Make a link in the Android browser start up my app?

Is it possible to make a link such as:

<a href="https://stackoverflow.com/questions/3469908/anton://useful_info_for_anton_app">click me!</a>

cause my Anton app to start up?

I know that this works for the Android Market app with the market protocol, but can something similar be done with other apps?

Here is an example of a link that will start up the Android Market:

<a href="https://stackoverflow.com/questions/3469908/market://search?q=pname:com.nytimes.android">click me!</a>

Update:
The answer I accepted provided by eldarerathis works great, but I just want to mention that I had some trouble with the order of the subelements of the <intent-filter> tag. I suggest you simply make another <intent-filter> with the new subelements in that tag to avoid the problems I had. For instance my AndroidManifest.xml looks like this:

<activity android:name=".AntonWorld"
          android:label="@string/app_name">
    <intent-filter>
        <action android:name="android.intent.action.MAIN" />
        <category android:name="android.intent.category.LAUNCHER" />
    </intent-filter>
    <intent-filter>
        <data android:scheme="anton" />
        <action android:name="android.intent.action.VIEW" />
        <category android:name="android.intent.category.BROWSABLE" />
        <category android:name="android.intent.category.DEFAULT" />
    </intent-filter>
</activity>