Dose conformity is an essential parameter used in radiotherapy and radiosurgery that measures the correspondence of the dose distribution derived from a Treatment Planning System (TPS) with the actual volume to be treated, the Planning Treatment Volume (PTV). The present work uses a method based on the expansion of dose distributions and PTVs by three-dimensional Zernike polynomials and further comparison of their moments to define a general criterion of dose conformity. To carry on this study, data coming from 20 patients comprising 80 datasets exported from the TPS, which included imaging data (PTVs) and dose distributions corresponding to different treatment modalities: three-dimensional conformal radiotherapy, intensity-modulated radiotherapy (IMRT) and volumetric modulated arc therapy (VMAT), were used. The expansions in Zernike polynomials were obtained up to order 6 and reconstructed dose distributions and PTVs were obtained and compared, and several definitions for a general dose conformity index were proposed. Results indicate agreement between the proposed dose conformity index and the Conformation Number CN. The proposed method allows for a systematic approach to the analysis of dose distributions with further extensions in AI applications.

Object retrieval systems measure the degree of similarity of the shape of 3D models. They search for the elements of the 3D model databases that resemble the query model. In structural bioinformatics, the query model is a protein tertiary/quaternary structure and the objective is to find similarly shaped molecules in the Protein Data Bank. With the ever-growing size of the PDB, a direct atomic coordinate comparison with all its members is impractical. To overcome this problem, the shape of the molecules can be encoded by fixed-length feature vectors. The distance of a protein to the entire PDB can be measured in this low-dimensional domain in linear time. The state-of-the-art approaches utilize Zernike-Canterakis moments for the shape encoding and supply the retrieval process with geometric data of the input structures. The BioZernike descriptors are a standard utility of the PDB since 2020. However, when trying to calculate the ZC moments locally, the issue of the deficiency of libraries readily available for use in custom programs (i.e., without relying on external binaries) is encountered, in particular programs written in Python. Here, a fast and well-documented Python implementation of the Pozo-Koehl algorithm is presented. In contrast to the more popular algorithm by Novotni and Klein, which is based on the voxelized volume, the PK algorithm produces ZC moments directly from the triangular surface meshes of 3D models. In particular, it can accept the molecular surfaces of proteins as its input. In the presented PK-Zernike library, owing to Numba\'s just-in-time compilation, a mesh with 50,000 facets is processed by a single thread in a second at the moment order 20. Since this is the first time the PK algorithm is used in structural bioinformatics, it is employed in a novel, simple, but efficient protein structure retrieval pipeline. The elimination of the outlying chain fragments via a fast PCA-based subroutine improves the discrimination ability, allowing for this pipeline to achieve an 0.961 area under the ROC curve in the BioZernike validation suite (0.997 for the assemblies). The correlation between the results of the proposed approach and of the 3D Surfer program attains values up to 0.99.

Digital image-correlation (DIC) algorithms rely heavily on the accuracy of the initial values provided by whole-pixel search algorithms for structural displacement monitoring. When the measured displacement is too large or exceeds the search domain, the calculation time and memory consumption of the DIC algorithm will increase greatly, and even fail to obtain the correct result. The paper introduced two edge-detection algorithms, Canny and Zernike moments in digital image-processing (DIP) technology, to perform geometric fitting and sub-pixel positioning on the specific pattern target pasted on the measurement position, and to obtain the structural displacement according to the change of the target position before and after deformation. This paper compared the difference between edge detection and DIC in accuracy and calculation speed through numerical simulation, laboratory, and field tests. The study demonstrated that the structural displacement test based on edge detection is slightly inferior to the DIC algorithm in terms of accuracy and stability. As the search domain of the DIC algorithm becomes larger, its calculation speed decreases sharply, and is obviously slower than the Canny and Zernike moment algorithms.

Accurate real-time prediction of microalgae density has great practical significance for taking countermeasures before the advent of Harmful algal blooms (HABs), and the non-destructive and sensitive property of excitation-emission matrix fluorescence (EEMF) spectroscopy makes it applicable to online monitoring and control. In this study, an efficient image preprocessing algorithm based on Zernike moments (ZMs) was proposed to extract compelling features from EEM intensities images. The determination of the highest order of ZMs considered both reconstruction error and computational cost, then the optimal subset of preliminarily extracted 36 ZMs was screened via the BorutaShap algorithm. Aureococcus anophagefferens concentration prediction models were developed by combining BorutaShap and ensemble learning models (random forest (RF), gradient boosting decision tree (GBDT), and XGBoost). The experimental results show that BorutaShap_GBDT preserved the superior subset of ZMs, and the integration of BorutaShap_GBDT and XGBoost achieved the highest prediction accuracy. This research provides a new and promising strategy for rapidly measuring microalgae cell density.

