How to increase delta value of a multiple valued field +1? I would like to output the delta value of a multiple image field as a affix for the image title in a view, but increased with 1. So, it should start with 1 not with 0. How can I do this? 

Why do I need this? I need to reference to the images from articles using the scheme Fig. 1, Fig. 2 etc. There for the view output should look like:

+----------------+
|                |
|    an image    |
|    delta 0     |
|                |
+----------------+
Fig. 1: Image Title

+----------------+
|                |
|    an image    |
|    delta 1     |
|                |
+----------------+
Fig. 2: Image Title

+----------------+
|                |
|    an image    |
|    delta 2     |
|                |
+----------------+
Fig. 3: Image Title


The first thing I tried is, to sort the view by delta and than output "Global: View result counter", but this does not work if a filter is applied to the view. If a filter is in action, the numeration would not be concordant with the delta anymore.

Do I have to write an custom formatter? And when, where do I start, I don't have an idea.
It depends upon what you're planning to do with that delta. Here's a possible solution for you:

Use Aggregation on the view and use "max" for the delta.  Hide the field and then do a math operation to add +1 to the value of the delta.

If you could expound on the "why" it would help.