Hierarchical structure invariance and optimal approximation for proximity data

Fuzzy closure relations

In this paper, we introduce a new method which lets us utilize uncertain data for precise decision rules learning. We focus our investigation on a proximity-based fuzzy relational database as it provides convenient mechanisms for the storage and interpretation of uncertain information. In proximity-based fuzzy databases the lack of certainty about obtained information can be represented via insertion of multiple (i.e. non-atomic) attribute values. In addition the database extends classical equivalence relations with fuzzy proximity relations, which provide users with extraordinary analytical capabilities. In this paper we take advantage of both of these properties when developing our approach to induction of decision trees from imperfect information.

Similarity relations are reflexive, symmetric, and transitive fuzzy relations. They help to make approximate inferences, replacing the notion of equality. Similarity-based unification has been quite intensively investigated, as a core computational method for approximate reasoning and declarative programming. In this paper we consider solving constraints over several similarity relations, instead of a single one. Multiple similarities pose challenges to constraint solving, since we can not rely on the transitivity property anymore. Existing methods for unification with fuzzy proximity relations (reflexive, symmetric, non-transitive relations) do not provide a solution that would adequately reflect particularities of dealing with multiple similarities. To address this problem, we develop a constraint solving algorithm for multiple similarity relations, prove its termination, soundness, and completeness properties, and discuss applications.

A three node two-dimensional laminated composite curved beam finite element formulation for linear static analysis is presented where the displacement approximation for the laminate is piecewise hierarchical and is derived based on p-version. The displacement approximation for the element is developed by establishing a hierarchical displacement approximation for each lamina of the laminate and then by imposing interlamina continuity conditions of displacement at the interfaces between the laminas. The approximation functions and the nodal variables for each lamina are derived directly from the Lagrange family of interpolation functions of order pξand pη. This is accomplished by first establishing one-dimensional hierarchical approximation functions and the corresponding nodal variable operators in the ξ and η directions for the three and one node equivalent configurations that correspond to pξ+1 and pη+1 equally spaced nodes in the ξ and η directions and then taking their products. The nodal variables for the entire laminate are derived from the nodal variables of the laminas and the interlamina continuity conditions of displacements. The element formulation ensures C0 continuity of displacement across the interelement as well as interlamina boundaries.

The notion of Rough sets introduced by Pawlak has been extended in many directions to enhance its modelling power. One such approach is to reduce the restriction of the base relation being an equivalence relation. Adding the flavour of fuzzy sets to it a fuzzy proximity relation was used to generate a fuzzy approximation space by De et al. in 1999 and hence the rough sets on fuzzy approximation spaces could be generated. These are much more general than the basic rough sets and also the rough sets defined on proximity relations. However, some of the results established in this direction by De et al. have been found to be faulty. In this paper we show through examples that the results are actually faulty and provide their correct versions. Also, we establish some more properties of these rough sets. A real life application is provided to show the application of the results.

A new methodology for fuzzification of rough sets based on α-indiscernibility

Hierarchical quotient space structure (HQSS), as a typical description of granular computing (GrC), focuses on hierarchically granulating fuzzy data and mining hidden knowledge. The key step of constructing HQSS is to transform the fuzzy similarity relation into fuzzy equivalence relation. However, on one hand, the transformation process has high time complexity. On the other hand, it is difficult to mine knowledge directly from fuzzy similarity relation due to its information redundancy, i.e., sparsity of effective information. Therefore, this article mainly focuses on proposing an efficient granulation approach for constructing HQSS by quickly extracting the effective value of fuzzy similarity relation. First, the effective value and effective position of fuzzy similarity relation are defined according to whether they could be retained in fuzzy equivalence relation. Second, the number and composition of effective values are presented to confirm that which elements are effective values. Based on these above theories, redundant information and sparse effective information in fuzzy similarity relation could be completely distinguished. Next, both isomorphism and similarity between two fuzzy similarity relations are researched based on the effective value. The isomorphism between two fuzzy equivalence relations is discussed based on the effective value. Then, the algorithm with low time complexity for extracting effective values of fuzzy similarity relation is introduced. On the basis, the algorithm for constructing HQSS is presented to realize efficient granulation of fuzzy data. The proposed algorithms could accurately extract effective information from the fuzzy similarity relation and construct the same HQSS with the fuzzy equivalence relation while greatly reducing the time complexity. Finally, relevant experiments on 15 UCI datasets, 3 UKB datasets, and 5 image datasets are shown and analyzed to verify the effectiveness and efficiency of the proposed algorithm.

