Edge detection: Difference between revisions

Revision as of 02:40, 9 October 2023

Revision as of 23:48, 13 October 2023

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<math>I_r = \lim_{x \rightarrow \infty} f(x)</math>. The scale parameter <math>\sigma</math> is called the blur scale of the edge. Ideally this scale parameter should be adjusted based on the quality of image to avoid destroying true edges of the image.{{citation needed|date=September 2015}}

== Difficulty ==

== Why it is a non-trivial task ==

ToOutside illustrateof whyimages with simple objects or featuring well-controlled lighting, edge detection is not a trivial task, considersince theit problemcan ofbe detectingdifficult edgesto determine what threshold should be used to define an edge between two pixels.<ref name=lin98/> For example, in the following one-dimensional signal. Here, wemost maywould intuitively say that there should beis an edge between the 4th and 5th pixels.:

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IfHowever, if the intensity difference were smaller between the 4th and the 5th pixels and if the intensity differences between the adjacent neighboring pixels were highersmaller, it would not be as easy to say that there should be an edge in the corresponding region. MoreoverSimilarly, oneif couldthe argueintensity thatdifferences thisbetween casethe isadjacent oneneighboring inpixels whichwere therehigher, isone could argue that more than one edge should be considered to exist, or even none at all.

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Hence, to firmly state a specific threshold on how large the intensity change between two neighbouring pixels must be for us to say that there should be an edge between these pixels is not always simple.<ref name=lin98/> Indeed, this is one of the reasons why edge detection may be a non-trivial problem unless the objects in the scene are particularly simple and the illumination conditions can be well controlled (see for example, the edges extracted from the image with the girl above).

== Approaches ==