{"id":388,"date":"2011-09-02T17:49:43","date_gmt":"2011-09-02T21:49:43","guid":{"rendered":"https:\/\/blogs.mathworks.com\/steve\/2011\/09\/02\/area-opening-terminology-question\/"},"modified":"2019-10-29T16:52:53","modified_gmt":"2019-10-29T20:52:53","slug":"area-opening-terminology-question","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/steve\/2011\/09\/02\/area-opening-terminology-question\/","title":{"rendered":"“Area opening” terminology question"},"content":{"rendered":"
\r\n

An experienced user of our products recently told us we got it wrong when we named bwareaopen<\/tt>. This function removes foreground objects from a binary image that are smaller in area than a given threshold. The user said\r\n (paraphrased) that \"bwareaopen isn't doing an opening at all, it's just doing connected-component labeling. And I would look\r\n for some variation of 'size filter' in the name or description, and that doesn't appear at all.\"\r\n <\/p>\r\n

This is a good example of a terminology question that arises in toolbox design fairly often. When do we use a term that is\r\n familiar to specialists in the area but might not be familiar to other users? In this case, the term area opening<\/i> is familiar to those who know a lot about mathematical morphology as applied to image processing.\r\n <\/p>\r\n

In morphology, this operation is indeed called an area opening, and that's why I named the function this way about ten years\r\n ago. The morphology folks have a fairly general notion of openings. Area opening is a type of opening they call an \"algebraic\r\n opening.\" Such openings are characterized by the following properties:\r\n <\/p>\r\n

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    \r\n
  • Increasing. Operator \\( T\\{\\cdot\\} \\) is increasing<\/i> if, for all images \\( f \\) and \\( g \\), \\( f <= g \\) implies \\( T\\{f\\} <= T\\{g\\} \\).\r\n <\/li>\r\n <\/ul>\r\n <\/div>\r\n
    \r\n
      \r\n
    • Anti-extensive. Operator \\( T\\{\\cdot\\} \\) is anti-extensive<\/i> if, for all images \\( f \\), \\( T\\{f\\} <= f \\).\r\n <\/li>\r\n <\/ul>\r\n <\/div>\r\n
      \r\n
        \r\n
      • Idempotent. Operator \\( T\\{\\cdot\\} \\) is idempotent<\/i> if, for all images \\( f \\), \\( T\\{T\\{f\\}\\} = T\\{f\\} \\).\r\n <\/li>\r\n <\/ul>\r\n <\/div>\r\n

        Morphological opening (erosion followed by dilation), which is the most familiar kind of opening, satisfies these properties,\r\n and so does the area opening.\r\n <\/p>\r\n

        That said, I appreciate the merit in considering a different term that is less \"jargony.\" We might kick around the idea of\r\n renaming this function.\r\n <\/p>\r\n

        Readers, do you have any suggestions? I have an idea that I kind of like, but I'd like to hear what you have to say first.<\/p>