C#-Code

using System;
using System.Collections.Generic;
using System.Linq;
using System.Windows;
using System.Windows.Media;
using System.Windows.Media.Imaging;

using System.Drawing;
using System.IO;

namespace aufgabe_180_WPF   {

    public partial class MainWindow : Window    {

        Random rand = new Random();
        public int[] random_pixel;
        int Empty_BitMapImage_h = 400, Empty_BitMapImage_w = 400;

        public static BitmapImage Create_Empty_BitMapImage(int width, int height)
        {            
            Bitmap bitmap = new Bitmap(width, height);
            BitmapImage image = new BitmapImage();
            using (MemoryStream memory = new MemoryStream())
            {
                bitmap.Save(memory, System.Drawing.Imaging.ImageFormat.Bmp);
                memory.Position = 0;
                image.BeginInit();
                image.StreamSource = memory;
                image.CacheOption = BitmapCacheOption.OnLoad;
                image.EndInit();
            }
            return image;
        }

        public MainWindow()        { InitializeComponent(); }        

        public void bt_1_Click(object sender, RoutedEventArgs e)
        {
            BitmapImage EmptyImage = Create_Empty_BitMapImage(Empty_BitMapImage_w, Empty_BitMapImage_h);

            BitmapSource bitmapSource = new FormatConvertedBitmap(EmptyImage, PixelFormats.Default, null, 0);
            WriteableBitmap RandomImage = new WriteableBitmap(bitmapSource);
            int h = RandomImage.PixelHeight;
            int w = RandomImage.PixelWidth;

            int[] pixelData = new int[w * h];
            int widthInByte = 4 * w;

            this.random_pixel = new int[w * h];
            for (var i = 0; i < random_pixel.Length; i++)
                random_pixel[i] = rand.Next(int.MinValue, int.MaxValue);

            RandomImage.WritePixels(new Int32Rect(0, 0, w, h), random_pixel, widthInByte, 0);
           
            image_org.Source = RandomImage;
        }

        private void bt_2_Click(object sender, RoutedEventArgs e)
        {
            BitmapImage EmptyImage = Create_Empty_BitMapImage(Empty_BitMapImage_w, Empty_BitMapImage_h);

            BitmapSource bitmapSource = new FormatConvertedBitmap(EmptyImage, PixelFormats.Default, null, 0);
            WriteableBitmap modifiedImage = new WriteableBitmap(bitmapSource);            
            int h = modifiedImage.PixelHeight;
            int w = modifiedImage.PixelWidth;

            int[] new_pixelData = new int[w * h];
            int widthInByte = 4 * w;

            int counter1 = 0, counter2 = 0;

            for (var y = 0; y < w; y++) {

                Dictionary<int, double> dict = new Dictionary<int, double>();
                for (int x = 0; x < h; x++) {
                    System.Drawing.Color c = System.Drawing.Color.FromArgb(random_pixel[counter1]);
                    dict.Add(counter1, c.GetHue());
                    counter1++;
                }

                var items = from pair in dict
                            orderby pair.Value ascending
                            select pair;
                               
                foreach (KeyValuePair<int, double> index_x in items)    {
                    new_pixelData[counter2] = random_pixel[index_x.Key];
                    counter2++;
                }
            }

            modifiedImage.WritePixels(new Int32Rect(0, 0, w, h), new_pixelData, widthInByte, 0);

            image_sorted.Source = modifiedImage;

            BmpBitmapEncoder bmpEncoder = new BmpBitmapEncoder();
            bmpEncoder.Frames.Add(BitmapFrame.Create(modifiedImage));

            using (System.IO.FileStream file = System.IO.File.OpenWrite("test.bmp"))    {
                bmpEncoder.Save(file);
            }
        }
    }
}

C#-Code

<Window x:Class="aufgabe_180_WPF.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:aufgabe_180_WPF"
        mc:Ignorable="d"
        Title="colour sorting WPF" Height="350" Width="525">
    <Grid>
        <Grid.ColumnDefinitions>
            <ColumnDefinition Width="1*"/>
            <ColumnDefinition Width="1*"/>
            <ColumnDefinition Width="1*"/>
            <ColumnDefinition/>
        </Grid.ColumnDefinitions>
        <Grid.RowDefinitions>
            <RowDefinition Height="45"/>
            <RowDefinition/>
            <RowDefinition Height="1*"/>
        </Grid.RowDefinitions>
        <Button x:Name="bt_1" Content=" random colours " HorizontalAlignment="Center" Margin="5" VerticalAlignment="Center" Click="bt_1_Click" Grid.ColumnSpan="2"/>
        <Button x:Name="bt_2" Content=" sort colours " Grid.Column="2" HorizontalAlignment="Center" Margin="5" VerticalAlignment="Center" Click="bt_2_Click" Grid.ColumnSpan="2"/>
        <Image x:Name="image_org" Grid.ColumnSpan="2" Margin="10,0,10,10" Grid.Row="1" Grid.RowSpan="2" />
        <Image x:Name="image_sorted" Grid.ColumnSpan="2" Margin="10,0,10,10" Grid.Row="1" Grid.Column="2" Grid.RowSpan="2"/>

    </Grid>
</Window>