In this work, we demonstrate that the theory of cone-beam tomography image reconstruction on chords can be modified for use with local tomography problems. Our analysis reveals that discontinuities in the profiles of the object function along chords can be reconstructed readily. By consideration of all possible chords, an image that de-scribes the location of boundaries within an object can be reconstructed. A preliminary numerical study is conducted to validate and demonstrate the reconstruction method. In this work, we demonstrate that the theory of cone-beam tomography image reconstruction on chords can be modified for use with local tomography problems. Our analysis reveals that discontinuities in the profiles of the object function along chords can be reconstructed readily. By consideration of all possible chords, an image that de-scribes the location of boundaries within an object can be reconstructed. A preliminary numerical study is conducted to validate and demonstrate the reconstruction method.