Contour Vertices Research Articles

Application of harmonized elliptic Fourier transform coefficients for comparing the shapes of biological structures (on the example of the attachment organs of monogenea)

Elliptic Fourier transform is a common method of describing the shape of objects by an unique sequence of coefficients that allow comparing the shapes by mathematical methods. However, raw coefficients contain unnecessary data unrelated to the shape, which does not provide a correct comparison. For this reason the coefficients are normalised. This removes some of the superfluous data, but leaves information about mirror symmetry and the order in which the contour vertices are declared, that are encoded in the signs of the coefficients. This also interfere with shape comparison. The paper describes an algorithm for harmonizing the coefficients, leveling the influence of the mentioned information. On the example of attachment organs of monogeneas, the advantages of using harmonized coefficients for comparing the shapes of biological structures are shown.

Thermo-Hydrodynamic Lubrication Analysis of Slipper Pair Considering Wear Profile

The profile of sealing land is a sensitive factor affecting the thermo-hydrodynamic lubrication characteristics of the slipper pair. In this paper, the non-uniform wear of the running surface under the slipper was presented and defined as the boundary condition. Based on the finite volume method and the successive over-relaxation iteration method, a discrete numerical model coupled with the temperature, pressure, and thickness of the oil film was constructed. The Newton and sequential circulation methods were used to solve the coupling equations. The influence of the wear profile on the film thickness, sliding attitude, and leakage were discussed. The analyzed results show that the control of the wear on the outer side of sealing land and the contour vertex position, and the avoidance of the wear on the inner side of sealing land could improve the thermo-hydrodynamic lubrication performance of the slipper pair.

BuildMapper: A fully learnable framework for vectorized building contour extraction

Deep learning based methods have significantly boosted the study of automatic building extraction from remote sensing images. However, delineating vectorized and regular building contours like a human does remains very challenging, due to the difficulty of the methodology, the diversity of building structures, and the imperfect imaging conditions. In this paper, we propose the first end-to-end learnable building contour extraction framework, named BuildMapper, which can directly and efficiently delineate building polygons just as a human does. BuildMapper consists of two main components: 1) a contour initialization module that generates initial building contours; and 2) a contour evolution module that performs both contour vertex deformation and reduction, which removes the need for complex empirical post-processing used in existing methods. In both components, we provide new ideas, including a learnable contour initialization method to replace the empirical methods, dynamic predicted and ground truth vertex pairing for the static vertex correspondence problem, and a lightweight encoder for vertex information extraction and aggregation, which benefit a general contour-based method; and a well-designed vertex classification head for building corner vertices detection, which casts light on direct structured building contour extraction. We also built a suitable large-scale building dataset, the WHU-Mix (vector) building dataset, to benefit the study of contour-based building extraction methods. The extensive experiments conducted on the WHU-Mix (vector) dataset, the WHU dataset, and the CrowdAI dataset verified that BuildMapper can achieve a state-of-the-art performance, with a higher mask average precision (AP) and boundary AP than both segmentation-based and contour-based methods. We also confirmed that more than 60.0/50.8% of the building polygons predicted by BuildMapper in the WHU-Mix (vector) test sets I/II, 84.2% in the WHU building test set, and 68.3% in the CrowdAI test set are on par with the manual delineation level.

SMOOTHED CONTOUR DETECTION METHOD FOR ARBITRARY SHAPE OBJECT OF IMAGES

Description of initial raster image objects by a set of contour vertices coordinates leads to increase efficiency of the retrieval, classification and recognition of graphical data in information systems. In this paper the smoothed contour detection method for objects of raster images is considered. The developed method is based on application of interpolation function for partial differential equation solutions and smoothed function for post-processing of detected contours. The accuracy of contour reproduction for raster image objects is increased on 4.87% by applying the developed method compared to the discrete method of contour detection.

Modelling of buildings from aerial LiDAR point clouds using TINs and label maps

This paper presents a new framework for automatically creating compact building models from aerial LiDAR point clouds, where each point is known to belong to the class building. The approach addresses the issues of non-uniform point density and outlier detection to extract and refine semantic roof structures by a sequence of operations on a label map. We first partition the points into some coarse regions based on a region growing method over the Triangulated Irregular Network (TIN) model. The region label IDs are then projected to a 2D grid map, which is used to refine the roof regions and their boundaries. We design an energy optimization approach on the label map to optimize the region labels. In order to regularize the contours of roof regions extracted from the label map, we propose a new method for refining contour segment vertices, which iteratively filters the normals of contour segments and uses them to guide the update of contour vertices. The effectiveness of this method is evaluated on LiDAR point clouds from different scenes, and its performance is validated by extensive comparisons to state-of-the-art techniques.

