Pablo Flores-Vidal

Aggregation functions are vital across diverse domains, including data fusion, decision-making, and image processing. While conventionally defined in continuous spaces, their translation into discrete spaces is crucial for pre-processing tasks such as image smoothing. This study is devoted to the notion of pre-aggregation functions and presents an innovative perspective on directional monotonicity, specifically suited for discrete lattice structures. We analyze the shortcomings of current directional monotonicity concepts within discrete environments and develop an improved framework that more accurately reflects their behavior. This approach is tested by redefining RGB image smoothing. Among others, a new class of median filters, named 'Discrete median', is presented. This and other redefined functions must satisfy two fundamental characteristics: operation within a discrete domain and monotonicity. To implement these functions for RGB images, the concept of decomposable functions is established. The efficacy of this methodology is illustrated by adjusting two established approaches based on the mean and median, and by a third, the Medoid utilizing different distances: Manhattan distance (L 1) and Euclidean distance. Ultimately, the benefits of the suggested decomposable discrete median method (and its proof equivalent medoid with L 1 distance) compared with conventional smoothing techniques are highlighted.

The majority of edge detection algorithms only deal with grayscale images, while their use with color images remains an open problem. This paper explores different approaches to aggregate color information of RGB and HSV images for edge extraction purposes through the usage of the Sobel operator and Canny algorithm. This paper makes use of Berkeley’s image data set, and to evaluate the performance of the different aggregations, theF-measure is computed. Higher potential of aggregations with HSV channels than with RGB channels is found. This article also shows that depending on the type of image used, RGB or HSV, some methods are more appropriate than others.

In this paper, machine learning (ML) techniques are applied at an early stage of Image Processing (IP). The learning procedures are usually applied from at least the image segmentation level, whereas, in this paper, this is done from a lower processing level: the edge detection level (ED). The main objective is to solve the edge detection problem through ML techniques. The proposed methodology is based on a classification of edges made pixel by pixel, but the predictors employed for the ML task include information about the pixel neighborhood and structures of connected pixels called edge segments. The Sobel operator is employed as input. Making use of 50 images that belong to the Berkeley Computer Vision data set, the average performance of the validation sets when employing our Neural Networks method reached an F-measure significatively higher than with the Sobel operator. The experiment results show that our post-processing technique is a promising new approach for ED.