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Three-dimensional voxel models are widely applied in various fields such as 3D imaging, industrial design, and medical imaging. The advancement of 3D modeling techniques and measurement devices has made the generation of three-dimensional models more convenient. The exponential increase in the number of 3D models presents a significant challenge for model retrieval. Currently, these models are numerous and typically represented as point clouds or meshes, resulting in sparse data and high feature dimensions within the retrieval database. Traditional methods for 3D model retrieval suffer from high computational complexity and slow retrieval speeds. To address this issue, this paper combines spatial-filling curves with octree structures and proposes a novel approach for representing three-dimensional voxel model sequence data features, along with a similarity measurement method based on symbolic operators. This approach enables efficient similarity calculations and rapid dimensionality reduction for the three-dimensional model database, facilitating efficient similarity calculations and expedited retrieval.

Fermatean fuzzy sets (FFSs) serve as a nascent yet potent approach for coping with fuzziness, with their efficacy recently being demonstrated across a spectrum of practical contexts. Nevertheless, the scholarly literature remains limited in exploring the similarity and distance measures tailored for FFSs. The limited existing measures on FFSs sometimes yield counter-intuitive outcomes, which can obfuscate the accurate quantification of similarity and difference among FFSs. This paper introduces a suite of similarity and distance measures tailored for FFSs, drawing inspiration from the Tanimoto measure. We delve into the characteristics of these novel measures and offer some comparative studies with existing FFSs measures, highlighting their superior efficacy in the processing of fuzzy data from FFSs. Our proposed measures effectively rectify the counter-intuitive situations encountered with many existing measures and demonstrate a significant enhancement in differentiating between diverse FFSs. Moreover, we showcase the real-world applicability of our proposed measures through case studies in pattern recognition, medical diagnostics, and multi-attribute decision-making.

Abstract The similarity measures are essential concepts to discuss the closeness between sets. Fuzzy similarity measures and intuitionistic fuzzy similarity measures dealt with the incomplete and inconsistent data more efficiently. With time in decision-making theory, a complex frame of the environment that occurs cannot be specified entirely by these sets. A generalization like the Pythagorean fuzzy set can handle such a situation more efficiently. The applicability of this set attracted the researchers to generalize it into N-Pythagorean, interval-valued N-Pythagorean, and N-cubic Pythagorean sets. For this purpose, first, we define the overlapping ratios of N-interval valued Pythagorean and N-Pythagorean fuzzy sets. In addition, we define similarity measures in these sets. We applied this proposed measure for comparison analysis of plagiarism software.

Pythagorean fuzzy set (PFS) is a broadening of intuitionistic fuzzy set that can represent the situations where the sum of membership and the non-membership values exceeds one. Adding parameterization to PFS, we obtain a structure named as Pythagorean fuzzy soft set (PFSS). It has a higher capacity to deal with vagueness as it captures both the structures of a PFS and a soft set. Several practical situations demand the measure of similarity between two structures, whose sum of membership value and non-membership value exceeds one. There are no existing tools to measure the similarity between PFSS and this paper put forward similarity measures for PFSS. An axiomatic definition for similarity measure is proposed for PFSS and certain expressions for similarity measure are introduced. Further, some theorems which express the properties of similarity measures are proved. A comparative study between proposed expressions for similarity measure is carried out. Also, a clustering algorithm based on PFSS is introduced by utilizing the proposed similarity measure. [ABSTRACT FROM AUTHOR]

Software projects reckon on the bug tracking systems to guide software maintenance activities. The critical information about the nature of the crash is carried by the bug reports which are submitted to bug repositories. This information is in free form text format and is submitted by users or developers. A large amount of bug reports gets collected in bug repositories. Out of these submitted bugs, many reports are mere identical of the already existing bugs. Furthermore, not all non-duplicate bugs are reproducible in nature. This paper introduces DENATURE, a two step framework for detecting duplication and identifying bug type. The proposed framework will help to minimize time and developer's effort utilized in resolution of bug reports which will further improvise overall software quality. Information retrieval techniques are used for finding duplicate bugs and machine learning classification techniques are used for identifying the type of bug report. Through experiments, we found that the proposed framework obtained prediction accuracy up to 88.81%. [ABSTRACT FROM AUTHOR]

