Exercises

Summary

Chapter 2

Exercise 2.1 (Simple morph)

Given: two gray-scale images: P1 and P2

Input: U(t) = P1

Initial state: X(0) = P2

Boundary conditions: white frame

Output: Y(t) = a transition from P2 to P1.

Task

Design a single template, which implements this transition.

Example

Exercise 2.2 (Hexagonal neighborhood)

The standard CNN definition specifies that the cells form a rectangular grid. Anther feasible form could be a hexagonal grid.

Task

Give a formula for the side length and the area of a hexagon (measured in cells) in the case of a hexagonal cell grid, when the sphere of influence equals r.

Exercise 2.3 (Triangular neighborhood)

The standard CNN definition specifies that the cells form a rectangular grid. There are only three possibilities to cover the plane. These are rectangular, hexagonal, and triangular.

Task

Give a formula for the area of a triangle in the case of a triangular cell grid, when the sphere of influence equals r.

Chapter 3

Exercise 3.1 (Separate connected objects)

The problem to be solved is to separate connected objects. The example shows a test image where objects are all similar in size. All objects should be separated but their sizes must be preserved.