A Survey of Orthogonal Moments for Image Representation: Theory, Implementation, and Evaluation

Image representation is an important topic in computer vision and pattern recognition. It plays a fundamental role in a range of applications toward understanding visual contents. Moment-based image representation has been reported to be effective in satisfying the core conditions of semantic description due to its beneficial mathematical properties, especially geometric invariance and independence. This article presents a comprehensive survey of the orthogonal moments for image representation, covering recent advances in fast/accurate calculation, robustness/invariance optimization, definition extension, and application. We also create a software package for a variety of widely used orthogonal moments and evaluate such methods in a same base. The presented theory analysis, software implementation, and evaluation results can support the community, particularly in developing novel techniques and promoting real-world applications.

New Cubic Trigonometric Bezier-Like Functions with Shape Parameter: Curvature and Its Spiral Segment

This work presents the new cubic trigonometric Bézier-type functions with shape parameter. Basis functions and the curve satisfy all properties of classical Bézier curve-like partition of unity, symmetric property, linear independent, geometric invariance, and convex hull property and have been proved. The C 3 and G 3 continuity conditions between two curve segments have also been achieved. To check the applicability of proposed functions, different types of open and closed curves have been constructed. The effect of shape parameter and control points has been observed. It is observed that, by decreasing the value of shape parameter, the curve moves toward the control polygon and vice versa. The CT-Bézier curve is closer to the cubic Bézier curve for a fixed value of shape parameter. The proposed CT-Bézier curve can be used to represent ellipse. Using proposed basis functions, we have constructed the spiral segment which is very useful to construct fair curves and desirable to design trajectories of mobile robots, highway, and railway routes’ designing.

Invariant Image Representation Using Novel Fractional-Order Polar Harmonic Fourier Moments

Continuous orthogonal moments, for which continuous functions are used as kernel functions, are invariant to rotation and scaling, and they have been greatly developed over the recent years. Among continuous orthogonal moments, polar harmonic Fourier moments (PHFMs) have superior performance and strong image description ability. In order to improve the performance of PHFMs in noise resistance and image reconstruction, PHFMs, which can only take integer numbers, are extended to fractional-order polar harmonic Fourier moments (FrPHFMs) in this paper. Firstly, the radial polynomials of integer-order PHFMs are modified to obtain fractional-order radial polynomials, and FrPHFMs are constructed based on the fractional-order radial polynomials; subsequently, the strong reconstruction ability, orthogonality, and geometric invariance of the proposed FrPHFMs are proven; and, finally, the performance of the proposed FrPHFMs is compared with that of integer-order PHFMs, fractional-order radial harmonic Fourier moments (FrRHFMs), fractional-order polar harmonic transforms (FrPHTs), and fractional-order Zernike moments (FrZMs). The experimental results show that the FrPHFMs constructed in this paper are superior to integer-order PHFMs and other fractional-order continuous orthogonal moments in terms of performance in image reconstruction and object recognition, as well as that the proposed FrPHFMs have strong image description ability and good stability.

GraphQA: protein model quality assessment using graph convolutional networks

Motivation Proteins are ubiquitous molecules whose function in biological processes is determined by their 3D structure. Experimental identification of a protein’s structure can be time-consuming, prohibitively expensive and not always possible. Alternatively, protein folding can be modeled using computational methods, which however are not guaranteed to always produce optimal results. GraphQA is a graph-based method to estimate the quality of protein models, that possesses favorable properties such as representation learning, explicit modeling of both sequential and 3D structure, geometric invariance and computational efficiency. Results GraphQA performs similarly to state-of-the-art methods despite using a relatively low number of input features. In addition, the graph network structure provides an improvement over the architecture used in ProQ4 operating on the same input features. Finally, the individual contributions of GraphQA components are carefully evaluated. Availability and implementation PyTorch implementation, datasets, experiments and link to an evaluation server are available through this GitHub repository: github.com/baldassarreFe/graphqa. Supplementary information Supplementary data are available at Bioinformatics online.

Approaches to taking into account horizontal movements of foundations in the work of wooden reinforced cables

The behavior of a wooden stress ribbon structures reinforced with steel rope under the action of a load evenly distributed along the entire length of the cable was investigated. The analysis of the results of static tests of the wooden reinforced cable of the VD-3.1 series is given. A criterion is proposed according to which a wooden stress ribbon structures reinforced with steel rope can be considered according to the theory of rigid threads. To ensure the stability and geometric invariance of the structures formed by rigid threads, an important role is played by taking into account the pliability of the supports that perceive the horizontal support reactions (spacing of the cable). Deformation of the supports of rigid cables causes the appearance of significant bending moments in the body of the cable, and also leads to an increase in the deflection of the structure. Therefore, special attention was paid to the study of the pliability of supports during the tests of wooden stress ribbon structures reinforced with steel rope to the action of a load evenly distributed along the length of the cable. The pliability of supports during experimental tests of wooden stress ribbon structures reinforced with steel rope was investigated. The obtained results are compared with the calculated value of the pliability of the supports, calculated based on the deformability of the installation for testing cable structures. The methods of calculating the deflections of the cables, which take into account the pliability of the supports, were tested. The influence of the pliability of the supports on the deflection of the cable is determined. At the level of the pliability of the supports, the deformability of the cable was influenced by the pliability of the nodal joints of the wooden elements of the cable. Based on this, the deformability of the joints of the wooden elements of the cable on the punched metal plate fasteners and its effect on the deflection of the cable were investigated. The coefficient of deformability of joints was suggested, which took into account the nonlinear dependence of the deformation of joints of wooden elements of the cable on the applied load. Due to the need to take into account the joint work of the wooden body of the cable and the steel rope, the calculated characteristics of the reduced cross section of the wooden cable reinforced with steel rope were calculated. A static calculation of a wooden stress ribbon structures reinforced with steel rope according to the theory of rigid threads is performed and the results of calculations are compared with experimental data.

3D Radon Transform for Shape Retrieval Using Bag-of-Visual-Features

In order to improve the accuracy and efficiency of extracting features for 3D models retrieval, a novel approach using 3D radon transform and Bag-of-Visual-Features is proposed in this paper. Firstly the 3D radon transform is employed to obtain a view image using the different features in different angels. Then a set of local descriptor vectors are extracted by the SURF algorithm from the local features of the view. The similarity distance between geometrical transformed models is evaluated by using K-means algorithm to verify the geometric invariance of the proposed method. The numerical experiments are conducted to evaluate the retrieval efficiency compared to other typical methods. The experimental results show that the change of parameters has small effect on the retrieval performance of the proposed method

Multi-scale and Discriminative Part Detectors Based Features for Multi-label Image Classification

Convolutional neural networks (CNNs) have shown their promise for image classification task. However, global CNN features still lack geometric invariance for addressing the problem of intra-class variations and so are not optimal for multi-label image classification. This paper proposes a new and effective framework built upon CNNs to learn Multi-scale and Discriminative Part Detectors (MsDPD)-based feature representations for multi-label image classification. Specifically, at each scale level, we (i) first present an entropy-rank based scheme to generate and select a set of discriminative part detectors (DPD), and then (ii) obtain a number of DPD-based convolutional feature maps with each feature map representing the occurrence probability of a particular part detector and learn DPD-based features by using a task-driven pooling scheme. The two steps are formulated into a unified framework by developing a new objective function, which jointly trains part detectors incrementally and integrates the learning of feature representations into the classification task. Finally, the multi-scale features are fused to produce the predictions. Experimental results on PASCAL VOC 2007 and VOC 2012 datasets demonstrate that the proposed method achieves better accuracy when compared with the existing state-of-the-art multi-label classification methods.