Some Aspects of Developing Video Games Using Methods of Computational Geometry

The article deals with the general problems associated with the development of video games, in particular, the creation of a reliable system deformation game environment.The purpose of the article is to study and describe some possible solutions for optimizing the process of building and modifying video game objects that can be deformed in a two‐dimensional space.The main research methods are the methods of computational geometry over the external and internal contours of graphic objects of a video game. The article describes the process of creating a gaming world with a digital image, including the use of computer vision techniques – the removal of image contours. The problem of withdrawal of discrete objects of the image, which allows to represent these objects in the gaming environment, is considered. The contours should describe the object as accurately as possible, while it is necessary to ensure high performance of the collision detection system, for which optimization was performed to reduce the number of contour vertices while maintaining the detail of the object. The algorithm used for tracing contours based on the use of vector algebra is described.The novelty of the study is a modified contour tracing algorithm developed by the authors, which is based on the use of vector algebra and is distinguished by the correctness of finding external and internal contours with arbitrary input parameters.The main conclusions of the survey are the simplification in the creation and operation of the subsystem of the landscape deformation. The proposed modified algorithm for tracing the external contour provides a system for deforming the landscape. The results of using the contour tracing algorithm in the practical development of an interactive computer crossplatform video game are presented.

On the contour of bipartite graphs

A vertex of a connected graph is a contour vertex provided the eccentricity of the vertex is at least as large as that of each of its neighbors. We consider the question of whether the set S of contour vertices of a connected graph is geodetic, i.e., whether every vertex of the graph lies on a shortest path (geodesic) between some pair of vertices in S. In general, it is known that when long induced cycles are forbidden (for chordal graphs) the answer is in the affirmative, but otherwise (even for weakly chordal graphs) the answer is in the negative. For bipartite graphs, it is known that when long induced cycles are allowed, the answer is in the negative. In contrast, we show that when long induced cycles are forbidden in bipartite graphs, namely for chordal bipartite graphs, the answer is in the affirmative. Our result also shows that while the answer is in the negative for bipartite graphs and weakly chordal graphs, for a graph that is both bipartite and weakly chordal, the answer is in the affirmative.

Computational and structural analysis of the contour of graphs

AbstractLet be a finite, simple, and connected graph. The closed interval of a set is the set of all vertices lying on a shortest path between any pair of vertices of S. The set S is geodetic if . The eccentricity of a vertex v is the number of edges in the greatest shortest path between v and any vertex w of G. A vertex v is a contour vertex if no neighbor of v has eccentricity greater than v. The contour of G is the set formed by the contour vertices of G. We consider two problems: the problem of determining whether the contour of a graph class is geodetic; the problem of determining if there exists a graph such that is not geodetic. We obtain a sufficient condition that is useful for both problems; we prove a realization theorem related to problem and show two infinite families such that is not geodetic. Using computational tools, we establish the minimum graphs for which is not geodetic; and show that all graphs with , and all bipartite graphs with , are such that is geodetic.

On the geodetic iteration number of the contour of a graph

Let G be a graph and S be a subset of vertices of G. With I[S] we denote the set of all vertices on some geodesic (shortest path) between two vertices of S. A contour vertex of a graph is one whose eccentricity is at least as big as all its neighbors’ eccentricities. Let C be the set of contour vertices of a graph. We provide the first example of a graph where I[I[C]] do not coincide with the vertex set of the graph.

Geodeticity of the contour of chordal bipartite graphs

A vertex of a connected graph is a contour vertex provided the eccentricity of the vertex is at least as large as that of each of its neighbors. We consider the question of whether the set S of contour vertices of a connected graph is geodetic, i.e., whether every vertex of the graph lies on a shortest path (geodesic) between some pair of vertices in S. In general, it is known that when long induced cycles are forbidden (for chordal graphs) the answer is in the affirmative, but otherwise (even for weakly chordal graphs) the answer is in the negative. For bipartite graphs, it is known that when long induced cycles are allowed, the answer is in the negative. In contrast, we show that when long induced cycles are forbidden in bipartite graphs, namely for chordal bipartite graphs, the answer is in the affirmative. Our result also shows that while the answer is in the negative for bipartite graphs and weakly chordal graphs, for a graph that is both bipartite and weakly chordal, the answer is in the affirmative.

