Clickable Row, Except One Column?

I have created a table to organize data, and upon clicking a row, the user is taken to that data to manage related information to that data. Everything works fine, but something came up where I would like to give them the ability to delete items from that listing. I would like to add an additional column for each row, that will store an image, when clicked on, deletes that item in the database.

My question is: how do you cancel an action based upon a column that is clicked? I'm sure there is, and I don't mind adding a class to the image column for detection... I am unsure how to look further into the DOM event to see what particular td was clicked, if I could, I could then use $(this.attr("class"); to look to check if that specific column was clicked, and to cancel the action accordingly.

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