Resumen de Image processing with interval-valued fuzzy sets: edge detection. Contrast

Edurne Barrenechea Tartas

• Some of the most useful information that can be found in an image are the edges, for, because they outline the objects, they define the limits between them and the background and between the objects themselves. Therefore edge detection on an image is a very important problem in artificial vision and is often the step prior to many algorithms of object identification. On the other hand we know that the main reasons why Fuzzy Set Theory has been widely applied in image processing are the following: a) Fuzziness is inherently embedded in nature and is reflected in the images. b) Images are the 2D projections of a 3D world so some information is lost during mapping. c) The grey levels are considered as imprecise constants. d) Many of the definitions such as image boundaries and edges are vague in nature. From the four considerations above it is made clear that the detection of the edges of the objects that compose an image is not a simple problem due to, among other things, the vague or imprecise character of the concept itself of edge. That is, two different people, depending on what they want to highlight in an image, can detect two different edges. Normally, the object of the techniques used in edge detection is the localization of the points where there is a variation in the intensity (going from one grey level to a different one). For us the edge of the objects that compose an image is going to be a set. The elements of said set are going to be the pixels of the image that have associated a big enough change in intensity with respect to their neighbours.

  Evidently, the pixels that have associated a change in intensity with their neighbours that is null or small do not belong to the edge. Therefore, an edge is a set of pixels such that each one of them has associated a numerical value. Said value informs us of the local variations of intensity that take place in the surroundings of the pixel in question.Also, we know that in Fuzzy Set Theory, an i