Decision-making in a vague, undetermined and imprecise environment has been a great issue in real-life problems. Many mathematical theories like fuzzy, intuitionistic and neutrosophic sets have been proposed to handle such kinds of environments. Intuitionistic fuzzy sets (IFSS) were formulated by Atanassov in 1986 and analyze the truth membership, which assists in evidence, along with the fictitious membership. This article describes a composition of the intuitionistic fuzzy set (IFS) with the hypersoft set, which assists in coping with multi-attributive decision-making issues. Similarity measures are the tools to determine the similarity index, which evaluates how similar two objects are. In this study, we develop some distance and similarity measures for IFHSS with the help of aggregate operators. Also, we prove some new results, theorems and axioms to check the validity of the proposed study and discuss a real-life problem. The air quality index (AQI) is one of the major factors of the environment which is affected by air pollution. Air pollution is one of the extensive worldwide problems, and now it is well acknowledged to be deleterious to human health. A decision-maker determines ϸ = region (different geographical areas) and the factors{ᵹ=human activiteis,Ϥ=humidity level,ζ=air pollution} which enhance the AQI by applying decision-making techniques. This analysis can be used to determine whether a geographical area has a good, moderate or hazardous AQI. The suggested technique may also be applied to a large number of the existing hypersoft sets. For a remarkable environment, alleviating techniques must be undertaken. [ABSTRACT FROM AUTHOR]

In recent years, the increased use of smart devices and digital business opportunities has generated massive heterogeneous JSON data daily, making efficient data storage and management more difficult. Existing research uses different similarity metrics and clusters the documents to support the above tasks effectively. However, extant approaches have focused on either structural or semantic similarity of schemas. As JSON documents are application-specific, differently annotated JSON schemas are not only structurally heterogeneous but also differ by the context of the JSON attributes. Therefore, there is a need to consider the structural, semantic, and contextual properties of JSON schemas to perform meaningful clustering of JSON documents. This work proposes an approach to cluster heterogeneous JSON documents using the similarity fusion method. The similarity fusion matrix is constructed using structural, semantic, and contextual measures of JSON schemas. The experimental results demonstrate that the proposed approach outperforms the existing approaches significantly. [ABSTRACT FROM AUTHOR]

Software fault prediction is one of the most essential measures employed to evaluate software quality. There are many testing processes that are utilized to predict software faults, and among them, Black Box Testing (BBT) is used to predict faults without knowing the internal functioning of the application. In this article, a K-mean-based Machine Learning (ML) approach is explored to predict faults in software projects. The proposed model is divided into four phases. In the initial phase, the attributes of OOPs metrics that contribute to the accurate prediction of software faults are identified. In second phase, similarity between the metrics attributes is analysed using Cosine, Jaccard, and hybrid similarity measures. In the third stage, clustering of the correlated metrics attributes is performed using K-means as a clustering approach. At the last stage, Neural Network (NN) is applied as the ML approach for training and later on used for validation of the designed model. The comparative analysis is performed against the BBT and the existing work in terms of Positive Rate (TPR), Positive Predictive Value (PPV), F-score, and accuracy. The designed software fault prediction model using ML approach shows an overall classification accuracy of 94.3%. [ABSTRACT FROM AUTHOR]

Clustering methods in data mining aim to group a set of patterns based on their similarity. In a data survey, heterogeneous information is established with various types of data scales like nominal, ordinal, binary, and Likert scales. A lack of treatment of heterogeneous data and information leads to loss of information and scanty decision-making. Although many similarity measures have been established, solutions for heterogeneous data in clustering are still lacking. The recent entropy distance measure seems to provide good results for the heterogeneous categorical data. However, it requires many experiments and evaluations. This article presents a proposed framework for heterogeneous categorical data solution using a mini batch k-means with entropy measure (MBKEM) which is to investigate the effectiveness of similarity measure in clustering method using heterogeneous categorical data. Secondary data from a public survey was used. The findings demonstrate the proposed framework has improved the clustering’s quality. MBKEM outperformed other clustering algorithms with the accuracy at 0.88, v-measure (VM) at 0.82, adjusted rand index (ARI) at 0.87, and Fowlkes-Mallow’s index (FMI) at 0.94. It is observed that the average minimum elapsed time-varying for cluster generation, k at 0.26 s. In the future, the proposed solution would be beneficial for improving the quality of clustering for heterogeneous categorical data problems in many domains. [ABSTRACT FROM AUTHOR]

