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

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

Object Attention Patches for Text Detection and Recognition in Scene Images using SIFT

Natural urban scene images contain many problems for character recognition such as luminance noise, varying font styles or cluttered backgrounds. Detecting and recognizing text in a natural scene is a difficult problem. Several techniques have been proposed to overcome these problems. These are, however, usually based on a bottom-up scheme, which provides a lot of false positives, false negatives and intensive computation. There- fore, an alternative, efficient, character-based expectancy-driven method is needed. This paper presents a modeling approach that is usable for expectancy-driven techniques based on the well-known SIFT algorithm. The produced models (Object Attention Patches) are evaluated in terms of their individual provisory character recognition performance. Subsequently, the trained patch models are used in preliminary experiments on text detection in scene images. The results show that our proposed model-based approach can be applied for a coherent SIFT-based text detection and recognition process

Multi-Scale Edge Detection Algorithms and Their Information-Theoretic Analysis in the Context of Visual Communication

The unrealistic assumption that noise can be modeled as independent, additive and uniform can lead to problems when edge detection methods are applied to low signal-to-noise ratio (SNR) images. The main reason for this is because the filter scale and the threshold for the gradient are difficult to determine at a regional or local scale when the noise estimate is on a global scale. Therefore, in this dissertation, we attempt to solve these problems by using more than one filter to detect the edges and discarding the global thresholding method in the edge discrimination. The proposed multi-scale edge detection algorithms utilize the multi-scale description to detect and localize edges. Furthermore, instead of using the single default global threshold, a local dynamic threshold is introduced to discriminate between edges and non-edges. The proposed algorithms also perform connectivity analysis on edge maps to ensure that small, disconnected edges are removed. Experiments where the methods are applied to a sequence of images of the same scene with different SNRs show the methods to be robust to noise. Additionally, a new noise reduction algorithm based on the multi-scale edge analysis is proposed. In general, an edge—high frequency information in an image—would be filtered or suppressed after image smoothing. With the help of multi-scale edge detection algorithms, the overall edge structure of the original image could be preserved when only the isolated edge information that represents noise gets filtered out. Experimental results show that this method is robust to high levels of noise, correctly preserving the edges. We also propose a new method for evaluating the performance of edge detection algorithms. It is based on information-theoretic analysis of the edge detection algorithms in the context of an end-to-end visual communication channel. We use the information between the scene and the output of the edge-detection algorithm, ala Shannon, to evaluate the performance. An edge detection algorithm is considered to have high performance only if the information rate from the scene to the edge approaches the maximum possible. Therefore, this information-theoretic analysis becomes a new method to allow comparison between different edge detection operators for a given end-to-end image processing system

Aplicació de mètriques fuzzy en la millora computacional d'algorismes de filtratge d'imatges en color

El filtrado de imágenes 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 imágenes como, por ejemplo, la detección de bordes o el reconocimiento de patrones u objetos y, por lo tanto, el ruido debe ser reducido. Del mismo modo, el aumento de la resolución y el tamaño de las imágenes nos conduce a requerimientos computacionales más altos, los cuales hemos de intentar rebajar sobre todo para aplicaciones en tiempo real o similares. 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 imágenes 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 que proponen técnicas de filtrado vectorial, son las conocidas técnicas del filtro de mediana vectorial (VMF) o el filtro direccional vectorial (VDF). Desafortunadamente, estas técnicas no se adaptan a las características locales de la imagen, lo que implica que habitualmente los bordes y detalles de las imágenes se emborronan y pierden calidad. A fin de solventar este problema, se han propuesto recientemente varios filtros vectoriales adaptativos, entre los que destacan las técnicas de peer group. En los últimos años ha aparecido la teoría de los denominados conjuntos fuzzy, borrosos o difusos (lógica, métricas y topologías), que se ha demostrado es una herramienta adecuada para el filtrado de imágenes. En la presente Tesis Doctoral las metas principales son: (i) el esCamarena Estruch, JG. (2009). Aplicació de mètriques fuzzy en la millora computacional d'algorismes de filtratge d'imatges en color [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/4339Palanci