A problem of the optimal approximation to a fuzzy tolerance relation is discussed in this paper. Specifically, our aim is to get the optimal fuzzy equivalence relation from a given fuzzy tolerance relation. Firstly, we discuss the relationship between the covering and the partition of a set. Then, we give the concept of distance between coverings (or partitions) and put forward the algorithms to get the optimal partition from a given covering. Main results include: 1) give the sufficient and necessary conditions for the optimal approximation of coverings in union sets; 2) give the necessary condition for absolutely optimal approximation of coverings; 3) based on the optimal approximation of each covering in the covering chain, the optimal fuzzy equivalence relation is obtained from the given fuzzy tolerance relation.KeywordsFuzzy Tolerance RelationEquivalence RelationQuotient SpaceOptimal Approximation

Abstract. In this article the new method for iris image features extraction based on phase congruency is proposed. Iris image key points are calculated using the convolutions with Hermite transform functions. At each key point the feature vector characterizing this key point is obtained based on the phase congruency method. Iris key point descriptor contains phase congruency values at points located on concentric circles around the key point. To compare the key points, Euclidean metric between the key points descriptors is calculated. The distance between the iris images is equal to the number of matched iris key points. The proposed method was tested using the images from CASIA−IrisV4−Interval database and the value of EER = 0.226% was obtained.

Objective To explore the effects of assessment system based on key points in clinical skills training among nursing interns. Methods Nursing interns of the Affiliated Cancer Hospital of Zhengzhou University were selected as study subjects from January to December 2016 by the method of convenience sampling. They were divided into experimental group (n=50, practice started from January 2016) and control group (n=50, practice started from June 2016) according to the order of internship. Students in control group adopted the conventional skill training and assessment, while students in experimental group received the assessment system based on key points. Critical thinking skills of nursing interns of both groups were compared with the critical thinking disposition inventory (CTDI) . Results After training, the total score of CTDI of students (299.82±26.95) in experimental group was higher than that (283.41±24.24) in control group with a significant difference (t=3.201, P=0.002) . The scores of 7 dimensions in CTDI were (41.18±4.12) , (40.27±3.16) , (46.10±2.00) , (40.11±5.31) , (42.97±5.05) , (43.96±3.88) , (45.23±3.08) significantly higher than those in control group[ (39.62±3.09) , (38.62±4.15) , (42.04±2.95) , (37.92±3.65) , (39.50±3.57) , (41.82±5.17) , (43.51±2.64) ] (t=2.142, 2.237, 8.074, 2.402, 3.967, 2.341, 2.981; P<0.05) . Conclusions The assessment system based on key points can effectively improve the critical thinking skills of nursing interns. It is worth to be used widely. Key words: Nursing care; Intern; Key point; Clinical skill; Critical thinking

With the rise of computer vision, it is becoming more and more important to accurately recognize and evaluate human actions. However, the complexity, intraclass differences, and viewing angle changes of human actions significantly impact the accuracy of identification human actions. This paper proposed an action recognition and evaluation method based on skeleton information extraction. Briefly, We use Lightweight OpenPose to extract the key points of human skeleton and perform processing work, including video data cutting, deleting some key points, supplementing missing key points, filtering processing, feature extraction, etc. Through an in-depth exploration of related theoretical technologies, we proposed a model for recognition and evaluation of human table tennis actions with an ordinary camera. The support vector machine algorithm (SVM) classification model is used to identify table tennis actions in real-time. Then the dynamic time regularization (DTW) algorithm calculates the similarity of each human skeleton key point in the action sequence. The low-scoring bone key points are marked to evaluate the human table tennis action in real time. The results show that a recognition rate of more than 95% is achieved in the test set, which proves the method's effectiveness. In addition, we compared the results with previous work using inertial sensors for action recognition, which shows our method can preserve the same accuracy with a much lower cost of implementation.

