Consider an n-vertex planar graph G. We present an O(n)-time algorithm for computing an embedding of G with minimum distance from the external face. This bound improves on the best previous bound by an O(n log n) factor. As a side effect, our algorithm improves the bounds of several algorithms that require the computation of a minimum distance embedding.

A graph G is an apex graph if it contains a vertex w such that G − w is a planar graph. It is easy to see that the genus g(G) of the apex graph G is bounded above by τ − 1, where τ is the minimum face cover of the neighbors of w, taken over all planar embeddings of G−w. The main result of this paper is the linear lower bound g(G) ≥ τ/160 (if G − w is 3-connected and τ > 1). It is also proved th...

We study the Art Gallery Problem for face guards in polyhedral environments. The problem can be informally stated as: how many (not necessarily convex) windows should we place on the external walls of a dark building, in order to completely illuminate it? We consider both closed and open face guards (i.e., faces with or without their boundary), and we give some upper and lower bounds on the min...

In this paper, we present an automated face recognition (AFR) system that contains two components: eye detection and face recognition. Based on invariant radial basis function (IRBF) networks and knowledge rules of facial topology, a hybrid neural method is proposed to localize human eyes and segment the face region from a scene. A dual eigenspaces method (DEM) is then developed to extract alge...

In this paper we compare the performance of face recognition systems based on two deformable shape models and on three classification approaches. Face contours have been extracted by using two methods: the Active Shapes and the Bayesian Tangent Shapes. The Normal Bayes Classifiers and the Minimum Distance Classifiers (based on the Euclidean and Mahalanobis metrics) have been designed and then c...

Biometric system have evolved very well in last few years and in this digital era secure automatic solution for face spoofing is needed. Combining existing anti-spoofing approaches to come up with more robust mechanism is needed for preventing system from various spoofing types. In this paper, detecting face from image and extracting data from it and then optimizing that information with datase...

A face irregular entire k-labeling φ : V ∪E ∪F → {1,2, . . . ,k} of a 2-connected plane graph G = (V,E,F) is a labeling of vertices, edges and faces of G in such a way that for any two different faces f and g their weights wφ ( f ) and wφ (g) are distinct. The weight of a face f under a k-labeling φ is the sum of labels carried by that face and all the edges and vertices incident with the face....

Realistic face modeling and animation is a challenging topic in computer graphics. In this paper, we develop an approach to create realistic human face with minimum user interaction. The face created is animatable and MPEG-4 compatible. The system takes cylinder mapped texture image and sparse or dense range data, which can be obtained from any available resources, as input. After locating 11 m...

Objectives Today, creating a balanced and attractive smile is the main goal of treatment in modern orthodontics. The buccal corridor is one of the controversial aspects of the smile attractiveness. The aim of this study was to compare the impact of buccal corridor on smile attractiveness of women with Mesoprosopic, Leptoprosopic, and Euryprosopic face types, from the perspective of orthodontist...