The contour of a bridged graph is geodetic

The eccentricity of a vertex v in a graph G is the maximum distance of v from any other vertex of G and v is a contour vertex of G if each vertex adjacent to v has eccentricity not greater than the eccentricity of v. The set of contour vertices of G is geodetic if every vertex of G lies on a shortest path between a pair of contour vertices. An induced connected subgraph H of G is isometric if, every two vertices of H, have in H the same distance as in G. A graph is bridged if it does not contains an isometric cycle with length greater than 3. In this note, we show that the contour of a bridged graph is geodetic.

On the geodeticity of the contour of a graph

The eccentricity of a vertex v in a graph G is the maximum distance of v from any other vertex of G and v is a contour vertex of G if each vertex adjacent to v has eccentricity not greater than the eccentricity of v. The set of contour vertices of G is geodetic if every vertex of G lies on a shortest path between a pair of contour vertices. In this paper, we firstly investigate the existence of operations on graphs that allow to construct graphs in which the contour is geodetic. Then, after providing an alternative proof of the fact that the contour is geodetic in every HHD-free graph, we show that the contour is geodetic in every cactus and in every graph whose blocks are HHD-free or cycles or cographs. Finally, we generalize the above result by introducing the concept of geodetic-contour-preserving class of graphs and by proving that, if each block B in a graph G belongs to a class GB of graphs which is geodetic-contour-preserving, then the contour of G is geodetic.

A New Snake Model for Pupil Localization Using Orthogonal Polynomials Transform

 Abstract—In this paper a new approach for representing and evolving deformable contour or snake model to accurately detect pupil boundary for improving the performance of iris recognition systems is proposed. The proposed model extracts the boundary with computationally efficient Laplacian of Guassian (LoG) mask. The LoG mask is obtained from the set of polynomial basis operators derived from Orthogonal Polynomials Transform. Two types of controlling force models, introduced as internal and external forces are designed to properly activate the contour and locate it over the pupil boundary. The internal forces are designed to smooth the contour as well as to keep it close to a boundary by pushing the contour vertices towards the boundary of interest. The external forces are responsible for pulling the contour vertices towards the pupil boundary and the contour is deformed into a new shape in response to the effective force. A revised contour estimate of the selected boundary based on the execution of the contour tracing algorithm is generated. The results are highly encouraging to capture the contour of non-circular shaped pupil of iris. Experimental results on the CASIA v1.0 iris database demonstrate that the proposed snake model outperforms in both accuracy and speed.

A Moving Grid Framework for Geometric Deformable Models.

Geometric deformable models based on the level set method have become very popular in the last decade. To overcome an inherent limitation in accuracy while maintaining computational efficiency, adaptive grid techniques using local grid refinement have been developed for use with these models. This strategy, however, requires a very complex data structure, yields large numbers of contour points, and is inconsistent with the implementation of topology-preserving geometric deformable models (TGDMs). In this paper, we investigate the use of an alternative adaptive grid technique called the moving grid method with geometric deformable models. In addition to the development of a consistent moving grid geometric deformable model framework, our main contributions include the introduction of a new grid nondegeneracy constraint, the design of a new grid adaptation criterion, and the development of novel numerical methods and an efficient implementation scheme. The overall method is simpler to implement than using grid refinement, requiring no large, complex, hierarchical data structures. It also offers an extra benefit of automatically reducing the number of contour vertices in the final results. After presenting the algorithm, we demonstrate its performance using both simulated and real images.

As-rigid-as-possible shape deformation and interpolation

We provide a detailed analysis of the 2D deformation algorithm based on non-linear least squares optimization, and prove that different mesh structure is of critical importance to deforming result. Based on triangle mesh, preserving the length of edges during deforming is enough to preserve the local, global and boundary properties of the shape. Sufficient theoretical analysis and experiments proved the advantage of the algorithm: (1) It is more stable. The constraint of edges length is strong enough to preserve the stability of triangle, thus the local and global structure are stable. (2) Due to less constraints, the calculating cost is reduced and the performance is improved. (3) The problem of parameter adjusting is solved in the approach. Further more, the algorithm has the ability to control facial expression and to adjust the area of shape etc. In addition, a new approach to shape interpolation is presented. The inputs of the shape interpolation algorithm are bitmap represented images without any topology information in both the original and the target shapes. The strategy is to extract the topology of the original shape, and set up the correspondence between the original and the target shapes, which is to find the matching contour vertices between the original and target shapes. And the shape deformation algorithm is applied using the interpolation of the matching vertices as controlling points. The algorithm guarantees as-rigid-as-possible and rotation invariant shape interpolation. The interpolated shapes have the same topology structure with the original and the target shapes. Experiments indicate that the algorithm is stable and well performed.