BackgroundDrosophila melanogaster is an important organism used in many fields of biological research such as genetics and developmental biology. Drosophila wings have been widely used to study the genetics of development, morphometrics and evolution. Therefore there is much interest in quantifying wing structures of Drosophila. Advancement in technology has increased the ease in which images of Drosophila can be acquired. However such studies have been limited by the slow and tedious process of acquiring phenotypic data.ResultsWe have developed a system that automatically detects and measures key points and vein segments on a Drosophila wing. Key points are detected by performing image transformations and template matching on Drosophila wing images while vein segments are detected using an Active Contour algorithm.The accuracy of our key point detection was compared against key point annotations of users. We also performed key point detection using different training data sets of Drosophila wing images. We compared our software with an existing automated image analysis system for Drosophila wings and showed that our system performs better than the state of the art. Vein segments were manually measured and compared against the measurements obtained from our system.ConclusionOur system was able to detect specific key points and vein segments from Drosophila wing images with high accuracy.

Biharmonic deformation transfer with automatic key point selection

Abstract. Remote sensing techniques are an important tool in fluvial transport monitoring, since they allow for effective evaluation of the volume of transported material. Nevertheless, there is no methodology for automatic calculation of movement parameters of individual rocks. These parameters can be determined by point cloud registration. Hence, the goal of this study is to develop a robust algorithm for terrestrial laser scanning point cloud registration. The registration is based on Iterative Closest Point algorithm, which requires well established initial parameters of transformation. Thus, we propose to calculate the initial parameters based on key points representing the maximum of Gaussian curvature. For each key point the set of geometrical features is calculated. The key points are then matched between two point clouds as a nearest neighbor in feature domain. Different combinations of neighborhood sizes, feature subsets, metrics and number of nearest neighbors were tested to obtain the highest ratio between properly and improperly matched key points. Finally, RANSAC algorithm was used to calculate the initial transformation parameters between the point clouds and the ICP algorithm was used for calculation of final transformation parameters. The investigations carried out on sample point clouds representing rocks enabled the adjustment of parameters of the algorithm and showed that the Gaussian curvature can be used as a 3-dimentional key point detector for such objects. The proposed algorithm enabled to register point clouds with the mean distance between point clouds equal to 3 mm.

In this paper is presented a method to capture the motion of the human body from multi image video sequences without using markers. The process is composed of five steps: acquisition of video sequences, calibration of the system, surface measurement of the human body for each frame, 3-D surface tracking and tracking of key points. The image acquisition system is currently composed of three synchronized progressive scan CCD cameras and a frame grabber which acquires a sequence of triplet images. Self calibration methods are applied to gain exterior orientation of the cameras, the parameters of internal orientation and the parameters modeling the lens distortion. From the video sequences, two kinds of 3-D information are extracted: a three-dimensional surface measurement of the visible parts of the body for each triplet and 3-D trajectories of points on the body. The approach for surface measurement is based on multi-image matching, using the adaptive least squares method. A full automatic matching process determines a dense set of corresponding points in the triplets. The 3-D coordinates of the matched points are then computed by forward ray intersection using the orientation and calibration data of the cameras. The tracking process is also based on least squares matching techniques. Its basic idea is to track triplets of corresponding points in the three images through the sequence and compute their 3-D trajectories. The spatial correspondences between the three images at the same time and the temporal correspondences between subsequent frames are determined with a least squares matching algorithm. The results of the tracking process are the coordinates of a point in the three images through the sequence, thus the 3-D trajectory is determined by computing the 3-D coordinates of the point at each time step by forward ray intersection. Velocities and accelerations are also computed. The advantage of this tracking process is twofold: it can track natural points, without using markers; and it can track local surfaces on the human body. In the last case, the tracking process is applied to all the points matched in the region of interest. The result can be seen as a vector field of trajectories (position, velocity and acceleration). The last step of the process is the definition of selected key points of the human body. A key point is a 3-D region defined in the vector field of trajectories, whose size can vary and whose position is defined by its center of gravity. The key points are tracked in a simple way: the position at the next time step is established by the mean value of the displacement of all the trajectories inside its region. The tracked key points lead to a final result comparable to the conventional motion capture systems: 3-D trajectories of key points which can be afterwards analyzed and used for animation or medical purposes.