15887745
The Rotation Graphs of Perfect Matchings of Plane Bipartite Graphs
Abstract In the present paper, the minimal proper alternating cycle (MPAC) rotation graph R(G) of perfect matchings of a plane bipartite graph G is defined. We show that an MPAC rotation graph R(G) of G is a directed rooted tree, and thus extend such a result for generalized polyhex graphs to arbitrary plane bipartite graphs. As an immediate result, we describe a one-to-one correspondence between MPAC systems and perfect matchings in G.
46427487
The Clar Covering Polynomial of Hexagonal Systems I
Abstract In this paper the Clar covering polynomial of a hexagonal system is introduced. In fact it is a kind of F polynomial [4] of a graph, and can be calculated by recurrence relations. We show that the number of aromatic sextets (in a Clar formula), the number of Clar formulas, the number of Kekule structures and the first Herndon number for any Kekulean hexagonal system can be easily obtained by its Clar covering polynomial. In addition, we give some theorems to calculate the Clar covering polynomial of a hexagonal system. As examples we finally derive the explicit expressions of the Clar covering polynomials for some small hexagonal systems and several types of catacondensed hexagonal systems. A relation between the resonance energy and the Clar covering polynomial of a hexagonal system is considered in the next paper.
34749580
Plane elementary bipartite graphs
A connected graph is called elementary if the union of all perfect matchings forms a connected subgraph. In this paper we mainly study various properties of plane elementary bipartite graphs so that many important results previously obtained for hexagonal systems are treated in a unified way. Firstly, we show that a plane bipartite graph G is elementary if and only if the boundary of each face (including the infinite face) is an alternating cycle with respect to some perfect matching of G. For a plane bipartite graph G all interior vertices of which are of the same degree, a stronger result is obtained; namely, G is elementary if and only if the boundary of the infinite face of G is an alternating cycle with respect to some perfect matching of G. Second, the concept of the Z-transformation graph Z(G) of a hexagonal system G (whose vertices represent the perfect matchings of G) is extended to a plane bipartite graph G and some results analogous to those for hexagonal systems are obtained. A peripheral face f of G is called reducible if the removal of the internal vertices and edges of the path that is the intersection of f and the exterior face of G results in a plane elementary bipartite graph. Thirdly, we obtain the reducible face decomposition for plane elementary bipartite graphs. Furthermore, sharp upper and lower bounds for the number of reducible faces are derived. Conversely, we can construct any plane elementary bipartite graphs by adding new peripheral faces one by one. As applications of this approach, we give simple construction methods for several types of plane elementary bipartite graphs G that contain a forcing edge (which belongs to exactly one perfect matching of G) and whose Z-transformation graphs Z(G) contain vertices of degree one.
8279644
Z-transformation graphs of maximum matchings of plane bipartite graphs
Let G be a plane bipartite graph. The Z-transformation graph Z(G) and its orientation Z(G) on the maximum matchings of G are defined. If G has a perfect matching, Z(G) and Z(G) are the usual Z-transformation graph and digraph. If G has neither isolated vertices nor perfect matching, then Z(G) is not connected. This paper mainly shows that some basic results for Z-transformation graph (digraph) of a plane elementary bipartite graph still hold for every nontrivial component of Z(G) (Z(G)). In particular, by obtaining a result that every shortest path of Z(G) from a source of Z(G) corresponds to a directed path of Z(G), we show that every nontrivial component of Z(G) has exactly one source and one sink. Accordingly, it follows that the block graph of every nontrivial component of Z(G) is a path. In addition, we give a simple characterization for a maximum matching of G being a cut-vertex of Z(G).
6097933
The Clar covering polynomial of hexagonal systems III
Abstract The Clar covering polynomial is a recently proposed concept of hexagonal systems by which some important topological indices such as perfect matching count, Clar number, first Herndon number, etc., can be easily obtained. In this paper we establish a relationship between the Clar covering polynomial and sextet polynomial. A lower bound of the Clar number and some properties of coefficients of the Clar covering polynomial are thus deduced. It is mentioned that the summation of coefficients of Clar covering polynomial can be used to calculate the number of perfect matchings of a certain kind of polyominoes relating to crystal physics.
