A portioning system (10) includes a scanner (16) for scanning a passing poultry breast (14). A cutting device (18), a slicing device (20) and/or other equipment may be used to portion, trim, or otherwise process the poultry breast under the control of a computer (22). The computer also utilizes the information from the scanner to determine position and the angular orientation of the poultry breast relative to a reference line by determining directional lines corresponding to physical attributes of the poultry breast. One directional line is related to the principal axis of the poultry breast, determined from the axis of least inertia of the poultry breast. Other directional lines may correspond to the locations of notches, projections, linear depressions, or other physical anatomical features of the poultry breast.