The S-kernel: A measure of symmetry of objects

In this paper we introduce a new symmetry feature named “symmetry kernel” (SK) to support a measure of symmetry. Given any symmetry transform S, SK of a pattern P is the maximal included symmetric sub-set of P for all directions and shifts. We provide a first algorithm to exhibit this kernel where the centre of symmetry is assumed to be the centre of mass. Then we prove that, in any direction, the optimal axis corresponds to the maximal correlation of a pattern with its symmetric version. That leads to a second algorithm. The associated symmetry measure is a modified difference between the respective surfaces of a pattern and its kernel. A series of experiments supports the actual algorithm validation.     

Optimization leads to symmetry

The science of complexity studies the behavior and properties of complex systems in mture and human society.Particular interest has been put on their certain simple common properties. Symmetry is one of such properties. Symmetric phenomena can be found in many complex systems. The purpose of this paper is to reveal the internal reason of the symmetry.Using some physical systems and geometric objects,the paper shows that many symmetries are caused by optinfizadon under certain criteria. It has also been revealed that an evolutional process may lead to symmetry.     

Recognising symmetry in solid models

Although the symmetry of solids has been studied for over 50 years, it is still not easy to find a method for detecting symmetry in objects represented by B-rep solid models documented in the literature. The need for such a method comes from the requirements of an environment for ‘Assembly Oriented Design’ which includes ‘Design for Assembly’ analyses. This paper begins with definition of terminology used to describe the different types of symmetry that may occur in components and then gives a detailed review in which the benefits and limitations of the many existing methods used for symmetry detection in other applications are discussed. Since none of the methods appear to provide a solution, which can be easily adapted to the Assembly Oriented Design application, the requirements of any new method are then more precisely identified. It appears that human perception of symmetry is considerably more robust than any computational method in existence and therefore the cognitive processes involved in human symmetry detection are examined to attempt to identify promising directions for an alternative approach. As a result of this study, a new method for symmetry detection, which uses the comparison of face loops has been devised. This proves to be an effective technique for the detection of symmetry, which also satisfies the requirements of the particular application. One implementation of a procedure is described in detail together with results of its use on several test cases. Finally, since this method has a demanding practical application, the computational efficiency of the method is examined at length.     

Understanding the impact of perceived visual aesthetics on user evaluations: An emotional perspective

Studies aimed at predicting user judgments have been dominated by the usability and efficiency perspective. An important assumption of this perspective is that higher order judgments such as quality perception and download intention are mainly cognitive processes. Increasingly, research has shown that this perspective is incapable of fully explaining user judgments. Emerging research posits that emotions and emotional subcomponents that arise from aesthetic-based design factors are at least equally important for understanding how users form higher order judgments such as quality perception and attractiveness. In this article, light is shed on the role of emotions in affecting these judgments. This is performed for the particular case of mobile apps. Specifically, the relationship between various aesthetic subdimensions (classical and expressive) and emotional subcomponents (valence and arousal) is explored. First, an explanatory model from theories of aesthetics, emotions, and visual perception is derived. Second, a laboratory experiment is conducted, and it provides empirical evidence for the relationships between visual aesthetics, emotions, and higher order evaluations such as users' quality perceptions and the intentions to download. Specifically, significant relationships were found between aesthetic subdimensions and valence, whereas arousal was partially significant. Selective emotional subdimensions also significantly impacted quality perceptions, attractiveness, and intention to download. Finally, implications for theory and practice are discussed.     

Beyond the lab: Investigating early adolescents' cognitive,emotional, and arousal responses to violent games

Cognitive, emotional, and arousal responses to violent games play a central role in theoretical explanations of how violent media may affect aggression. However, existing research has focused on a relatively narrow range of responses to violent games in experimental settings. This limits our understanding of whether and how violent game-induced responses relate to aggression in real life. To address these gaps, this study investigated how cognitive effort, emotional valence, and arousal in response to violent games relate to early adolescents' aggression, both cross-sectionally and over a period of one year. In addition, we investigated how a social context variable (i.e., family conflict) predicts these responses to violent games and subsequent aggression. A sample of 448 early adolescents (10–14 years) completed survey questions and media diaries that measured their responses to violent games. Results showed that, outside the lab, a positive cross-sectional relationship between violent game-induced arousal and aggression exists. In addition, arousal mediated the relationship between family conflict and aggression. Study findings justify increased research attention to media responses outside the lab and a need for further theoretical and methodological refinement.     