The characterization of ship routes and route similarity measurement based on Automatic Identification System (AIS) data are topics of various scientific interests. Common route research approaches use available AIS identifiers of ship types. However, assessing route and similarity profiles for individual fleets requires collecting data from secondary sources, dedicated software libraries or the creation of specific methods. Using an open-source approach, public AIS and ship data, we evaluate route characteristics for the container ships of a single fleet in a six-month period, calling on two selected ports of the shipping line on the USA East Coast. We evaluate the routes in terms of length, duration and speed, whereas for the similarity measurement we employ the discrete Fréchet distance (DFD). The voyage length, duration and average speed distributions were observed to be moderately positive (0.77), negative (−0.62), and highly positively skewed based on the adjusted Fisher–Pearson coefficient of skewness (1.23). The most similar voyages were from the same ships, with the lowest discrete Fréchet distance similarity value (0.9 NM), whereas 2 different ships had the most dissimilar voyages, with the highest DFD value (14.1 NM). The proposed methodology enables assessment of similarities between individual ships, or between fleets. [ABSTRACT FROM AUTHOR]

So far, the most prominent measure for actual truthlikeness, i.e. the likeness of a theory to the actual truth, is Ilkka Niiniluoto’s minsum definition, which is purely based on distances. A competing definition is the average distance measure proposed by Pavel Tichy and Graham Oddie. We will define three related, distance and size based, measures for actual truthlikeness and compare them with the two well-known options. However, we will start, Sect. 2, from a trio of such measures for nomic truthlikeness. The nomic truth, or the true theory, here refers to what is nomically, e.g. physically, possible. In a nomic (and factual) context there are two basic kinds of theories, viz. either based on an exclusion claim or on an inclusion claim. Two-sided theories combine these claims, with the maximal claim as extreme special case. We will base truthlikeness measures for exclusion, inclusion, two-sided, and hence maximal, nomic theories on two similarity measures, one in terms of distances between conceptual possibilities and the other in terms of sizes of sets of such possibilities. In Sect. 3 we will treat actual truthlikeness as extreme special case of nomic truthlikeness, viz. assuming that there is just one nomic possibility, the actual one. Next we will compare the resulting measures mutually and with the above mentioned measures of Niiniluoto and Tichy & Oddie. Finally, in Sect. 4, we will sum up the results and explore five questions for further research. [ABSTRACT FROM AUTHOR]

Problem: Similarity measures are widely used as an approved method for spectral discrimination or identification with their applications in different areas of scientific research. Even though a range of works have been presented, only a few showed slightly promising results for human tissue, and these were mostly focused on pathological and non-pathological tissue classification. Methods: In this work, several spectral similarity measures on hyperspectral (HS) images of in vivo human tissue were evaluated for tissue discrimination purposes. Moreover, we introduced two new hybrid spectral measures, called SID-JM-TAN(SAM) and SID-JM-TAN(SCA). We analyzed spectral signatures obtained from 13 different human tissue types and two different materials (gauze, instruments), collected from HS images of 100 patients during surgeries. Results: The quantitative results showed the reliable performance of the different similarity measures and the proposed hybrid measures for tissue discrimination purposes. The latter produced higher discrimination values, up to 6.7 times more than the classical spectral similarity measures. Moreover, an application of the similarity measures was presented to support the annotations of the HS images. We showed that the automatic checking of tissue-annotated thyroid and colon tissues was successful in 73% and 60% of the total spectra, respectively. The hybrid measures showed the highest performance. Furthermore, the automatic labeling of wrongly annotated tissues was similar for all measures, with an accuracy of up to 90%. Conclusion: In future work, the proposed spectral similarity measures will be integrated with tools to support physicians in annotations and tissue labeling of HS images. [ABSTRACT FROM AUTHOR]

The choice of similarity measure (SM) plays an important role in distinguishing between objects. Similarity measure of Pythagorean fuzzy sets (PFSs) is very useful and effective in discriminating between different Pythagorean fuzzy sets. Therefore, in this paper, we suggest a new similarity measure for PFSs based on converting the PFSs into their lower, upper and middle fuzzy sets (FSs) to calculate their degree of similarity. We construct an axiomatic definition for a new SM of PFSs. Furthermore, we put forward a new way to express the similarity measure of PFSs to show its competency, reliability and applicability. For establishing reasonability and usefulness of the proposed methods, we present several practical examples related to pattern recognition and multicriteria decision making problems. Finally, we construct an algorithm for Portuguese of interactive and multiple attributes decision making (TODIM) method based on the proposed similarity measures, for handling complex multicriteria decision making problems related to day to day life. Our final results show that the suggested method is reasonable, reliable and useful in managing different complex decision making problems in the context of Pythagorean fuzzy sets as the domain. [ABSTRACT FROM AUTHOR]

