How can I set a dependency property on a static resource?

I'm trying to get around the fact that I can't specify a dynamic value for ConverterParameter. See my other question for why I need to bind a dynamic value to ConverterParameter - I don't like the solutions currently posted because they all require what I feel should be unnecessary changes to my View Model.

To attempt to solve this, I have created a custom converter, and exposed a dependency property on that converter:

public class InstanceToBooleanConverter : DependencyObject, IValueConverter
{
    public object Value
    {
        get { return (object)GetValue(ValueProperty); }
        set { SetValue(ValueProperty, value); }
    }

    public static readonly DependencyProperty ValueProperty =
        DependencyProperty.Register("Value", typeof(object), typeof(InstanceToBooleanConverter), null);

    public object Convert(object value, Type targetType, object parameter, System.Globalization.CultureInfo culture)
    {
        return value != null && value.Equals(Value);
    }

    public object ConvertBack(object value, Type targetType, object parameter, System.Globalization.CultureInfo culture)
    {
        return value.Equals(true) ? Value : Binding.DoNothing;
    }
}

Is there a way to set this value using a binding (or style setter, or other crazy method) in my XAML?

<ItemsControl ItemsSource="{Binding Properties}">
    <ItemsControl.ItemTemplate>
        <DataTemplate DataType="{x:Type local:SomeClass}">
            <DataTemplate.Resources>
                <!-- I'd like to set Value to the item from ItemsSource -->
                <local:InstanceToBooleanConverter x:Key="converter" Value="{Binding Path=???}" />
            </DataTemplate.Resources>
<!- ... ->

The examples I've seen so far only bind to static resources.

Edit:

I got some feedback that there is only one converter instance with the XAML I posted.

I can work around this by placing the resource in my control:

<ItemsControl ItemsSource="{Binding Properties}">
    <ItemsControl.ItemTemplate>
        <DataTemplate DataType="{x:Type local:SomeClass}">
            <RadioButton Content="{Binding Name}" GroupName="Properties">
                <RadioButton.Resources>
                    <!-- I'd like to set Value to the item from ItemsSource -->
                    <local:InstanceToBooleanConverter x:Key="converter"
                                                      Value="{Binding Path=???}" />
                </RadioButton.Reso开发者_运维知识库urces>
                <RadioButton.IsChecked>
                    <Binding Path="DataContext.SelectedItem"
                             RelativeSource="{RelativeSource AncestorType={x:Type Window}}"
                             Converter="{StaticResource converter}" />
                </RadioButton.IsChecked>
            </RadioButton>
<!- ... ->

So this problem isn't blocked by having to share an instance of the converter :)

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Unfortunately this isn't going to work - I've been down this road before and it turns out all the Items in the ItemsControl share the same Converter. I think this is due to the way the XAML parser works.

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Firstly you can specify the converter at a higher level resource dictionary and set x:Shared to false, secondly if you want to "set the Value to the item from ItemsSource" as you annotated you can just specify an empty binding (Value="{Binding}").