Size influence on shape of handwritten characters loops

In the practice of forensic handwriting experts, the size of the writing on a questioned document may be different from that of known samples. In this study, the hypothesis of shape invariance of handwritten closed loops across size increasing was tested. A Fourier methodology was applied to 2325 small letters (591 a loops, 547 d loops, 596 o loops and 591 q loops) and 692 enlarged letters (162 a loops, 173 d loops, 173 o loops and 184 q loops), in a population of 13 writers who were asked to write letters in their usual size and about three times larger. Most of the writers presented similar modifications when increasing the size of the loops; they produced enlarged loops significantly more round and less slanted towards the right or the left. Furthermore, a discrimination was demonstrated between the writers on the basis of the enlarged loops, with a correct classification rate superior to 90%, whatever the letter (a, d, o or q). A classification of the enlarged loops in their corresponding writer was then possible. On the contrary, when comparing the enlarged loops to the small ones, almost one half of the enlarged loops were allocated to a wrong writer. Shape invariance was thus not supported for this particular application. Consequently, when comparing documents with a different writing size, differences in loops shape should be interpreted cautiously because they may be due to a different writer, but they may also be due to an enlargement of the loops. Therefore, reference material of similar writing size to that of the questioned writing should be requested for the comparison of handwritten loops.