posedness results for first order stochastic differential inclusions more precisely for sweeping process with a stochastic perturbation these results are provided in combining both deterministic sweeping process theory recently developed in edmond and thibault 2005 2006 18 19 and methods concerning the reflection of a brownian motion lions and sznitman 1984 23 and saisho 1987 31 in addition we prove convergence results for an euler scheme discretizing these stochastic differential inclusions

well posedness and output regulation for implicit time varying evolution variational inequalities a class of evolution variational inequalities evis which comprises ordinary differential equations odes coupled with variational inequalities vis associated with time varying set valued mappings is proposed in this paper we first study the conditions for existence and uniqueness of solutions the central idea behind the proof is to rewrite the system dynamics as a differential inclusion which can be decomposed into a single valued lipschitz map and a time dependent maximal monotone operator regularity assumptions on the set valued mapping determine the regularity of the resulting solutions complementarity systems with time dependence are studied as a particular case we then use this result to study the problem of designing state feedback control laws for output regulation in systems described by evis the derivation of control laws for output regulation is based on the use of internal model principle and two cases are treated first a static feedback control law is derived when full state feedback is available in the second case only the error to be regulated is assumed to be available for measurement and a dynamic compensator is designed as applications we demonstrate how control input resulting from the solution of a variational inequality results in regulating the output of the system while maintaining polyhedral state constraints another application is seen in designing control inputs for regulation in power converters

estimation of elastic parameters in a nonlinear elliptic model of a plate we consider the estimation of an elastic parameter in a nonlinear von karman model of large deformations of a thin plate with uniform cross section but with variable young s modulus it is well known that these equations may possess multiple solutions and thus the parameter to state mapping is no longer well defined in spite of this it is still possible to give meaning to a regularized output least squares formulation of the parameter estimation problem we introduce a model error function and determine conditions under which a solution and its differentiability may be analyzed locally we also discuss stability and the application of the augmented lagrangian method in this case if the conditions are not satisfied we provide an analysis of the penalty method applied to the problem finally we report the results of numerical experiments

towards a unified framework for pose expression and occlusion tolerant automatic facial alignment we propose a facial alignment algorithm that is able to jointly deal with the presence of facial pose variation partial occlusion of the face and varying illumination and expressions our approach proceeds from sparse to dense landmarking steps using a set of specific models trained to best account for the shape and texture variation manifested by facial landmarks and facial shapes across pose and various expressions we also propose the use of a novel ell 1 regularized least squares approach that we incorporate into our shape model which is an improvement over the shape model used by several prior active shape model asm based facial landmark localization algorithms our approach is compared against several state of the art methods on many challenging test datasets and exhibits a higher fitting accuracy on all of them

nonsmooth neural network for convex time dependent constraint satisfaction problems this paper introduces a nonsmooth ns neural network that is able to operate in a time dependent td context and is potentially useful for solving some classes of ns td problems the proposed network is named nonsmooth time dependent network ntn and is an extension to a td setting of a previous ns neural network for programming problems suppose c t t ge 0 is a nonempty td convex feasibility set defined by td inequality constraints the constraints are in general ns nondifferentiable functions of the state variables and time ntn is described by the subdifferential with respect to the state variables of an ns td barrier function and a vector field corresponding to the unconstrained dynamics this paper shows that for suitable values of the penalty parameter the ntn dynamics displays two main phases in the first phase any solution of ntn not starting in c 0 at t 0 is able to reach the moving set c cdot in finite time t h whereas in the second phase the solution tracks the moving set i e it stays within c t for all subsequent times t ge t h ntn is thus able to find an exact feasible solution in finite time and also to provide an exact feasible solution for subsequent times this new and peculiar dynamics displayed by ntn is potentially useful for addressing some significant td signal processing tasks as an illustration this paper discusses a number of examples where ntn is applied to the solution of ns td convex feasibility problems

prox regular sets and epigraphs in uniformly convex banach spaces various regularities and other properties we continue the study of prox regular sets that we began in a previous work in the setting of uniformly convex banach spaces endowed with a norm both uniformly smooth and uniformly convex e g l p w m p spaces we prove normal and tangential regularity properties for these sets and in particular the equality between mordukhovich and proximal normal cones we also compare in this setting the proximal normal cone with different holderian normal cones depending on the power types s q of moduli of smoothness and convexity of the norm in the case of sets that are epigraphs of functions we show that j primal lower regular functions have prox regular epigraphs and we compare these functions with poliquin s primal lower nice functions depending on the power types s q of the moduli the preservation of prox regularity of the intersection of finitely many sets and of the inverse image is obtained under a calmness assumption a conical derivative formula for the metric projection mapping of prox regular sets is also established among other results of the paper it is proved that the attouch wets convergence preserves the uniform r prox regularity property and that the metric projection mapping is in some sense continuous with respect to this convergence for such sets