Gaussian Mixture Models (GMMs) are used in many traditional expert systems and modern artificial intelligence tasks such as automatic speech recognition, image recognition and retrieval, pattern recognition, speaker recognition and verification, financial forecasting applications and others, as simple statistical representations of underlying data. Those representations typically require many high-dimensional GMM components that consume large computing resources and increase computation time. On the other hand, real-time applications require computationally efficient algorithms and for that reason, various GMM similarity measures and dimensionality reduction techniques have been examined to reduce the computational complexity. In this paper, a novel GMM similarity measure is proposed. The measure is based on a recently presented nonlinear geometry-aware dimensionality reduction algorithm for the manifold of Symmetric Positive Definite (SPD) matrices. The algorithm is applied over SPD representations of the original data. The local neighborhood information from the original high-dimensional parameter space is preserved by preserving distance to the local mean. Instead of dealing with high-dimensional parameter space, the method operates on much lower-dimensional space of transformed parameters. Resolving the distance between such representations is reduced to calculating the distance among lower-dimensional matrices. The method was tested within a texture recognition task where superior state-of-the-art performance in terms of the trade-off between recognition accuracy and computational complexity has been achieved in comparison with all baseline GMM similarity measures. [ABSTRACT FROM AUTHOR]

There exist multiple online collections and data bases of scientific articles publicly available, to take full advantage of these resources, it is necessary to process, arrange and correlate texts with respect to a classification or ontology. To achieve an efficient organization and a more relevant correlation between texts, it is necessary to use a similarity measure for short texts. However, determining the best method to calculate the similarity between texts is an arduous task, since there are many similarity measures reported in literature. Additionally, the collection of texts to which the similarity measures are applied should be considered; while some measures are useful for some types of information sources, they fail when the collection of data changes. Therefore, it is necessary to count with a method to evaluate the performance of similarity measures from a statistical perspective and in terms of the accuracy achieved by each measure. [ABSTRACT FROM AUTHOR]

A similarity measure is used to tackle many issues that include indistinct and blurred information, excluding is not able to deal with the general fuzziness and obscurity of the problems that have various information. The neutrosophic hypersoft set is the most generalized and advanced extension of neutrosophic sets, which deals with the multi sub-attributes of the considered parameters. In this paper, we study some basic concepts which are helpful to build the structure of the article, such as soft set, neutrosophic soft set, hypersoft set, and neutrosophic hypersoft set, etc. The main objective of the present research is to develop a cosine similarity measure and set-theoretic similarity measure for an NHSS with their necessary properties. A decision-making approach has been established by using cosine and set-theoretic similarity measures. Furthermore, we used to develop a technique to solve multi-criteria decision-making problems. Finally, the advantages, effectiveness, flexibility, and comparative analysis of the algorithms are given with prevailing methods.

In the past few decades recommender system has reshaped the way of information filtering between websites and the users. It helps in identifying user interest and generates product suggestions for the active users. This paper presents an enlightening analysis of various recommender system such as content-based, collaborative-based and hybrid recommendation techniques along with few optimization models that has been applied to improvise the parameters being considered by the aforementioned techniques. We explored 125 articles published from 1992 to 2019 in order to discuss the problems associated with the existing models. Various advantages and disadvantages of each recommendation model including the input methods has been elaborated. Critical review on research problems based on the explored techniques and future directions has also been covered.

