How do you bind to an objects method in this scenario in WPF?

public class RootObject
{
    public string Name { get; }

    public ObservableCollection<ChildObject> GetChildren() {...}
}

public class ChildObject
{
    public string Name { get; }
}

XAML:

<TreeView ItemsSource="some list of RootObjects">
    <TreeView.Resources>
        <HierarchicalDataTemplate DataType="{x:Type data:RootObject}" 
                                  ItemsSource="???">
            <TextBlock Text="{Binding Path=Name}" />
        </HierarchicalDataTemplate>
        <HierarchicalDataTemplate DataType="{x:Type data:ChildObject}">
            <TextBlock Text="{Binding Path=Name}" />
        </HierarchicalDataTemplate>
    </TreeView.Resources>
</TreeView>

Here I want to bind to the GetChildren method on each RootObject of the tree.

EDIT Binding to an ObjectDataProvider doesn't seem to work because I'm binding to a list of items, and the ObjectDataProvider needs either a static method, or it creates it's own instance and uses that.

For example, using Matt's answer I get:

System.Windows.Data Error: 33 : ObjectDataProvider cannot create object; Type='RootObject'; Error='Wrong parameters for constructor.'

System.Windows.Data Error: 34 : ObjectDataProvider: Failure trying to invoke method on type; Method='GetChildren'; Type='RootObject'; Error='The specified member cannot be invoked on target.' TargetException:'System.Reflection.TargetException: Non-static method requires a target.