About the converter Attribute

The value of a converter attribute can be a String or a value binding expression.

When the converter value is a string, it indicates the ID of a converter. Use to register on a component a standard converter that does not have a supplied tag, or use to register a custom converter. In either case, supply the converter's ID or a fully qualified class name, which must have been registered in the application's configuration file (faces-config.xml).
When the converter value is a value binding expression, it indicates an object of the javax.faces.convert.Converter interface. Use to register a custom converter on a component.

If you use the converter attribute with a value binding expression that yields an object of the Converter interface (see code sample below), then you can access the converter in a page without defining it in a configuration file.

<h:outputText ... converter="#{someBean.someProperty}"/>

where someProperty is of type Converter