Figuring out where a mouse click is under an image

I want to create a JFrame (or JPanel) where the whole area is one big gif (or icon etc) and I want to make some areas of this panel react to mouse clicks and other areas display messages.
There are two ways that I can think of doing this.
The first is that I figure out the x and y coordinates of each area and check to see if each mouse click is within that area.
The second way is to see if I can figure out how to put something like transparent JButtons over the areas that I want to accept mouse clicks (all the areas will be rectangular) and just do what JButtons do normally.
The second way sounds easier but I don't know how to do that.
Does anyone have opinions on which way I should do it?
Thanks

To me the first method sounds eaiser.
A third possible idea? Add a bunch of JPanels to the frame and have split the image into several pieces that are painted by each JPanel. Then use a mouse listener to detect clicks. (Seems easier than trying to make JButton transparent and placing it at the correct point).

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    Thanks. I'm working with different hosts and I guess thats where the confusion for me is coming in. In bluehost, I simply submit my form through form action to http://www.bluehost/bluemail. With the php form construction it 's form action is contact.php. Does this mean that the server I'm working with will uinderstand how to process contact.php and where to send it based on paramaters previously submitted? Or do I instruct the server via the php form? Thanks again
    Date: Wed, 8 Feb 2012 13:50:11 -0700
    From: [email protected]
    To: [email protected]
    Subject: Newbie for the life of me can't figure out where in contact.php you tell it where to send form?
        Re: Newbie for the life of me can't figure out where in contact.php you tell it where to send form?
        created by mhollis55 in Dreamweaver - View the full discussion
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         To unsubscribe from this thread, please visit the message page at http://forums.adobe.com/message/4194407#4194407. In the Actions box on the right, click the Stop Email Notifications link.
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          *         (for all (char)i in b : (Character)i in s)
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          *          (target in #b) ==> (b union {target} = #b)
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