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
- using the tool
Struc. El. 3x3 to generate 3x3 planar elements;
- using the tool
Disk str. el. to generate any disk using three distance metrics:
euclidean, city-block and chess-board;
- using the tool
Viff-> Str.El. to convert any viff file to a structural
element.
To build a workspace to experiment with dilation:
- select the dilcond.xv image;
- visualize the image using display image;
- create a structural element using Struc. El. 3x3;
- update the dilation operator parameters;
- visualize the result of the dilation process;
Exercises
- 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.
- Implement the dilation by an octagon from the sequential composition
of the dilation by a 3x3 square and a 3x3 cross.
- Let (n,m) be a generic vector. Using two dilation operators and
two count loops, implement the translation of an image by (n,m).
- Implement the dilation by a 3x3 cross as the union
of translations. Use the dilation operator to perform the translations.
- Implement the dilation by the edges of a 5x5 square
using just dilations by subsets of the 3x3 square and the union
operation.
- 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.