The default value type does not match the type of the property

Default value for DP does not match your type.

Change

public static readonly DependencyProperty ToothProperty =
        DependencyProperty.Register("Tooth", typeof(Tooth), typeof(ToothUI),
                                         new PropertyMetadata(0));

to

public static readonly DependencyProperty ToothProperty =
        DependencyProperty.Register("Tooth", typeof(Tooth), typeof(ToothUI),
                                      new PropertyMetadata(default(Tooth)));

Or simply omit setting default value for your DP:

public static readonly DependencyProperty ToothProperty =
        DependencyProperty.Register("Tooth", typeof(Tooth), typeof(ToothUI));