Structuring element

<p>In <a href="/facts/Mathematical_morphology/qVpYux75">mathematical morphology</a>, a  structuring element is a shape, used to probe or interact with a given image, with the purpose of drawing conclusions on how this shape fits or misses the shapes in the image. It is typically used in morphological operations, such as <a href="/facts/Dilation_(morphology)/P3NbEmoS">dilation</a>, <a href="/facts/Erosion_(morphology)/CkHHo65Q">erosion</a>, <a href="/facts/Opening_(morphology)/tss6523A">opening</a>, and <a href="/facts/Closing_(morphology)/PjW0c7en">closing</a>, as well as the <a href="/facts/Hit-or-miss_transform/RKp29C4G">hit-or-miss transform</a>.
</p><p>According to <a href="/facts/Georges_Matheron/SURrhm0g">Georges Matheron</a>, knowledge about an object (e.g., an image) depends on the manner in which we probe (observe) it. In particular, the choice of a certain structuring element for a particular morphological operation influences the information one can obtain. There are two main characteristics that are directly related to structuring elements: 
</p>
<ul><li>Shape. For example, the structuring element can be a "ball" or a line; convex or a ring, etc. By choosing a particular structuring element, one sets a way of differentiating some objects (or parts of objects) from others, according to their shape or spatial orientation.</li>
<li>Size. For example, one structuring element can be a 
  
    
      
        3
        ×
        3
      
    
    {\displaystyle 3\times 3}
  
 square or a 
  
    
      
        21
        ×
        21
      
    
    {\displaystyle 21\times 21}
  
 square. Setting the size of the structuring element is similar to setting the observation scale, and setting the criterion to differentiate image objects or features according to size.</li></ul>

Structuring element open-in-new

Structuring element