Geodetic and Steiner geodetic sets in 3-Steiner distance hereditary graphs

Let G be a connected graph and S ⊆ V ( G ) . Then the Steiner distance of S, denoted by d G ( S ) , is the smallest number of edges in a connected subgraph of G containing S. Such a subgraph is necessarily a tree called a Steiner tree for S. The Steiner interval for a set S of vertices in a graph, denoted by I ( S ) is the union of all vertices that belong to some Steiner tree for S. If S = { u , v } , then I ( S ) is the interval I [ u , v ] between u and v . A connected graph G is 3-Steiner distance hereditary ( 3 - SDH ) if, for every connected induced subgraph H of order at least 3 and every set S of three vertices of H, d H ( S ) = d G ( S ) . The eccentricity of a vertex v in a connected graph G is defined as e ( v ) = max { d ( v , x ) | x ∈ V ( G ) } . A vertex v in a graph G is a contour vertex if for every vertex u adjacent with v , e ( u ) ⩽ e ( v ) . The closure of a set S of vertices, denoted by I [ S ] , is defined to be the union of intervals between pairs of vertices of S taken over all pairs of vertices in S. A set of vertices of a graph G is a geodetic set if its closure is the vertex set of G. The smallest cardinality of a geodetic set of G is called the geodetic number of G and is denoted by g ( G ) . A set S of vertices of a connected graph G is a Steiner geodetic set for G if I ( S ) = V ( G ) . The smallest cardinality of a Steiner geodetic set of G is called the Steiner geodetic number of G and is denoted by sg ( G ) . We show that the contour vertices of 3 - SDH and HHD -free graphs are geodetic sets. For 3 - SDH graphs we also show that g ( G ) ⩽ sg ( G ) . An efficient algorithm for finding Steiner intervals in 3 - SDH graphs is developed.

Steiner intervals and Steiner geodetic numbers in distance-hereditary graphs

A Steiner tree for a set S of vertices in a connected graph G is a connected subgraph of G with a smallest number of edges that contains S. The Steiner interval I ( S ) of S is the union of all the vertices of G that belong to some Steiner tree for S. If S = { u , v } , then I ( S ) = I [ u , v ] is called the interval between u and v and consists of all vertices that lie on some shortest u – v path in G. The smallest cardinality of a set S of vertices such that ⋃ u , v ∈ S I [ u , v ] = V ( G ) is called the geodetic number and is denoted by g ( G ) . The smallest cardinality of a set S of vertices of G such that I ( S ) = V ( G ) is called the Steiner geodetic number of G and is denoted by sg ( G ) . We show that for distance-hereditary graphs g ( G ) ⩽ sg ( G ) but that g ( G ) / sg ( G ) can be arbitrarily large if G is not distance hereditary. An efficient algorithm for finding the Steiner interval for a set of vertices in a distance-hereditary graph is described and it is shown how contour vertices can be used in developing an efficient algorithm for finding the Steiner geodetic number of a distance-hereditary graph.