Clustering is a fundamental task in data analysis, aiming to partition a set of samples into subsets called clusters based on their similarity. Agglomerative Hierarchical Clustering (AHC) is a common hierarchical clustering method in which clusters are formed bottom-up. The AHC-based ensemble clustering technique has emerged as an important extension of classical clustering problems and is one of the most recent advances in unsupervised learning. The aim of this technique is to combine the output results of several individual AHC-based methods to achieve a consensus with higher accuracy. In this study, we address the problem of semi-supervised ensemble clustering, which combines ensemble clustering methods and semi-supervised clustering techniques to improve clustering accuracy. We propose a novel framework that integrates AHC methods to create primary partitions, leveraging the diversity offered by AHC to enhance clustering quality. Our approach includes a comprehensive selection process to reduce computational complexity and a new similarity measure developed using a flexible weighting mechanism. The purpose of this mechanism is to describe the consistency between semi-supervised clustering methods used to generate base partitions. In general, the three main steps of the proposed method include creating primary clusters with different AHC methods based on constraint information, developing an innovative similarity measure to calculate the similarity between objects, and finally re-clustering the primary clusters to create final clusters. We conducted experiments on real-world datasets to evaluate the effectiveness of the proposed method. The findings show significant improvements in clustering accuracy compared to equivalent methods. • Presenting a robust semi-supervised method based on ensemble learning. • Configuration of an AHC-based clustering framework by joining ECM and SSC. • Introducing a new similarity measure based on a flexible weighting mechanism. • Development of a merit-based selection strategy to reduce complexity in consensus. • The proposed method performs well in sparse and large-scale data. [ABSTRACT FROM AUTHOR]

Scientific progression has allowed researchers to develop novel and innovative ways to deal with uncertainty in data, allowing for the development of more precise and accurate data representation models. This paper aims to extend an already reported concept of Cubic Pythagorean fuzzy set to Cubic Pythagorean Fuzzy Soft Set (C P F S s) as it incorporates both interval-valued Pythagorean fuzzy sets (IVPFS) and Pythagorean fuzzy sets (PFS) at the same time, providing a more targeted approach to deal with uncertainty. This hybrid structure can better handle data in comparison to the ones in the literature by having the characteristics of PFS and soft sets, leading to a more targeted approach to handle attributes in decision-making studies. In this study, we defined various internals and externals of C P F S s , set operators, aggregation operators, and developed an algorithm based on distance measures for ( C P F S s ), which are applied in a disease diagnostic decision-making problem. [ABSTRACT FROM AUTHOR]

Two famous matrix factorization techniques, the Singular Value Decomposition (SVD) and the Nonnegative Matrix Factorization (NMF), are popularly used by recommender system applications. Recommender system data matrices have many missing entries, and to make them suitable for factorization, the missing entries need to be filled. For matrix completion, we use mean, median and mode as three different cases of imputation. The natural clusters produced after factorization are used to formulate simple out-of-sample extension algorithms and methods to generate recommendation for a new user. Two cluster evaluation measures, Normalized Mutual Information (NMI) and Purity are used to evaluate the quality of clusters. [ABSTRACT FROM AUTHOR]

In recent years, we have witnessed a surge of interests in learning distance metrics from various data mining tasks. Most existing methods aim to pull all the similar samples closer while push the dissimilar ones as far as possible. However, when some classes of the dataset exhibit multimodal distribution, these goals conflict and thus can hardly be concurrently satisfied. Additionally, to ensure a valid metric, many methods require a repeated eigenvalue decomposition process, which is time-consuming and numerically unstable. Therefore, how to effectively learn an appropriate distance metric from weakly supervised data remains an open but challenging problem. To address this issue, in this paper, we propose a novel weakly supervised metric learning algorithm, named MultimoDal aware weakly supervised Metric Learning (MDaML). MDaML partitions training data into several clusters and allocates the local cluster center and weight for each sample. Then, combining it with the weighted triplet loss can further enhance the local separability, which encourages local dissimilar samples to keep a large distance from local similar samples. Meanwhile, MDaML casts the metric learning problem into an unconstrained optimization on SPD manifold, which can be efficiently solved by Riemannian Conjugate Gradient Descent (RCGD). Extensive experiments conducted on 13 datasets validate the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

Link prediction is a widely studied topic in graph data analytics and finds numerous applications like friend recommendations in social networks and product recommendations in e-commerce. It refers to predicting new connections or edges that may arise in the near future amongst the nodes of the network. There exist various methods of link prediction generally based on either local, semi-local, or global features of networks and usually suffers from the problems of consistency in their performances over different and large size networks. In this paper, we intend to propose a generic and improved method of link prediction named as NSMLLP by integrating Node centralities, Similarity measures, and Machine Learning classifiers. We calculate popularity measures for every node and evaluate similarity measures for every pair of nodes in the network. The combined popularity and similarity measures form the features for every node pair in the network. The combined features of the nodes at the end of the edges, along with the positive or negative edge label, form a well-defined dataset for the task of link prediction. This dataset is then fed into machine learning classifiers like Random Forest classifier, AdaBoost classifier, and an ANN based classifier. The results obtained from these classifiers are then combined to make the final link prediction. We provide an information gain study aiming to quantify the improvement brought on by our proposed method. A feature importance study is also provided to comprehend better the relative importance of the various popularity and similarity measures used by us. The experimental results obtained on multiple real-life networks demonstrate that the proposed technique outperforms many existing popular methods of link predication based on several evaluation criteria. [ABSTRACT FROM AUTHOR]