Using symmetry in robust model fitting

The pattern recognition and computer vision communities often employ robust methods for model fitting. In particular, high breakdown-point methods such as least median of squares (LMedS) and least trimmed squares (LTS) have often been used in situations where the data are contaminated with outliers. However, though the breakdown point of these methods can be as high as 50% (they can be robust to up to 50% contamination), they can break down at unexpectedly lower percentages when the outliers are clustered. In this paper, we demonstrate the fragility of LMedS and LTS and analyze the reasons that cause the fragility of these methods in the situation when a large percentage of clustered outliers exist in the data. We adapt the concept of “symmetry distance” to formulate an improved regression method, called the least trimmed symmetry distance (LTSD). Experimental results are presented to show that the LTSD performs better than LMedS and LTS under a large percentage of clustered outliers and large standard variance of inliers.     

Order conditions and symmetry for two-step hybrid methods

In this study of two-step hybrid methods for second-order equations of the type y″?=?f(y), we apply P-series [Hairer, E., Lubich, C. and Wanner, G. (2002). Geometric Numerical Integration Structure-Preserving Algorithms for Ordinary Differential Equations. Springer Series in Computational Mathematics.] to formalise the approach of Chan [Chan, R. P. K. (2002). Two-step hybrid methods. Internal Publication.] to the order conditions, and present two characterizations of symmetry. Although order conditions can be obtained through the classical theory for the Nyström methods, it is of interest to derive particular simpler formulas for the class of two-step hybrid methods in order to facilitate the search for high-order methods. Moreover, the approach proves useful in analysing the symmetry of the hybrid methods.     

Duality and symmetry in constrained estimation and control problems

The Lagrangian dual of a constrained linear estimation problem is derived where the resulting dual system is a linear optimal control problem with projected cost variables. The symmetry between constrained estimation and optimal control is revealed when the primal problem is expressed in an equivalent form involving projected variables.     

Pointing movement visually controlled through a video display: adaptation to scale change

This study concerns the adaptation of motor system when the production of movement was visually controlled through a video display. The subjects had to perform a pointing movement in two visual-feedback conditions: they could see the displacement of their hand or only the final location of the hand on the videoscreen. By changing the zoom of the camera, the amplitude of the movement perceived on the screen was increased, decreased or held equal to the actual movement. Results showed that the movement adapted quickly to the apparent distance changes. In the full visual-feedback condition, the adaptation was smaller in magnitude than in the partial visual-feedback condition. Even though the actual movement was always the same, the subjects thought they carried out different movements. Therefore, the subjects did not use kinematic information provided by the kinaesthetic system but essentially visual information furnished by the video-screen. Taken together, these results show that adaptation to scale changes does not allow the achievement of the perception of a single working space but seems rather specific to each scale.     

Phase transitions and symmetry breaking in genetic algorithms with crossover

In this paper, we consider the role of the crossover operator in genetic algorithms. Specifically, we study optimisation problems that exhibit many local optima and consider how crossover affects the rate at which the population breaks the symmetry of the problem. As an example of such a problem, we consider the subset sum problem. In doing so, we demonstrate a previously unobserved phenomenon, whereby the genetic algorithm with crossover exhibits a critical mutation rate, at which its performance sharply diverges from that of the genetic algorithm without crossover. At this critical mutation rate, the genetic algorithm with crossover exhibits a rapid increase in population diversity. We calculate the details of this phenomenon on a simple instance of the subset sum problem and show that it is a classic phase transition between ordered and disordered populations. Finally, we show that this critical mutation rate corresponds to the transition between the genetic algorithm accelerating or preventing symmetry breaking and that the critical mutation rate represents an optimum in terms of the balance of exploration and exploitation within the algorithm.     

Sequential ballistic movement

Studies of sequential ballistic movements showed that strong interaction occurs between components of a complex movement task. Within an individual component of the motion, a good predictor of movement time was the square root of the movement amplitude. There was a statistically significant influence of the preceding amplitude on the movement time, apart from the first component where the movement time was dependent on the immediate subsequent movement amplitude. Models for movement times are proposed for the different components of sequential movements.     

