Fuzzy metrics and fuzzy logic for colour image filtering

El filtrado de imagen es una tarea fundamental para la mayoría de los sistemas de visión por computador cuando las imágenes se usan para análisis automático o, incluso, para inspección humana. De hecho, la presencia de ruido en una imagen puede ser un grave impedimento para las sucesivas tareas de procesamiento de imagen como, por ejemplo, la detección de bordes o el reconocimiento de patrones u objetos y, por lo tanto, el ruido debe ser reducido. En los últimos años el interés por utilizar imágenes en color se ha visto incrementado de forma significativa en una gran variedad de aplicaciones. Es por esto que el filtrado de imagen en color se ha convertido en un área de investigación interesante. Se ha observado ampliamente que las imágenes en color deben ser procesadas teniendo en cuenta la correlación existente entre los distintos canales de color de la imagen. En este sentido, la solución probablemente más conocida y estudiada es el enfoque vectorial. Las primeras soluciones de filtrado vectorial, como por ejemplo el filtro de mediana vectorial (VMF) o el filtro direccional vectorial (VDF), se basan en la teoría de la estadística robusta y, en consecuencia, son capaces de realizar un filtrado robusto. Desafortunadamente, estas técnicas no se adaptan a las características locales de la imagen, lo que implica que usualmente los bordes y detalles de las imágenes se emborronan y pierden calidad. A fin de solventar este problema, varios filtros vectoriales adaptativos se han propuesto recientemente. En la presente Tesis doctoral se han llevado a cabo dos tareas principales: (i) el estudio de la aplicabilidad de métricas difusas en tareas de procesamiento de imagen y (ii) el diseño de nuevos filtros para imagen en color que sacan provecho de las propiedades de las métricas difusas y la lógica difusa. Los resultados experimentales presentados en esta Tesis muestran que las métricas difusas y la lógica difusa son herramientas útiles para diseñar técnicas de filtrado,Morillas Gómez, S. (2007). Fuzzy metrics and fuzzy logic for colour image filtering [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/1879Palanci

Distance Measures for Reduced Ordering Based Vector Filters

Reduced ordering based vector filters have proved successful in removing long-tailed noise from color images while preserving edges and fine image details. These filters commonly utilize variants of the Minkowski distance to order the color vectors with the aim of distinguishing between noisy and noise-free vectors. In this paper, we review various alternative distance measures and evaluate their performance on a large and diverse set of images using several effectiveness and efficiency criteria. The results demonstrate that there are in fact strong alternatives to the popular Minkowski metrics

Adaptive Marginal Median Filter for Colour Images

This paper describes a new filter for impulse noise reduction in colour images which is aimed at improving the noise reduction capability of the classical vector median filter. The filter is inspired by the application of a vector marginal median filtering process over a selected group of pixels in each filtering window. This selection, which is based on the vector median, along with the application of the marginal median operation constitutes an adaptive process that leads to a more robust filter design. Also, the proposed method is able to process colour images without introducing colour artifacts. Experimental results show that the images filtered with the proposed method contain less noisy pixels than those obtained through the vector median filter

Robustifying Vector Median Filter

This paper describes two methods for impulse noise reduction in colour images that outperform the vector median filter from the noise reduction capability point of view. Both methods work by determining first the vector median in a given filtering window. Then, the use of complimentary information from componentwise analysis allows to build robust outputs from more reliable components. The correlation among the colour channels is taken into account in the processing and, as a result, a more robust filter able to process colour images without introducing colour artifacts is obtained. Experimental results show that the images filtered with the proposed method contain less noisy pixels than those obtained through the vector median filter. Objective measures demonstrate the goodness of the achieved improvement

On the importance of metrics in practical applications

[EN] Students motivation for learning mathematical concepts can be increased when showing the usefulness of these concepts in practical problems. One important mathematical concept is the concept of metric space and, more related to the applications, the concept of metric function. In this work we aim to illustrate how important is to appropriately choose the metric when dealing with a practical problem. In particular, we focus on the problem of detection of noisy pixels in colour images. In this context, it is very important to appropriately measure the distances and similarities between the image pixels, which is done by means of an appropriate metric. We study the performance of different metrics, including recent fuzzy metrics, within a specific filter to show that it is indeed a critical choice to appropriately solve the task.Camarena, J.; Morillas, S.; Cisneros, F. (2011). On the importance of metrics in practical applications. Modelling in Science Education and Learning. 4:119-128. doi:10.4995/msel.2011.3066SWORD119128

Fuzzy averaging filter for impulse noise reduction in colour images with a correction step

[EN] In this paper we propose a fuzzy detection and reduction method for impulse noise in colour images. Detection is based on the fuzzyfication of a well-known statistic called ROD. The noise degrees obtained are used to reduce impulses by employing a fuzzy averaging between the input colour vector and a robust estimate of noise-free colour vector within the input neighbourhood. Fuzzy averaging has some advantages in terms of both noise reduction and detail preservation in front of detect and replace approaches because of threshold based decisions of the latter. However, robustness of the former is lower. We solve this problem by including a correction mechanism that checks the fuzzy noise degree of the output and replaces it with a robust colour vector either when noise has not been properly reduced or when a colour artefact has been introduced. We carry out a thorough study of the method parameter setting and give a convenient and robust setting. Experimental results show that our approach is very robust in front of four different types of impulse noise.The authors are very grateful to the reviewers for their valuable suggestions. Valentin Gregori and Samuel Morillas acknowledges the support of Ministry of Economy and Competitiveness of Spain under grant MTM 2015-64373-P (MINECO/FEDER, UE). Bernardino Roig and Almanzor Sapena acknowledges the support of Generalitat Valencians under grant AICO/2017/059.Gregori Gregori, V.; Morillas, S.; Roig, B.; Sapena Piera, A. (2018). Fuzzy averaging filter for impulse noise reduction in colour images with a correction step. Journal of Visual Communication and Image Representation. 55:518-528. https://doi.org/10.1016/j.jvcir.2018.06.025S5185285

Adaptive geometric features based filtering impulse noise in colour images

An adaptive geometric features based filtering (AGFF) technique with a low computational complexity is proposed for removal of impulse noise in corrupted color images. The effective and efficient detection is based on geometric characteristics and features of the corrupted pixel and/or the pixel region. A progressive restoration mechanism is devised using multi-pass non-linear operations. Through extensive experiments conducted using a wide range of test color images, the proposed filtering technique has demonstrated superior performance to that of well-known benchmark techniques, in terms of objective measurements, the visual image quality and the computational complexity

Vision Sensors and Edge Detection

Vision Sensors and Edge Detection book reflects a selection of recent developments within the area of vision sensors and edge detection. There are two sections in this book. The first section presents vision sensors with applications to panoramic vision sensors, wireless vision sensors, and automated vision sensor inspection, and the second one shows image processing techniques, such as, image measurements, image transformations, filtering, and parallel computing