Gradient extraction operators for discrete interval-valued data

Abstract

Digital images are generally created as discrete measurements of light, as performed by dedicated sensors. Consequently, each pixel contains a discrete approximation of the light inciding in a sensor element. The nature of this measurement implies certain uncertainty due to discretization matters. In this work we propose to model such uncertainty using intervals, further leading to the generation of so-called interval-valued images. Then, we study the partial differentiation of such images, putting a spotlight on antisymmetric convolution operators for such task. Finally, we illustrate the utility of the interval-valued images by studying the behaviour of an extended version of the well-known Canny edges detection method.

An Approach Towards Image Edge Detection Based on Interval-Valued Fuzzy Mathematical Morphology and Admissible Orders

“…, 255u. The image O can be used to generate an interval-valued image O IV so as to count for the quantization and discretization errors [11]:…”

“…One of the problems one naturally faces when processing a digital image is the inherent uncertainty in the pixel values of a digital image due to image capture [13]. Even if the digital image is noiseless and if there is only one take of the image, uncertainty in the pixel values arises due to the following facts [11] 1. Quantization or Tonal Error: Any device will round captured values up or down so as to obtain one of the allowed values.…”

“…This uncertainty can be modelled by converting a given digital image O to an interval-valued image A [11]. Since an interval-valued image can be viewed as an interval-valued fuzzy set, it can be processed using techiques of interval-valued fuzzy mathematical morphology (IV-FMM).…”

Detecao de Bordas baseada em Morfologia Matemática Fuzzy Intervalar e as Funcoes de Agregacao K

“…Erro tonal: As imagens reais possuem um número ilimitado de tons de cinza, no processamento de imagens computacionais é necessário limitar o quantidade de tons de cinza a um número finito, assim dependo do dispositivo de digitalização, sobre cada pixel gera-se um erro tonal, neste trabalho foi considerado o erro tonal de ±1 como na referência [17].…”

“…Uma imagem digital possui incertezas e imprecisões inerentes ao processo de digita-lização. Lopez-Molina et al [17] modelaram esta imprecisão em forma de imagem intervalar para depois utilizá-las na detecção de bordas da imagem. A importância das bordas de uma imagem concentra-se na simplificação da análise das imagens e na redução drástica da quantidade de dados a serem processados.…”