According to available estimates with WHO, cancers are the sixth leading cause of global human morbidity and mortality. Prostate Cancer is the fifth-ranked most lethal among various cancers, and hence it warrants serious, dedicated research for improving its early detection. The employed methodologies such as prostate-specific antigen test, Gleason Score, and T2 Staging lack precision and accuracy in conditions where information is scarring, vague and uncertain. Consequently, in the present study, the innovative use of neutrosophic cubic fuzzy sets (NCFS) is employed to improve prostate cancer detection in situations where basic information is vague, imprecise, and uncertain. Specific and critical similarity measures are defined for using NCFS methodology for the evaluation of prostate cancer. This methodology is found reasonably better compared to the existing benchmark methods for the detection and grading of prostate cancer. [ABSTRACT FROM AUTHOR]

In this paper, we present the second generation of the nomclust R package, which we developed for the hierarchical clustering of data containing nominal variables (nominal data). The package completely covers the hierarchical clustering process, from dissimilarity matrix calculation, over the choice of a clustering method, to the evaluation of the final clusters. Through the whole clustering process, similarity measures, clustering methods, and evaluation criteria developed solely for nominal data are used, which makes this package unique. In the first part of the paper, the theoretical background of the methods used in the package is described. In the second part, the functionality of the package is demonstrated in several examples. The second generation of the package is completely rewritten to be more natural for the workflow of R users. It includes new similarity measures and evaluation criteria. We also added several graphical outputs and support for S3 generic functions. Finally, due to code optimizations, the calculation time of dissimilarity matrix calculation was substantially reduced. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new formula for the entropy based on similarity measures of intuitionistic fuzzy sets (IFS). The contribution of this work is the proof that the new formula satisfies all the conditions of entropy. The experimentation on some examples shows that the new entropy is useful. Besides, we use the new entropy and similarity measures to design an algorithm for ranking assets in stock markets. The numerical results on 5 benchmark data sets were reported. It points out that the entropy and the similarity measures of IFS may provide an alternative tool for solving portfolio selection problems. [ABSTRACT FROM AUTHOR]

The intuitionistic fuzzy sets (IFSs) have a more significant contribution to describing and dealing with uncertainty. The intuitionistic fuzzy measure is a significant consideration in the field of IFSs theory. However, Pythagorean fuzzy sets (PFSs) are an extension of the IFSs. PFSs are more capable of modelling uncertainties than IFSs in real-world decision-making scenarios. The majority of PFSs research has concentrated on establishing decision-making frameworks. A similarity measure is a key concept which measures the closeness of PFSs. IFSs-based similarity measures have been proposed in the literature. This type of similarity measure, however, has a drawback since it cannot satisfy the axiomatic definition of similarity by offering counter-intuitive examples. For this study, a similarity-based on logarithmic function for Pythagorean fuzzy sets (PFSs) is proposed as a solution to the problem. A decision-making approach is presented to ascertain the suitability of careers for aspirants. Additionally, numerical illustration is applied to determine the strength and validity of the proposed similarity measures. The application of the proposed similarity measures is also presented in this article. A comparison of the suggested measures with the existing ones is also demonstrated to ensure the reliability of the measures. The results show that the proposed similarity measures are efficient and reasonable from both numerical and realistic assessments. [ABSTRACT FROM AUTHOR]

A technique for compensating the influence of the image interpolation effect in the estimation algorithms of mutual spatial deformations of images has been proposed. The technique has been approved for some of the similarity measures of images used in the synthesis of algorithms, in particular, the mean square of the inter-frame difference in the image brightness, the inter-frame correlation coefficient, and the Shannon mutual information. The calculated expressions for compensating the influence of the bilinear and bicubic interpolations have been obtained. The developed technique is also applicable to other similarity measures used in the synthesis of the algorithms for estimating spatial deformations of images, as well as any other types of interpolations: spline, those using Lagrange polynomials, Newton, power functions, etc. [ABSTRACT FROM AUTHOR]