A real-time head pose and gaze estimation (HPGE) algorithm has excellent potential for technological advancements either in human-machine or human-robot interactions. For example, in high-accuracy advent applications such as Driver\'s Assistance System (DAS), HPGE plays a crucial role in omitting accidents and road hazards. In this paper, the authors propose a new hybrid framework for improved estimation by combining both the appearance and geometric-based conventional methods to extract local and global features. Therefore, the Zernike moments algorithm has been prominent in extracting rotation, scale, and illumination invariant features. Later, conventional discriminant algorithms were used to classify the head poses and gaze direction. Furthermore, the experiments were performed on standard datasets and real-time images to analyze the accuracy of the proposed algorithm. As a result, the proposed framework has immediately estimated the range of direction changes under different illumination conditions. We obtained an accuracy of ~85%; the average response time was 21.52 and 7.483 ms for estimating head poses and gaze, respectively, independent of illumination, background, and occlusion. The proposed method is promising for future developments of a robust system that is invariant even to blurring conditions and thus reaching much more significant performance enhancement.

Image segmentation still represents an active area of research since no universal solution can be identified. Traditional image segmentation algorithms are problem-specific and limited in scope. On the other hand, machine learning offers an alternative paradigm where predefined features are combined into different classifiers, providing pixel-level classification and segmentation. However, machine learning only can not address the question as to which features are appropriate for a certain classification problem. The article presents an automated image segmentation and classification platform, called Active Segmentation, which is based on ImageJ. The platform integrates expert domain knowledge, providing partial ground truth, with geometrical feature extraction based on multi-scale signal processing combined with machine learning. The approach in image segmentation is exemplified on the ISBI 2012 image segmentation challenge data set. As a second application we demonstrate whole image classification functionality based on the same principles. The approach is exemplified using the HeLa and HEp-2 data sets. Obtained results indicate that feature space enrichment properly balanced with feature selection functionality can achieve performance comparable to deep learning approaches. In summary, differential geometry can substantially improve the outcome of machine learning since it can enrich the underlying feature space with new geometrical invariant objects.

Reliable tools for artefact rejection and signal classification are a must for cosmic ray detection experiments based on CMOS technology. In this paper, we analyse the fitness of several feature-based statistical classifiers for the classification of particle candidate hits in four categories: spots, tracks, worms and artefacts. We use Zernike moments of the image function as feature carriers and propose a preprocessing and denoising scheme to make the feature extraction more efficient. As opposed to convolution neural network classifiers, the feature-based classifiers allow for establishing a connection between features and geometrical properties of candidate hits. Apart from basic classifiers we also consider their ensemble extensions and find these extensions generally better performing than basic versions, with an average recognition accuracy of 88%.

Many modern sensing systems rely on the accurate extraction of measurement data from digital images. The localization of edges and streaks in digital images is an important example of this type of measurement, with these techniques appearing in many image processing pipelines. Several approaches attempt to solve this problem at both the pixel level and subpixel level. While the subpixel methods are often necessary for applications requiring best-possible accuracy, they are often susceptible to noise, use iterative methods, or require pre-processing. This work investigates a unified framework for subpixel edge and streak localization using Zernike moments with ramp-based and wedge-based signal models. The method described here is found to outperform the current state-of-the-art for digital images with common signal-to-noise ratios. Performance is demonstrated on both synthetic and real images.

We propose a computational investigation on the interaction mechanisms between SARS-CoV-2 spike protein and possible human cell receptors. In particular, we make use of our newly developed numerical method able to determine efficiently and effectively the relationship of complementarity between portions of protein surfaces. This innovative and general procedure, based on the representation of the molecular isoelectronic density surface in terms of 2D Zernike polynomials, allows the rapid and quantitative assessment of the geometrical shape complementarity between interacting proteins, which was unfeasible with previous methods. Our results indicate that SARS-CoV-2 uses a dual strategy: in addition to the known interaction with angiotensin-converting enzyme 2, the viral spike protein can also interact with sialic-acid receptors of the cells in the upper airways.

Self-interacting proteins (SIPs) play a significant role in the execution of most important molecular processes in cells, such as signal transduction, gene expression regulation, immune response and enzyme activation. Although the traditional experimental methods can be used to generate SIPs data, it is very expensive and time-consuming based only on biological technique. Therefore, it is important and urgent to develop an efficient computational method for SIPs detection. In this study, we present a novel SIPs identification method based on machine learning technology by combing the Zernike Moments (ZMs) descriptor on Position Specific Scoring Matrix (PSSM) with Probabilistic Classification Vector Machines (PCVM) and Stacked Sparse Auto-Encoder (SSAE). More specifically, an efficient feature extraction technique called ZMs is firstly utilized to generate feature vectors on Position Specific Scoring Matrix (PSSM); Then, Deep neural network is employed for reducing the feature dimensions and noise; Finally, the Probabilistic Classification Vector Machine is used to execute the classification. The prediction performance of the proposed method is evaluated on S.erevisiae and Human SIPs datasets via cross-validation. The experimental results indicate that the proposed method can achieve good accuracies of 92.55% and 97.47%, respectively. To further evaluate the advantage of our scheme for SIPs prediction, we also compared the PCVM classifier with the Support Vector Machine (SVM) and other existing techniques on the same data sets. Comparison results reveal that the proposed strategy is outperforms other methods and could be a used tool for identifying SIPs.