A device operates on output signals from a light sensor arrangement in a touch-sensing apparatus to determine a position of an object on a touch surface. The apparatus includes a light transmissive panel that defines the touch surface and an opposite surface. A light source arrangement provides sheets of light inside the panel, wherein each sheet comprises light that propagates by internal reflection between the touch surface and the opposite surface from one or more incoupling points to a set of outcoupling points. The light sensor arrangement generates the output signals, which represent light reaching the outcoupling points. The apparatus is configured such that an object touching the touch surface locally attenuates at least two sheets of light. To determine the position, the device identifies, in the output signals, a set of signal profiles originating from said object. The device determines at least part of an attenuated light path across the panel based on each signal profile, and identifies the position of the object on the touch surface based on the thus-determined attenuated light paths. In determining the attenuated light path, the device applies a predetermined width function which is representative of a dependence of signal profile width on distance to the incoupling point due to light scattering caused by at least one of the touch surface and the opposite surface.