Augmented planar reflective symmetry transform

Symmetry has been playing an increasing role in 3D shape processing. Recently introduced planar reflective symmetry transform (PRST) has been found useful for canonical coordinate frame determination, shape matching, retrieval, and segmentation. Guided by the intuition that every imperfect symmetry is imperfect in its own way, we investigate the possibility of incorporating more information into symmetry transforms like PRST. As a step in this direction, the concept of augmented symmetry transform is introduced; we obtain a family of symmetry transforms indexed by a parameter. While the original PRST measures how much the symmetry is broken, the augmented PRST also gives some information about how it is broken. Several approaches to calculating the augmented transform are described. We demonstrate that the augmented transform is beneficial for shape retrieval.     

Automated symmetry exploitation in engineering analysis

In engineering analysis, geometric symmetry, when exploited, has two potential benefits: (1) it can significantly reduce the computational time, and (2) it can simultaneously improve the accuracy of the computed solution. Consequently, most CAD/CAE systems have standard ‘provisions’ for exploiting symmetry. These provisions are however inadequate in that they needlessly burden the design engineer with time consuming and error-prone tasks of: (1) symmetry detection, (2) symmetry cell construction, (3) boundary mapping and (4) symmetry reduction. In this paper, we propose a framework for automated symmetry exploitation in engineering analysis. By formalizing all four tasks listed above, and by unifying them under a single framework, we show how automated symmetry exploitation can be achieved. We discuss implementations of the proposed work within two commercially available CAD/CAE systems, namely FEMLAB^TM and SolidWorks^TM.

Generalized symmetry and its application to 3D shape generation

A new method for easily and rapidly generating three-dimensional shapes from two-dimensional line-drawings is presented. This method is based on the generalized symmetry constraint. Generalized symmetry is an extended concept of threedimensional symmetry and its axis is a 3D smooth curve. This paper first develops the definition and constraint of generalized symmetry, and then describes an algorithm which generates the three-dimensional shape of an object from its linedrawing. The generation algorithm is extended to generate generalized cylindrical objects from line-drawings. Several experiments by computer simulation verify that the algorithm can generate three-dimensional shapes from line-drawings.     

Optimal algorithms for symmetry detection in two and three dimensions

Exact algorithms for detecting all rotational and involutional symmetries in point sets, polygons and polyhedra are described. The time complexities of the algorithms are shown to be (n) for polygons and (n logn) for two- and three-dimensional point sets. (n logn) time is also required for general polyhedra, but for polyhedra with connected, planar surface graphs (n) time can be achieved. All algorithms are optimal in time complexity, within constants.     

A bootstrap test for symmetry based on ranked set samples

To test the hypothesis of symmetry about an unknown median we propose the maximum of a partial sum process based on ranked set samples. We discuss the properties of the test statistic and investigate a modified bootstrap ranked set sample bootstrap procedure to obtain its sampling distribution. The power of the new test statistic is compared with two existing tests in a simulation study.     

Skeleton-based intrinsic symmetry detection on point clouds

We present a skeleton-based algorithm for intrinsic symmetry detection on imperfect 3D point cloud data. The data imperfections such as noise and incompleteness make it difficult to reliably compute geodesic distances, which play essential roles in existing intrinsic symmetry detection algorithms. In this paper, we leverage recent advances in curve skeleton extraction from point clouds for symmetry detection. Our method exploits the properties of curve skeletons, such as homotopy to the input shape, approximate isometry-invariance, and skeleton-to-surface mapping, for the detection task. Starting from a curve skeleton extracted from an input point cloud, we first compute symmetry electors, each of which is composed of a set of skeleton node pairs pruned with a cascade of symmetry filters. The electors are used to vote for symmetric node pairs indicating the symmetry map on the skeleton. A symmetry correspondence matrix (SCM) is constructed for the input point cloud through transferring the symmetry map from skeleton to point cloud. The final symmetry regions on the point cloud are detected via spectral analysis over the SCM. Experiments on raw point clouds, captured by a 3D scanner or the Microsoft Kinect, demonstrate the robustness of our algorithm. We also apply our method to repair incomplete scans based on the detected intrinsic symmetries.     

Improved algorithm for the symmetry number problem on trees

The symmetry number of a tree is defined as the number of nodes of the maximum subtree of the tree that exhibits axial symmetry. The best previous algorithm for computing the symmetry number for an unrooted unordered tree is due to [P.P. Mitra, M.A.U. Abedin, M.A. Kashem, Algorithms for solving the symmetry number problem on trees, Inform. Process. Lett. 91 (2004) 163-169] and runs in O(n³) time. In this paper we show an improvement on this time complexity by encoding small trees. Our algorithm runs in time O(n³²(loglogn/logn)).