Dilation

Building the Cantata Workspace


Dilation is an elementary operator that accepts as its parameters an object and a structural element. This operator can be applied to signals, and to binary and gray scale images.

A structural element can be created by

  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 a workspace to experiment with dilation:

  1. select the dilcond.xv image;

  2. visualize the image using display image;

  3. create a structural element using Struc. El. 3x3;

  4. update the dilation operator parameters;

  5. visualize the result of the dilation process;


Exercises

  1. Apply the dilation 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 in the creation of structural elements.

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

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

  4. Implement the dilation by a 3x3 cross as the union of translations. Use the dilation operator to perform the translations.

  5. Implement the dilation by the edges of a 5x5 square using just dilations by subsets of the 3x3 square and the union operation.

  6. Implement a tool to build the colored illustrative images presented in the Dilation page. That is, build a workspace which creates a slide formed by the superposition of the original image, the structural elements positioned in some critical points, and the transformed image.