A method of estimating the displaced size of a knot in a lumber piece includes the steps of: translating the lumber piece downstream along a flow path between a radiation source and sensor while simultaneously irradiating the lumber piece with radiation from the first radiation source whereby the radiation is attenuated by the lumber piece; collecting a set of radiation intensity data from the radiation sensor as the lumber piece is irradiated; processing the set of radiation intensity data to sum the radiation intensity data and to provide radiation intensity profiles transversely of the flow path direction and corresponding density profiles transversely of the flow path direction; mapping the density profiles to model a set of three dimensional density profiles of the lumber piece; processing the radiation intensity data to determine a clear wood density threshold value for the lumber piece and a maximum density value of the density profiles; and, computing a ratio of the summed density profile values to the summed maximum density values for the density profiles and multiplying the ratio with the transverse width of the lumber piece.