InkCanvas をバックグラウンドで動かしたい

アプリケーション（現在作りたいアプリケーション）が起動中は
他のアプリを操作中（ゲームやブラウザ）でもアプリケーションのウインドウに線を描き続けたいのですが、方法がわかりません

よろしくお願いいたします。

C#

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Windows;
using System.Windows.Controls;
using System.Windows.Data;
using System.Windows.Documents;
using System.Windows.Ink;
using System.Windows.Input;
using System.Windows.Media;
using System.Windows.Media.Imaging;
using System.Windows.Shapes;

namespace mouz
{
    /// <summary>
    /// Mouz.xaml の相互作用ロジック
    /// </summary>
    public partial class Mouz : Window
    {
        public Mouz()
        {
            InitializeComponent();
        }

        private DrawingAttributes ink = new DrawingAttributes();
        private IntPtr hHook;


        private void left_mouz_down(object sender, MouseButtonEventArgs e)
        {

            changeColor(e);

        }

        private void left_mouz_up(object sender, MouseButtonEventArgs e)
        {
            mouzCanvas.Strokes.Clear();
        }
        private void mouz_move(object sender, MouseEventArgs e)
        {

            changeColor(e);
        }

        private void right_mouz_down(object sender, MouseEventArgs e)
        {
            mouzCanvas.Strokes.Clear();
        }

        private void MouzCanvas_Loaded(object sender, RoutedEventArgs e)
        {
            var mouse_capture = Mouse.Capture(this);

            ink.Width = 10;
            ink.Height = 10;
            Color myColor = (Color)ColorConverter.ConvertFromString("#30FFFFFF");

            ink.Color = myColor;

            mouzCanvas.DefaultDrawingAttributes = ink;
            _ = Mouse.Capture(this);
        }

        private void changeColor(MouseEventArgs e)
        {
            if (e.LeftButton == MouseButtonState.Pressed)
            {
                Color myColor = new Color();
                myColor = (Color)ColorConverter.ConvertFromString("#30FF0000");
                ink.Color = myColor;

                mouzCanvas.DefaultDrawingAttributes = ink;
            }
            else
            {
                Color myColor = new Color();
                myColor = (Color)ColorConverter.ConvertFromString("#30FFFFFF");
                ink.Color = myColor;

                mouzCanvas.DefaultDrawingAttributes = ink;
            }
        }
    }
}

xaml

<Window x:Class="mouz.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
        xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
        xmlns:local="clr-namespace:mouz"
        mc:Ignorable="d"
        Title="MainWindow" Height="337.271" Width="206.435"  Background="#FF000000" WindowStyle="SingleBorderWindow">
    <Grid>
        <Button Content="Start" HorizontalAlignment="Left" Margin="10,15,0,0" VerticalAlignment="Top" Width="175" Height="87" Click="Start_Button" FontSize="30"/>
        <Button Content="Quit" HorizontalAlignment="Left" Margin="10,129,0,0" VerticalAlignment="Top" Width="175" Height="87" Click="Quit_Button" FontSize="30"/>
        <Button Content="Quit" HorizontalAlignment="Left" Margin="10,226,0,0" VerticalAlignment="Top" Width="175" Height="87" Click="Button_Click" FontSize="30"/>

    </Grid>
</Window>