A new tomographic inversion technique is presented for the identification of plasma filaments in wide-angle visible camera data. The technique works on the assumption that background subtracted images of filaments can be represented as a superposition of uniformly emitting magnetic equilibrium field lines. A large collection of equilibrium magnetic field lines is traced and projected onto the camera field of view and combined to form a geometry matrix describing the coordinate transformation from magnetic field aligned coordinates to image pixel coordinates. Inverting this matrix enables the reprojection of the emission in the camera images onto a field aligned basis, from which filaments are readily identifiable. The inversion is a poorly conditioned problem which is overcome using a least-squares approach with Laplacian regularization. Blobs are identified using the "watershed" algorithm and 2D Gaussians are fitted to get the positions, widths, and amplitudes of the filaments. A synthetic camera diagnostic generating images containing experimentally representative filaments is utilized to rigorously benchmark the accuracy and reliability of the technique. 74% of synthetic filaments above the detection amplitude threshold are successfully detected, with 98.8% of detected filaments being true positives. The accuracy with which filament properties and their probability density functions are recovered is discussed, along with sources of error and methods to minimize them.