X-ray Depthmaps: Revealing the Hidden Structures

Objective: Our aim is to decompose a conventional X-ray image into several independent, non-overlapping depth layers, such that the sum resembles the original input.Material and Methods: Conventionally, the creation of one single X-ray image X is guided by Beer-Lambert’s law, X= I 0⋅ exp (−∫ 0 L μ (x) d x), where I 0 X-ray photons interact with human tissue of thickness L guided by the tissue attenuation function μ (x). The integral over thickness L can now be subdivided into k+ 1 ranges [0, d 1],] d 1, d 2],] d 2, d 3],…,] d k, L] introducing thickness layers d 1,…, d k (k∈¥). Setting k= 2, we can change Beer-Lambert’s law to X= I 0⋅ exp (−∫ 0 L μ (x) d x)= I 0⋅ exp (−∫ 0 d 1 μ (x) d x−∫ d 1 d 2 μ (x) d x−∫ d 2 L μ (x) d x).