Recently, one-two descriptor has been defined and it has been shown that it is a good predictor of the heat capacity at P constant (CP) and of the total surface area (TSA). In this paper, we analyze its generalizations by replacing the value 2 by arbitrary positive value α . We show that these analyses may be on interest, because even good predictions of CP and TSA can be slightly improved. Furthermore, it can be expected that this more general descriptor can find a wider range of application than the original one. The extremal values of trees have been found for all values of α .

Singular systems have been studied extensively during the last two decades due to their many practical applications. Such systems possess numerous properties not shared by the well-known state variable systems. This paper considers the linear tracking problem for the continuous-time singular systems. The Hamilton-Jacobi theory is used in order to compute the optimal control and associated trajectory. Two methods are presented for solving these trajectories. The first method uses the concept of the Drazin inverse, and the second involves the derivation and solution of a Riccati equation. Similar to the linear regulator problem, necessary and sufficient conditions for existence and uniqueness of a solution are stated.

This paper presents a novel Texture-Edge descriptor, TED, for background modeling and pedestrian detection in video sequences which models texture and edge information of each image block simultaneously. Each block is modeled as a group of adaptive TED histograms that are calculated for pixels of the block over a rectangular neighborhood. TED is an 8-bit binary code which is independent of the neighborhood size. Experimental results over real-world sequences from PETS database clearly show that TED outperforms LBP.

The Bertz indices, derived by counting the number of connecting edges of line graphs of a molecule were used in deriving the QSPR models for the physicochemical properties of alkanes. The inability of these indices to identify the hetero centre in a chemical compound restricted their applications to hydrocarbons only. In the present work, a novel molecular descriptor has been derived from the weighted line graph of the molecular structure and applied in correlating the physicochemical properties of alkane isomers with these descriptors. A weight is tagged at the vertex of the line graph, which consequently modifies the weight of the edge. These descriptors were found to classify the alkane isomers and served well in deriving the QSPR models for various physicochemical properties. The mathematical calculations include the quantitative treatment on the role of substituents (alkyl) in governing the properties under study of the alkane isomers. Further, the use of weighted line graph in the enumeration of the topological index opens up a new vista on application to heteroatomic systems.

Automatic, efficient, accurate, and stable image matching is one of the most critical issues in remote sensing, photogrammetry, and machine vision. In recent decades, various algorithms have been proposed based on the feature-based framework, which concentrate on detecting and describing local features. Understanding the characteristics of different matching algorithms in various applications increases the potential of successful matching in a given application. Numerous studies have evaluated and analyzed many of these algorithms in various applications. However, performance evaluation of image matching methods in multi-sensor images, especially optical-radar and noisy images, is really limited. This research will evaluate the performance of the state-of-theart-detectors, including SURF, KAZE, SIFT, PC, FAST, and Harris detectors for multi-sensor image matching. Moreover, we integrated the employed detectors with the uniform competency algorithm to identify the most reliable features with uniform distribution. Next, we employed a scaleinvariant version of the HOSS descriptor to describe the extracted features. The results show the superiority of the KAZE detector in the presence of noise and various geometric and radiometric distortions.

Image forgery, the manipulation of an image to hide some meaningful or helpful information, is widely used to manage the large amount of information being exchanged in the form of images. There are different forms of image forgery, and copy--move forgery is the most common form of it. The copy-move forgery is easy to perform yet challenging to detect due to the similarity between the original part of the image and the copied part. In this paper, we employ a keypoint descriptor inspired by the human visual system, namely the FREAK (Fast Retina Keypoint) descriptor, for robust copy-move forgery detection. This method uses the advantages of FREAK descriptor such as fast computing and low memory load compared to SIFT, SURF, and BRISK. Finally, geometric transformation parameters are extracted and discussed. Results confirm promising results in the case of image post-processing operations such as adding noise, illumination change, and geometric transformations such as rotation and scaling.

Investigating the geometric similarity of trajectory data to extract movement patterns in urban environments is an emerging area of research that has attracted several efforts over the past few years. This paper uses a convex-hull algorithm whose objective is first to identify curvatures and turning points in a given trajectory and secondly to provide a computable solution to identify the similarities of trajectories. Moreover, the present paper tries to detect additional capabilities that will support the exploration of regular patterns efficiently. This approach is supported by a series of geometrical definitions and algorithms that reduce the complexity of primary trajectories significantly and identify a trajectory geometrical decomposition modeled by an abstract trajectory descriptor (ATD). The main novelty of this paper is to find out the similarity between the row trajectory's geometry and the results of the ATD method using the known geometric measures as distance, orientation, complexity, and shape. Based on this decomposition principle, trajectory similarities can be studied using physical, geometrical, or both descriptors as considered in the ATD method. The proposed method has been evaluated using Geolife benchmark trajectory database. the results show that the proposed algorithm not only successfully identify curvatures and turning points at different scales, but also proved to provide relevant trajectory similarities with efficient computation times as the overall similarity difference value equals 0. 002 between the two row trajectories. The resulted trajectories using the ATD method applying less than 5% of the primary points. In addition, the computation time of about 93% is reduced using the detected critical geometric points using the ATD method.