a non convex setup for multivalued differential equations driven by oblique subgradients abstract the paper proves the existence and uniqueness of the solution for the following multivalued deterministic variational inequality with oblique subgradients considered in a non convex domain x t h t x t x t g t x t t 0 x 0 x 0 where stands for the frechet subdifferential of the semiconvex function and the matrix application x h x is a lipschitz mapping the presence of the oblique reflection brought by the term h leads to the use of different techniques comparing to the cases of standard reflection in non convex domains or oblique reflection in convex domains the last section of the article is focused on the qualitative analysis of a non convex skorohod problem with generalized reflection and as applications stochastic variational inequalities driven by oblique frechet subgradients are addressed

sweeping by a continuous prox regular set abstract the evolution problem known as sweeping process is considered for a class of nonconvex sets called prox regular or convex assuming essentially that such sets contain in the interior a suitable subset and move continuously w r t the hausdorff distance we prove local and global existence as well as uniqueness of solutions which are continuous functions with bounded variation some examples are presented

mixed semicontinuous perturbations of nonconvex sweeping processes in this paper we prove a theorem on the existence of a global solution of a differential inclusion governed by a class of nonconvex sweeping processes with unbounded pertubations the perturbations are not required to be convex valued

existence stability and optimality for optimal control problems governed by maximal monotone operators abstract we study optimal control problems governed by maximal monotone differential inclusions with mixed control state constraints in infinite dimensional spaces we obtain some existence results for this kind of dynamics and construct the discrete approximations that allows us to strongly approximate optimal solutions of the continuous type optimal control problems by their discrete counterparts our approach allows us to apply our results for a wide class of mappings that are applicable in mechanics and material sciences

additive logistic regression a statistical view of boosting boosting is one of the most important recent developments in classification methodology boosting works by sequentially applying a classification algorithm to reweighted versions of the training data and then taking a weighted majority vote of the sequence of classifiers thus produced for many classification algorithms this simple strategy results in dramatic improvements in performance we show that this seemingly mysterious phenomenon can be understood in terms of well known statistical principles namely additive modeling and maximum likelihood for the two class problem boosting can be viewed as an approximation to additive modeling on the logistic scale using maximum bernoulli likelihood as a criterion we develop more direct approximations and show that they exhibit nearly identical results to boosting direct multiclass generalizations based on multinomial likelihood are derived that exhibit performance comparable to other recently proposed multiclass generalizations of boosting in most situations and far superior in some we suggest a minor modification to boosting that can reduce computation often by factors of 10 to 50 finally we apply these insights to produce an alternative formulation of boosting decision trees this approach based on best first truncated tree induction often leads to better performance and can provide interpretable descriptions of the aggregate decision rule it is also much faster computationally making it more suitable to large scale data mining applications

active appearance models we describe a new method of matching statistical models of appearance to images a set of model parameters control modes of shape and gray level variation learned from a training set we construct an efficient iterative matching algorithm by learning the relationship between perturbations in the model parameters and the induced image errors

estimation of material parameters in a dynamic nonlinear plate model abstract the output least square estimation of flexural rigidity with observation of deformations is considered for a dynamic von karman system since such equations may have multiple solutions we develop a theory for the estimation of coefficients in systems with solution sets that are compact in suitable spaces we provide a convergence theory based on galerkin approximations and regularity of optimal estimators of the galerkin systems we also obtain stability results for the dependence of the optimal estimator upon the data a numerical estimation algorithm is developed and the results of numerical experiments are reported

a remark on the equation of a vibrating plate on considere les equations de von karman decrivant une plaque vibrante a bord encastree ou completement libre on obtient dans les deux cas une solution classique unique on utilise un ensemble d equations integrales obtenues a partir de la formule des variations des constantes

cadlag skorokhod problem driven by a maximal monotone operator abstract the article deals with the existence and uniqueness of the solution of the following differential equation a cadlag skorokhod problem driven by a maximal monotone operator and with singular input generated by the cadlag function m d x t a x t d t d k t d d m t t 0 x 0 m 0 where k d is a pure jump function the jumps outside of the constrained domain d a are counteracted through the generalized projection by taking x t x t m t whenever x t m t d a approximations of the solution based on discretization and yosida penalization are also considered

bv norm continuity of sweeping processes driven by a set with constant shape we prove the bv norm well posedness of sweeping processes driven by a moving convex set with constant shape namely the bv norm continuity of the so called play operator of elasto plasticity

bv solutions of nonconvex sweeping process differential inclusion with perturbation abstract this paper is devoted to the study of differential inclusions particularly discontinuous perturbed sweeping processes in the infinite dimensional setting on the one hand the sets involved are assumed to be prox regular and to have a variation given by a function which is of bounded variation and right continuous on the other hand the perturbation satisfies a linear growth condition with respect to a fixed compact subset finally the case where the sets move in an absolutely continuous way is recovered as a consequence