44874837
Z-transformation graphs of perfect matchings of plane bipartite graphs
Abstract Let G be a plane bipartite graph with at least two perfect matchings. The Z -transformation graph, Z F ( G ), of G with respect to a specific set F of faces is defined as a graph on the perfect matchings of G such that two perfect matchings M 1 and M 2 are adjacent provided M 1 and M 2 differ only in a cycle that is the boundary of a face in F . If F is the set of all interior faces, Z F ( G ) is the usual Z -transformation graph; If F contains all faces of G it is a novel graph and called the total Z -transformation graph. In this paper, we give some simple characterizations for the Z -transformation graphs to be connected by applying the above new idea. Furthermore, we show that the total Z -transformation graph of G is 2-connected if G is elementary; the total Z -transformation digraph of G is strongly connected if and only if G is elementary.
940067
Visibility representation of plane graphs via canonical ordering tree,
In a visibility representation (VR for short) of a plane graph G, each vertex of G is represented by a horizontal line segment such that the line segments representing any two adjacent vertices of G are joined by a vertical line segment. Rosenstiehl and Tarjan [Rectilinear planar layouts and bipolar orientations of planar graphs, Discrete Comput. Geom. 1 (1986) 343], Tamassia and Tollis [An unified approach to visibility representations of planar graphs, Discrete Comput. Geom. 1 (1986) 321] independently gave linear time VR algorithms for 2-connected plane graph. Afterwards, one of the main concerns for VR is the size of the representation. In this paper, we prove that any plane graph G has a VR with height bounded by ⌊5n/6⌋. This improves the previously known bound ⌊15n/16⌋. We also construct a plane graph G with n vertices where any VR of G requires a size of (⌊2n/3⌋) × (⌊4n/3⌋ - 3). Our result provides an answer to Kant's open question about whether there exists a plane graph G such that all of its VR require width greater that cn, where c > 1 [G. Kant, A more compact visibility representation, Internat. J. Comput. Geom. Appl. 7 (1997) 197].
15336204
Image Segmentation using Salient Points-Based Object Templates
Using prior knowledge about object(s) is greatly beneficial for accurate image segmentation. In this paper, we present an image segmentation method that performs segmentation using a set of user provided object templates. For the object templates, we call the salient points in the object the characteristic points of the object. Based on the correspondence between the salient points of an arbitrary image and the characteristic points of the objects, object templates are mapped onto the image as bit masks. All templates for the same object are combined to generate the final object/background segmentation. Experiments show that this method can create good segmentations.
1857778
Boosting image orientation detection with indoor vs. outdoor classification
Automatic detection of image orientation is a very important operation in photo image management. In this paper, we propose an automated method based on the boosting algorithm to estimate image orientations. The proposed method has the capability of rejecting images based on the confidence score of the orientation detection. Also, images are classified into indoor and outdoor, and this classification result is used to further refine the orientation detection. To select features more sensitive to the rotation, we combine the features by subtraction operation and select the most useful features by boosting algorithm. The proposed method has several advantages: small model size, fast classification speed, and effective rejection scheme.
10792862
A presentation authoring tool for media devices distributed environments
Many conference rooms are now equipped with multiple multi-media devices, such as plasma displays and surrounding speakers, to enhance presentation quality. However, most existing presentation authoring tools are based on the one-display-and-one-speaker assumption, which makes it difficult to organize and playback a presentation dispatched to multiple devices, thus hinders users from taking full advantage of additional multimedia devices. In this paper, we propose and implement a tool to facilitate authoring and playback of a multi-channel presentation in a media devices distributed environment. The tool, named PreAuthor, provides an intuitive and visual way to author a multi-channel presentation by dragging and dropping "hyper-slides" on corresponding visual representations of various devices. PreAuthor supports "hyper-slide" synchronization among various output devices during preview and playback. It also offers multiple options for the presenter to view the presentation in a rendered image sequence, live video, 3D VRML model, or real environment.
834526
Efficient 3D reconstruction for face recognition
Face recognition with variant pose, illumination and expression (PIE) is a challenging problem. In this paper, we propose an analysis-by-synthesis framework for face recognition with variant PIE. First, an efficient two-dimensional (2D)-to-three-dimensional (3D) integrated face reconstruction approach is introduced to reconstruct a personalized 3D face model from a single frontal face image with neutral expression and normal illumination. Then, realistic virtual faces with different PIE are synthesized based on the personalized 3D face to characterize the face subspace. Finally, face recognition is conducted based on these representative virtual faces. Compared with other related work, this framework has following advantages: (1) only one single frontal face is required for face recognition, which avoids the burdensome enrollment work; (2) the synthesized face samples provide the capability to conduct recognition under difficult conditions like complex PIE; and (3) compared with other 3D reconstruction approaches, our proposed 2D-to-3D integrated face reconstruction approach is fully automatic and more efficient. The extensive experimental results show that the synthesized virtual faces significantly improve the accuracy of face recognition with changing PIE.