WPF DataGrid: Selecting CellTemplate by DataType of ItemsSoure

I am Building a DataGrid where i want to switch the images inside a cell based on the underlying datatype of the current item.

Question: Is it possible to apply this type of template switching? Preferably in xaml-only?

ItemsSource is

ObservableCollection<BaseModel>

which contains Items of type

IncidentModel : BaseModel
ServiceModel : BaseModel

This is where i currently am:

<DataGrid 
    ItemsSource="{Binding TicketCollection,UpdateSourceTrigger=PropertyChanged,Mode=OneWay}"
    IsReadOnly="True"
    AutoGenerateColumns="False"
    DockPanel.Dock="Top">

    <DataGrid.Resources>
        <DataTemplate DataType="{x:Type models:IncidentModel}">
            <Image Source="pack://application:,,,/SMLib;component/Files/Images/16x16/Active_16.png" />

        </DataTemplate>
        <DataTemplate DataType="{x:Type models:ServiceModel}">
            <Image Source="pack://application:,,,/SMLib;component/Files/Images/16x16/IncidentMgmt_AllIncidents_16.png" />

        </DataTemplate>
    </DataGrid.Resources>

    <DataGrid.Columns>

        <DataGridTemplateColumn Header="Typ">
            <DataGridTemplateColumn.CellTemplate>
                <DataTemplate>

                </DataTemplate>
            </DataGridTemplateColumn.CellTemplate>
        </DataGridTemplateColumn>

        <DataGridTextColumn Header="Id" Binding="{Binding Id,UpdateSourceTrigger=PropertyChanged,Mode=OneWay}" />
        <DataGridTextColumn Header="Titel" Binding="{Binding Title,UpdateSourceTrigger=PropertyChanged,Mode=OneWay}" />
        <DataGridTextColumn Header="Status" Binding="{Binding Status,UpdateSourceTrigger=PropertyChanged,Mode=OneWay}" />
        <DataGridTextColumn Header="Erstellung" Binding="{Binding CreatedDate,UpdateSourceTrigger=PropertyChanged,Mode=OneWay}" />
    </DataGrid.Columns>
</DataGrid>

Thanks for every possible help!

You could use a DataTemplateSelector

public class MyTemplateSelector : DataTemplateSelector
{
    public DataTemplate IncidentTemplate { get; set; }
    public DataTemplate ServiceTemplate { get; set; }

    public override DataTemplate SelectTemplate
        (object item, DependencyObject container)
    {
        if (item is IncidentModel) return IncidentTemplate;
        else if (item is ServiceModel) return ServiceTemplate;
        else return base.SelectTemplate(item, container);
    }
}

XAML

<DataGrid 

    ...

    >
    <DataGrid.Resources>
        <DataTemplate x:Key="IncidentTemplate" DataType="{x:Type models:IncidentModel}">
            <Image Source="pack://application:,,,/SMLib;component/Files/Images/16x16/Active_16.png" />
        </DataTemplate>
        <DataTemplate x:Key="ServiceTemplate" DataType="{x:Type models:ServiceModel}">
            <Image Source="pack://application:,,,/SMLib;component/Files/Images/16x16/IncidentMgmt_AllIncidents_16.png" />
        </DataTemplate>

        <local:MyTemplateSelector x:Key="MyTemplateSelector"
            IncidentTemplate="{StaticResource IncidentTemplate}"
            ServiceTemplate="{StaticResource ServiceTemplate}" />

    </DataGrid.Resources>
    <DataGrid.Columns>
        <DataGridTemplateColumn Header="Typ" 
            CellTemplateSelector="{StaticResource MyTemplateSelector}" />

        ...

    </DataGrid.Columns>
</DataGrid>