The paper proposes a novel weighted convolution for signals defined on regular grids (2D images) by optimising a density function that scales the contribution of neighbouring pixels according to their distance from the central pixel. This choice differs from the uniform convolution, which treats all neighbouring pixels equally. Given a convolutional network, we compute the optimal density by minimising a loss functional, with the density function as the variable. Then, the weighted convolution is applied to CNNs to improve the accuracy of image-processing tasks (denoising, classification). The optimal density improves the convergence of the weights of the learning model with respect to the uniform density. The framework separates the optimisation of the convolutional kernel weights (using a stochastic gradient descent method) from the density optimisation (using the DIRECT-L algorithm). Experimental tests on SOTA learning models for image denoising and classification show that the weighted convolution significantly improves the performance compared to standard convolution. For example, the denoising of the DIV2K dataset with Gaussian noise through the DnCNN model with the weighted convolution reaches a PSNR of 31.02, compared to the 29.09 value of the model with the standard convolution. While our method increases execution time by on standard hardware and by on GPU in modern HPC environments, it is robust across several hyperparameters of the learning model. • We introduce an optimal weighted convolution that applies a density function to scale pixel contribution. • A density function is optimised to increase the accuracy of learning models. • Optimal weighted convolution improves image denoising and classification problems.

Abstract Purpose: Several applications require the super-resolution of noisy images and the preservation of geometrical and texture features. State-of-the-art super-resolution methods do not account for noise and generally enhance the output image’s artefacts (e.g., aliasing, blurring). Methods: We propose a learning-based method that accounts for the presence of noise and preserves the properties of the input image, as measured by quantitative metrics, e.g., normalised crossed correlation, normalised mean squared error, peak-signal-to-noise-ration, structural similarity feature-based similarity, universal image quality. We train our network to up-sample a low-resolution noisy image while preserving its properties. We perform our tests on the Cineca Marconi100 cluster, at the 26th position in the “top500” list. Results: The experimental results show that our method outperforms learning-based methods, has comparable results with standard methods, preserves the properties of the input image as contours, brightness, and textures, and reduces the artefacts. As average quantitative metrics, our approach has a PSNR value of 23.81 on the super-resolution of Gaussian noise images with a 2X up-sampling factor. In contrast, previous work has a PSNR value of 23.09 (standard method) and 21.78 (learning-based method). Conclusion: Our learning-based and quality-preserving super-resolution improves the high-resolution prediction of noisy images with respect to state-of-the-art methods with different noise types and up-sampling factors.

The F-transform has proven to be effective in various applications, such as time series analysis, numerical solutions of differential equations, and signal or image processing. The most important parameter of the F-transform is a fuzzy partition initially introduced for 1-D spaces, with a few generalizations to higher dimensional spaces. However, these generalizations have a limited application to signals defined on domains with arbitrary geometry. To overcome this limitation, we propose using nonseparable membership functions induced by kernels, allowing the application of the F-transform to more general domains. We introduce a universal concept of a fuzzy partition that includes a kernel representation, a fuzzy partition, and the corresponding F-transform. In addition, we discuss the main properties of this generalized F-transform and characterize the nonlocal Laplace operator in terms of the F-transform. We also discuss image denoising as the main application and compare our results with state-of-the-art methods and different noise types and intensities.

The definition of the F-transform has been limited mainly to 1D signals and 2D data due to the difficulty of defining membership functions, their centres, and support on a domain with arbitrary dimensionality and topology. We propose a novel method for the adaptive selection of the optimal centres and supports of a class of radial membership functions based on minimising the reconstruction error of the input signal as the Ftransform and its inverse, or as a weighted linear combination of the membership functions. Replacing uniformly sampled centres of the membership functions with adaptive centres and fixed supports with adaptive supports allows us to preserve the input signal's local and global features and achieve a good approximation accuracy with fewer membership functions. We compare our method with uniform sampling and previous work. As a result, we improve the image reconstruction with respect to compared methods and we reduce the underlying computational cost and storage overhead. Finally, our approach applies to any class of continuous membership functions.

Abstract Depth sensors of low-cost acquisition devices (e.g. Microsoft Kinect, Asus Xtion) are coming into widespread use; however, 3D acquired data are generally large, heterogeneous, and complex to analyse and interpret. In this context, our overall goal is the analysis of the action of a subject in a 3D video, e.g. the action of a human or the movement of its subparts. To this end, the action classification is achieved through the analysis of the temporal variation of geometric (e.g. centroid path, volume variation, activated voxels) and kinematic (e.g. speed) properties in consecutive frames. Then, these descriptors and the corresponding histograms are used to search a frame in a 3D video and to compare 3D videos. Our approach is applied to 3D videos represented as triangle meshes or point sets, and eventually to an underlying skeleton or to markers (if available). Our tests on the MIT, Berkley, i3DPost, NTU, and DUTH data sets confirm the usefulness of the proposed approach for the analysis and comparison of 3D videos, as well as for action classification.