Methods for extending a range for assigning attributes to an object in an image

A method for assigning an attribute to x-ray attenuation comprising:

• acquiring first and second reference material equivalent path length information associated with a first range of dual-energy x-ray attenuation information by a first model for expressing collectively each of the first reference material path lengths and the second reference material path lengths as a function of the associated first range of dual-energy x-ray attenuation information, the first range of dual-energy attenuation information being fitted with the first model by a first set of coefficients;
• acquiring third reference material equivalent path length information associated with a second range of dual-energy x-ray attenuation information by a second model for expressing collectively each of the third reference material equivalent path lengths as a function of the associated second range of dual-energy attenuation information, the second range of dual-energy being fitted with the second model by a second set of coefficients, the third reference material having an effective atomic number greater than that of the second reference material;
• combining the first set of coefficients and the second set of coefficients to provide a third set of coefficients for fitting the first and second range of dual-energy x-ray attenuation information with a third model for expressing collectively the first and third reference material path lengths as a function of the fitted first and second range of dual-energy x-ray attenuation information;
• and,
• for all points in the third model determine a volume fraction of one of the first and the third reference material which represents the second reference material path lengths to identify where in the third model path lengths representing the second reference material are represented.

A method for assigning an attribute to x-ray attenuation comprising:

• acquiring first and second reference material equivalent path length information associated with a first range of dual-energy x-ray attenuation information by a model for expressing collectively each of the first reference material path lengths and the second reference material path lengths as a function of the associated first range of dual-energy x-ray attenuation information;
• selecting an extrapolation range of dual-energy x-ray attenuation information over which first and second reference material path lengths are to be associated with dual-energy x-ray attenuation information of a first imposed material having a predetermined minimum effective atomic number less than an effective atomic number of the first reference material and a second imposed material having a predetermined maximum effective atomic number greater than an effective atomic number of the second reference material, wherein the first range is within the extrapolation range;
• selecting a set of fitting constraints for associating each of the first reference material path lengths and the second reference material path lengths over the extrapolation range of dual-energy attenuation information to define extrapolated first and second reference material equivalent path lengths over the extrapolation range;
• and,
• applying the set of fitting constraints to the model.