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Color image recognition has recently attracted more researchers' attention. Many methods based on quaternions have been developed to improve the classification accuracies. Some approaches have currently used quaternions with convolutional neural network (CNN). Despite the obtained results, these approaches have some weakness such as the computational complexity. In fact, the large size of the input color images necessitates a high number of layers and parameters during the learning process which can generate errors calculation and hence influence the recognition rate. In this paper, a new architecture called quaternion discrete orthogonal Hahn moments convolutional neural network (QHMCNN) for color image classification and face recognition is proposed to reduce the computational complexity of CNN while improving the classification rate. The quaternion Hahn moments are used to extract pertinent and compact features from images and introduced them in quaternion convolutional neural network. Experimental simulations conducted on various databases are demonstrated the performance of the proposed architecture QHMCNN against other relevant methods in state-of-the-art and the robustness under different noise conditions. [ABSTRACT FROM AUTHOR]

With the rapid development of 3D technology, 3D object classification has recently become a popular research topic in computer graphics and pattern recognition. Analyzing the shape of 3D models has become a common concern for researchers. A crucial technique for analyzing these 3D shapes is to capture features from 3D models that can sufficiently distinguish their shapes. While the 3D discrete orthogonal moments are powerful for the analysis and representation of 3D objects. It was proved that they have a better feature representation capability than the continuous orthogonal moments. This paper presents a new model for 3D shape classification named 3D Hahn moments neural networks (3DHMNNs) to improve the classification accuracy and decrease the computational complexity of 3D pattern recognition process. The proposed model is derived by introducing 3D Hahn moments as an input layer in neural network, largely utilized in various applications related to the pattern recognition. In fact, the advantages of image moments, especially discrete orthogonal moments have the property to extract relevant features from an object in lower orders and their robustness against image noise. Along with the efficiency of the neural networks, we can construct the proposed robust model. The main purpose of this work is to investigate the classification capabilities of the proposed model on rigid and non-rigid 3D shape datasets. The experiment simulations are conducted on the Articulated of McGill Princeton Shape Benchmark (PSB), SHREC'2011, ModelNet10 and ModelNet40 databases to assess the effectiveness of our proposed model. Two structures of the proposed model are constructed as noted 3DHMNNs6 layers and 3DHMNNs7 layers. The obtained results indicate that the proposed model provide a reasonable performance in terms of classification accuracy by achieving 90.96% on ModelNet10, 83.87% on ModelNet40, 97.66% on SHREC'2011 and over 90.16% on Articulated McGill outperforming other existing methods as well as being more robust under noisy conditions. [ABSTRACT FROM AUTHOR]

In recent years, with the rapid development of multimedia technologies, color face recognition has attracted more attention in various areas related to the computer vision. Extracting pertinent features from color image is a challenging problem due to the lack of efficient descriptors. Many methods in literature have been reported. However, some inconveniences arising from these methods are: insufficient color information and time consuming for features extraction. In this paper, a new model quaternion discrete orthogonal moments neural networks (QDOMNN) is proposed to improve the accuracy of color face recognition. The quaternion representation is used to represent color image in a holistic manner instead of monochromatic intensity information. Furthermore, the discrete orthogonal moments are used to extract compact and pertinent features from quaternion representation of image. The main purpose of the utilization of quaternion discrete orthogonal moments is to reduce the number of parameters in the input vector of the model, and consequently decreasing the computational time of training process, while improving the classification rate. The performance of our model is evaluated on some face databases, we obtain 100% as classification accuracy on faces94, grimace and GT, 91.93% on FEI, more than 94.72% on faces95 and more than 98.01% on faces96. Experiment results show the outperformance of our model (QDOMNN) against other existing methods in terms of classification rate, and robustness in noisy conditions. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new model based on 3D discrete orthogonal moments and deep neural networks (DNN) to improve the classification accuracy of 3D objects under geometric transformations and noise. However, the utilization of moment invariants presents some drawbacks: They can't describe the object efficiently, and their computation process is time consuming. Discrete orthogonal moments have the property to extract pertinent features from an image even in lower orders and are robust to noise. The main goal of this work is to investigate the robustness of the proposed model to geometric transformations like translation, scale and rotation and noisy conditions. The experiment simulations are conducted on datasets formed by applying some geometric transformations and noise on selected objects from McGill database. The obtained results indicate that the proposed model achieves high performance classification rates, robust to geometric transformations and noise degradation than other methods based on moment invariants. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new sets of 2D and 3D rotation, scaling and translation invariants based on orthogonal radial Racah moments. We also provide theoretical mathematics to derive them. Thus, this work proposes in the first case a new 2D radial Racah moments based on polar representation of an object by one-dimensional orthogonal discrete Racah polynomials on non-uniform lattice, and a circular function. In the second case, we present new 3D radial Racah moments using a spherical representation of volumetric image by one-dimensional orthogonal discrete Racah polynomials and a spherical function. Further 2D and 3D invariants are extracted from the proposed 2D and 3D radial Racah moments respectively will appear in the third case. To validate the proposed approach, we have resolved three problems. The 2D/ 3D image reconstruction, the invariance of 2D/3D rotation, scaling and translation, and the pattern recognition. The result of experiments show that the Racah moments have done better than the Krawtchouk moments, with and without noise. Simultaneously, the mentioned reconstruction converges rapidly to the original image using 2D and 3D radial Racah moments, and the test 2D/3D images are clearly recognized from a set of images that are available in COIL-20 database for 2D image, and PSB database for 3D image. [ABSTRACT FROM AUTHOR]

A correction is presented to the articles "Radial invariant of 2D and 3DRacah moments" and Multimed Tools Appl which appeared in the August 8, 2017, issue.