Measuring button thickness from side-view image using DIPlib in C++ (profile measurement)

I am working on a machine vision application in C++ and using the DIPlib library for image processing. I have a side-view (profile) grayscale image of a button-like part placed on a flat surface. My goal is to measure the physical thickness (height) of the button in pixels (later converted to mm).

Camera looks at the object from the side The object rests on a flat surface (floor) The button appears darker than the background

There may be reflection near the floor, so using a simple bounding box bottom is unreliable

My questions

Is this a reasonable approach in DIPlib for profile-based thickness measurement? Is there a simple and robust DIPlib method to detect the floor line, or compute object thickness from a side view?