Radiograph and passive data analysis using mixed variable optimization

Disclosed herein are representative embodiments of methods, apparatus, and systems for performing radiography analysis. For example, certain embodiments perform radiographic analysis using mixed variable computation techniques. One exemplary system comprises a radiation source, a two-dimensional detector for detecting radiation transmitted through a object between the radiation source and detector, and a computer. In this embodiment, the computer is configured to input the radiographic image data from the two-dimensional detector and to determine one or more materials that form the object by using an iterative analysis technique that selects the one or more materials from hierarchically arranged solution spaces of discrete material possibilities and selects the layer interfaces from the optimization of the continuous interface data.