Erosion

Building the Cantata Workspace


The erosion is an elementary operator that accepts as parameters a function and a structural element. This operator applies for signals, binary and gray scale images.

The structural elements can be created by the following ways:

  1. using the tool Struc. El. 3x3 to generate 3x3 planar elements;

  2. using the tool Disk str. el. to generate any disk, using three distance metrics: euclidean, city-block and chess-board.

  3. Using the tool Viff-> Str.El. to convert any viff file to a structural element.


To build and experiment a workspace that performs the erosion:

  1. select the dilcond.xv image;

  2. visualize the image using display image;

  3. create a structural element using sstruc. elem. 3x3;

  4. link the erosion operator with its parameters;

  5. visualize the result of the erosion;


Exercises

  1. Apply the erosion operator to the images letters.xv and danaus.xv, and to the 1D signal signal1.viff. For the non binary image choose flat and non flat structural elements. Use the three possibilities of definition of structural elements.

  2. Implement the erosion by an octagon from the sequential composition of the erosion of the 3x3 square and the 3x3 cross.

  3. Let (n, m) be a generic vector. Using two erosion operators and two count loops, implement the translation of an image by (n, m).

  4. Implement the erosion operator as the intersection of translations. Use the erosion operator to perform the translations.

  5. Implement the erosion by the edges of a 5x5 square using just erosions by subsets of the 3x3 square and the intersection operation.

  6. Implement the erosion operator for symmetrical structural elements using the dilation operator and the negation operation.

  7. Implement the dilation operator for symmetrical structural elements using the erosion operator and the negation operation.

  8. Implement a tool to build the colored illustrative pictures presented in the Erosion page, that is, build an workspace which creates a slide by the superposition of the original image, the structural elements positioned in some critical points and the transformed image.