projection process with definable right hand side we study the relation between sweeping processes with the cone of limiting normals and projection processes we prove the existence of a solution of a perturbed sweeping process with the cone of limiting normals and of nonstationary projection processes provided the sets involved are definable and are moving in a definable way in some o minimal structure an application to a crowd motion model is presented

sweeping process by prox regular sets in riemannian hilbert manifolds in this paper we deal with sweeping processes on possibly infinite dimensional riemannian hilbert manifolds we extend the useful notions proximal normal cone prox regularity already defined in the setting of a hilbert space to the framework of such manifolds especially we introduce the concept of local prox regularity of a closed subset in accordance with the geometrical features of the ambient manifold and we check that this regularity implies a property of hypomonotonicity for the proximal normal cone moreover we show that the metric projection onto a locally prox regular set is single valued in its neighborhood then under some assumptions we prove the well posedness of perturbed sweeping processes by locally prox regular sets

a numerical scheme for a class of sweeping processes the aim of this paper is to study a whole class of first order differential inclusions which fit into the framework of perturbed sweeping process by uniformly prox regular sets after obtaining well posedness results we propose a numerical scheme based on a prediction correction algorithm and we prove its convergence finally we apply these results to a problem coming from the modelling of crowd motion

second order sweeping process with a lipschitz perturbation abstract in this paper we prove a theorem concerning the existence of solutions for a second order sweeping process with a lipschitz single valued perturbation in hilbert space

existence of solutions to the nonconvex sweeping process abstract in this note we prove the existence of solutions for the sweeping process problem x t nc t x t a e x t c t x 0 x0 c 0 where c is an arbitrary hausdorff lipschitzean multifunction from i 0 t onto the set of nonempty closed subsets of r d this generalizes a well known result of j j moreau 1971 in sem d analyse convexe montpelier exp 15 in the convex case

regularization of differential variational inequalities with locally prox regular sets this paper studies for a differential variational inequality involving a locally prox regular set a regularization process with a family of classical differential equations whose solutions converge to the solution of the differential variational inequality the concept of local prox regularity will be termed in a quantified way as r alpha prox regularity

a continuity method for sweeping processes abstract we show that the existence and uniqueness of bv continuous sweeping processes can be easily reduced to the lipschitz continuous case by means of a suitable reparametrization of the associated moving convex set moreover we put this approach in the wider framework of rate independent operators acting on curves in metric spaces and we prove an extension theorem for such operators this abstract theorem is then applied in order to infer continuous dependence of the sweeping process on the data

local differentiability of distance functions recently clarke stern and wolenski characterized in a hilbert space the closed subsets c for which the distance function dc is continuously differentiable everywhere on an open tube of uniform thickness around c here a corresponding local theory is developed for the property of dc being continuously differentiable outside of c on some neighborhood of a point x c this is shown to be equivalent to the prox regularity of c at x which is a condition on normal vectors that is commonly fulfilled in variational analysis and has the advantage of being verifiable by calculation additional characterizations are provided in terms of dc being locally of class c 1 or such that dc 2 is convex around x for some 0 prox regularity of c at x corresponds further to the normal cone mapping nc having a hypomonotone truncation around x and leads to a formula for pc by way of nc the local theory also yields new insights on the global level of the clarke stern wolenski results and on a property of sets introduced by shapiro as well as on the concept of sets with positive reach considered by federer in the finite dimensional setting

a chain rule involving vector functions of bounded variation by f lbv i x we mean that f is a function of a real interval i to a banach space x with bounded variation on every compact subinterval of i to such f an x valued measure df called its differential measure classically corresponds let be an open convex subset of x and r two situations are investigated where the function f t f t belongs to lbv ir and some properties of the real measure d f are established in the first case is supposed convex and continuous in the subdifferential is invoked in the sense of convex analysis under the ordering of real measures d f is shown to satisfy some inequalities this generalizes previous results of one of the authors aimed at deriving energy like inequalities in nonsmooth mechanical evolution problems in the second case is supposed lipschitz on every bounded subset of and clarke s generalized gradient of is used in both situations if happens to be g teaux differentiable and f lbv i x continuous a chain rule of the familiar form is found to hold finally for frechet differentiable an expression of d f is obtained

identification of parameters in distributed parameter systems by regularization identification of spatially varying parameters in distributed parameter systems from noisy data is an ill posed problem the concept of regularization widely used in solving linear fredholm integral equations is developed for the identification of parameters in distributed parameter systems a general regularization identification theory is first presented and then applied to the identification of parabolic systems the performance of the regularization identification method is evaluated by numerical experiments on the identification of a spatially varying diffusivity in the diffusion equation

sweeping process with regular and nonregular sets abstract differential inclusions involving the normal cone to a moving set are investigated a special attention is paid to the sweeping process associated with sets for which no regularity assumption is required