Erode a region.

::erosion1 erodes the input regions with a structuring element. By applying ::erosion1 to a region, its boundary gets smoothed. In the process, the area of the region is reduced. Furthermore, connected regions may be split. Such regions, however, remain logically one region. The erosion is a set-theoretic region operation. It uses the intersection operation.

Let M (StructElement) and R (Region) be two regions, where M is the structuring element and R is the region to be processed. Furthermore, let m be a point in M. Then the displacement vector v(m) = (dx,dy) is defined as the difference of the center of gravity of M and the vector v(m). Let t(v(m))(R) denote the translation of a region R by a vector v(m). Then

                        
                       /  \
      erosion1(R,M) := |  | t     (R)
                       |  |  -v(m)
                      m in M

For each point m in M a translation of the region R is performed. The intersection of all these translations is the erosion of R with M. ::erosion1 is similar to the operator ::minkowski_sub1, the difference is that in ::erosion1 the structuring element is mirrored at the origin. The position of StructElement is meaningless, since the displacement vectors are determined with respect to the center of gravity of M.

The parameter Iterations determines the number of iterations which are to be performed with the structuring element. The result of iteration n-1 is used as input for iteration n. From the above definition it follows that the maximum region is generated in case of an empty structuring element.

Structuring elements (StructElement) can be generated with operators such as ::gen_circle, ::gen_rectangle1, ::gen_rectangle2, ::gen_ellipse, ::draw_region, ::gen_region_polygon, ::gen_region_points, etc.

Let F1 be the area of the input region, and F2 be the area of the structuring element. Then the runtime complexity for one region is:

    O(sqrt(F1) * sqrt(F2) * Iterations) .

::erosion1 returns H_MSG_TRUE if all parameters are correct. The behavior in case of empty or no input region can be set via:

  a) no region:    set_system('no_object_result',<RegionResult>)
  b) empty region: set_system('empty_region_result',<RegionResult>)

::threshold, ::regiongrowing, ::watersheds, ::class_ndim_norm, ::gen_circle, ::gen_ellipse, ::gen_rectangle1, ::gen_rectangle2, ::draw_region, ::gen_region_points, ::gen_struct_elements, ::gen_region_polygon_filled

::connection, ::reduce_domain, ::select_shape, ::area_center

::minkowski_sub1, ::minkowski_sub2, ::erosion2, ::erosion_golay, ::erosion_seq

::transpose_region

Morphology