A high-precision and fast algorithm for computation of Jacobi–Fourier moments (JFMs) is presented. A fast recursive method is developed for the radial polynomials that occur in the kernel function of the JFMs. The proposed method is numerically stable and very fast in comparison with the conventional direct method. Moreover, the algorithm is suitable for computation of the JFMs of the highest orders. The JFMs are generic expressions to generate orthogonal moments changing the parameters $\alpha$ and $\beta$ of Jacobi polynomials. The quality of the description of the proposed method with $\alpha$ and $\beta$ parameters known is studied. Also, a search is performed of the best parameters, $\alpha$ and $\beta$, which significantly improves the quality of the reconstructed image and recognition. Experiments are performed on standard test images with various sets of JFMs to prove the superiority of the proposed method in comparison with the direct method. Furthermore, the proposed method is compared with other existing methods in terms of speed and accuracy.

A detailed analysis of the quaternion generic Jacobi-Fourier moments (QGJFMs) for color image description is presented. In order to reach numerical stability, a recursive approach is used during the computation of the generic Jacobi radial polynomials. Moreover, a search criterion is performed to establish the best values for the parameters $α$ and $β$ of the radial Jacobi polynomial families. Additionally, a polar pixel approach is taken into account to increase the numerical accuracy in the calculation of the QGJFMs. To prove the mathematical theory, some color images from optical microscopy and human retina are used. Experiments and results about color image reconstruction are presented.

Human–robot interaction is becoming increasingly common to perform useful tasks in everyday life. From the human–machine communication perspective, achieving effective interaction in natural language is one challenge. To address it, natural language processing strategies have recently been used, commonly following a supervised machine learning framework. In this context, most approaches rely on the use of linguistic resources (e.g., taggers or embeddings), including training corpora. Unfortunately, such resources are scarce for some languages in specific domains, increasing the complexity of solution approaches. Motivated by these challenges, this paper explores deep learning methods for understanding natural language commands emitted to service robots that guide their movements in low-resource scenarios, defined by the use of Spanish and Nahuatl languages, for which linguistic resources are scarcely unavailable for this specific task. Particularly, we applied natural language understanding (NLU) techniques using deep neural networks and transformers-based models. As part of the research methodology, we introduced a labeled dataset of movement commands in the mentioned languages. The results show that models based on transformers work well to recognize commands (intent classification task) and their parameters (e.g., quantities and movement units) in Spanish, achieving a performance of 98.70% (accuracy) and 96.96% (F1) for the intent classification and slot-filling tasks, respectively). In Nahuatl, the best performance obtained was 93.5% (accuracy) and 88.57% (F1) in these tasks, respectively. In general, this study shows that robot movements can be guided in natural language through machine learning models using neural models and cross-lingual transfer strategies, even in low-resource scenarios.

Bees play a critical role in pollination and food production, so their preservation is essential, particularly highlighting the importance of detecting diseases in bees early. The Varroa destructor mite is the primary factor contributing to increased viral infections that can lead to hive mortality. This study presents an innovative method for identifying Varroa destructors in honey bees using multichannel Legendre–Fourier moments. The descriptors derived from this approach possess distinctive characteristics, such as rotation and scale invariance, and noise resistance, allowing the representation of digital images with minimal descriptors. This characteristic is advantageous when analyzing images of living organisms that are not in a static posture. The proposal evaluates the algorithm’s efficiency using different color models, and to enhance its capacity, a subdivision of the VarroaDataset is used. This enhancement allows the algorithm to process additional information about the color and shape of the bee’s legs, wings, eyes, and mouth. To demonstrate the advantages of our approach, we compare it with other deep learning methods, in semantic segmentation techniques, such as DeepLabV3, and object detection techniques, such as YOLOv5. The results suggest that our proposal offers a promising means for the early detection of the Varroa destructor mite, which could be an essential pillar in the preservation of bees and, therefore, in food production.

Color image reconstruction provides a measure of the feature representation capability of the moment functions. In this work, we present the quaternion Fourier-Legendre moments in polar pixels, which are computationally faster and have a high-precision compared with other methods. In addition, to improve the performance of the array of polar pixels, we use an inherent property of the Legendre polynomials for the accurate calculation of kernel integration. Moreover, the presented new set of quaternion Fourier-Legendre moments is compared with other families proposed, such as quaternion Zernike moments, quaternion pseudo-Zernike moments, quaternion orthogonal Fourier-Mellin moments, and quaternion Bessel-Fourier moments. Experimental results show the superiority of the new quaternion moments in terms of the reconstruction error.