Special Issue: Dedicated to INES 2005 and SISY 2005 Conferences

The current issue contains 12 papers presented at the <I>IEEE 9th International Conference on Intelligent Engineering Systems (INES 2005), Cruising on the Mediterranean Sea</I>, on September 16-19, 2005, and <I>3rd Serbian-Hungarian Joint Symposium on Intelligent Systems (SISY 2005), in Subotica, Serbia and Montenegro</I>, on August 31-September 1, 2005. The topics of the two conferences are very close to each other and regard Intelligent Systems both from practical and theoretical point of view. These successful conferences brought together active participants and joined researchers from several countries working on this very quickly developing, more and more important field. After a preliminary selection made by the section chairs and the International Program Committees, we have selected 12 papers to be published in extended form in the current Special Issue of the <I>Journal of Advanced Computational Intelligence and Intelligent Informatics</I>. We would like to express our thanks to our sponsors, the organizers and mainly to the participants, who made these scientific events possible. Also, we express our thanks to the Editors of the Journal of Advanced Computational Intelligence and Intelligent Informatics, for publishing this Special Issue. In the following we briefly describe each paper. A. Almeida, G. Marreiros present a model to support collaborative scheduling in complex dynamic manufacturing environments. This model considers the interaction between an Agent based Scheduling Module and a Group Decision Support Module. P. Baranyi, Z. Petres, P. L. Várkonyi, P. Korondi and Y. Yam study in their paper how the Tensor Product model transformation is capable of determining different types of convex hulls of the Linear Time Invariant models. The study is conducted through the example of the prototypical aeroelastic wing section. B. Bede, H. Nobuhara, J. Fodor and K. Hirota propose the study of the problem if usual sum and product can be substituted by max and product operations in defining approximation operators. In this sense max-product Shepard approximation operators are defined and studied. B. Benyó, P. Somogyi and B. Paláncz address the problem of classification of cerebral blood flow signals in order to identify the disorders of the cerebral circulation. The experimental results provided in the paper confirm the effectiveness of the proposed methods. J. Gáti and Gy. Kártyás propose a model based distance learning in the every day higher education practice in their contribution. They survey some important issues and methodological elements of virtual classrooms in comparison with demands for teaching procedures, programs, and materials. L. Horváth and I. J. Rudas propose a methodology for intelligent communication and change management for engineering modeling. This study motivated by increasing of importance of change management because of continuous product development. M. Maleković and M. Čubrilo describe in their contribution how to incorporate infatuation in multi-agent systems. Infatuation stands for the focusing on a single attractive or desirable characteristic of another agent and then considering the total agent as that one positive characteristic. E. Pap and M. Takács study two dimensional copulas as binary aggregation operators in their paper. Invariant copulas and an application of copulas in the theory of aggregation operators are discussed and a result on approximation of associative copulas by strict and nilpotent triangular norms is obtained. B. Reskó, Á. Csapó and P. Baranyi present in their contribution a visual cortex inspired cognitive model for contour and vertex detection. The contour detection and vertex extraction is performed by a vast network of simple units of computation simultaneously processing the visual data. The computational units are organized in a special structure, the Visual Feature Array. M. Takács addresses investigation of the problem of the approximate reasoning in the fuzzy systems, by reviewing a specific case, where the investigated structure is a real semi-ring with pseudo-operations. It is the investigation of special-type fuzzy sets, special g-generated t-norms and implications in approximate reasoning. J. K. Tar, I. J. Rudas and A. Rontó present in their paper a simple adaptive controller that creates only temporal and situation dependent system model. The temporal model can be built up and maintained step-by-step on the basis of slow elimination of fading information by the use of simple updating rules consisting of finite algebraic steps of lucid geometric interpretation. A. R. Várkonyi-Kóczy, A. Rövid and P. Várlaki present a new fuzzy based tone reproduction pre-processing algorithm which may help in developing the hardly or non-viewable features and content of the images making easier the further processing of it.

Cognitive Vision Inspired Contour and Vertex Detection

This paper presents a visual cortex inspired cognitive model for contour and vertex detection. The model is strongly based on the receptive field characteristics of cortical neurons of the visual cortex. As a step forward compared to the previous version of the model, a new dimension has been added, which replaces the binary signals and operations by operations on real values. The resulting system yields a better approximation of the biological system, as well as provides stronger and more distinct contour lines and vertices. The contour detection and vertex extraction is performed by a vast network of simple units of computation simultaneously processing the visual data. The computational units are organized in a special structure, the Visual Feature Array (VFA), which allows the structural representation of complex operations. The goal of the model is to extract abstract information from an image, which in turn may be used as input for the recognition process of even more abstract visual objects. In order to achieve constant time execution of the model, the aspects of hardware implementation are also treated in this paper.

Rebuilding convex sets in graphs

The usual distance between pairs of vertices in a graph naturally gives rise to the notion of an interval between a pair of vertices in a graph. This in turn allows us to extend the notions of convex sets, convex hull, and extreme points in Euclidean space to the vertex set of a graph. The extreme vertices of a graph are known to be precisely the simplicial vertices, i.e., the vertices whose neighborhoods are complete graphs. It is known that the class of graphs with the Minkowski–Krein–Milman property, i.e., the property that every convex set is the convex hull of its extreme points, is precisely the class of chordal graphs without induced 3-fans. We define a vertex to be a contour vertex if the eccentricity of every neighbor is at most as large as that of the vertex. In this paper we show that every convex set of vertices in a graph is the convex hull of the collection of its contour vertices. We characterize those graphs for which every convex set has the property that its contour vertices coincide with its extreme points. A set of vertices in a graph is a geodetic set if the union of the intervals between pairs of vertices in the set, taken over all pairs in the set, is the entire vertex set. We show that the contour vertices in distance hereditary graphs form a geodetic set.