Abstract: Local tomography is enhanced to determine the location and value of a discontinuity between a first internal density of an object and a second density of a region within the object. A beam of radiation is directed in a predetermined pattern through the region of the object containing the discontinuity. Relative attenuation data of the beam is determined within the predetermined pattern having a first data component that includes attenuation data through the region. In a first method for evaluating the value of the discontinuity, the relative attenuation data is inputted to a local tomography function .function..sub..LAMBDA. to define the location S of the density discontinuity. The asymptotic behavior of .function..sub..LAMBDA. is determined in a neighborhood of S, and the value for the discontinuity is estimated from the asymptotic behavior of .function..sub..LAMBDA.. In a second method for evaluating the value of the discontinuity, a gradient value for a mollified local tomography function .gradient..

Abstract: Local tomographic data is used to determine the location and value of a discontinuity between a first internal density of an object and a second density of a region within the object. A beam of radiation is directed in a predetermined pattern through the region of the object containing the discontinuity. Relative attenuation data of the beam is determined within the predetermined pattern having a first data component that includes attenuation data through the region. The relative attenuation data is input to a pseudo-local tomography function, where the difference between the internal density and the pseudo-local tomography function is computed across the discontinuity. The pseudo-local tomography function outputs the location of the discontinuity and the difference in density between the first density and the second density.