Since you already have your algorithms written, just create a new GUI and drug three buttons and one axis on the form. Automatically created .m file will contain all the code necessary to run the GUI. By clicking on each button in the gui editor, the callback functions (in the .m file) will be created for each respectively. Just paste your algorithm scripts into each corresponding callback function.
I don't completely understand your question. Assuming your algorithms are working, just put the code of each algorithm in the corresponding callback function. Since each algorithm will import the image, you dont really need to pass any parameters between other functions. Essential parameters such as handles are passed to the callback functions automatically: function pushbutton_callback(Object, handles...) or something like that. All necessary variables will be created within the callback function and dont need to be used outside that function (unless you are writing something more complicated). Of course, it is not the best way to write a program because every time you press a button the script will have to import the image, however it would be a good start to make sure each part of the script works properly. Later, you could create a separate function that will import the image, which could be used by all three algorithms instead of importing it three times. You could write this function in the main text or create another callback fucntion for a button that will be used to import image(s). In this case, your 'global' variables such as image data must be stored as handles.Yourvariable.