Point- and line-based invariance methods are used for both image and object transfer 2D planar objects. Invariance yields equations of straight lines the intersections of which give the positions of the points to be transferred. For non-redundant 4-point invariance, the sequence of points used yields line pairs of different geometric strengths. In redundant cases, using different point sequences to form linear condition equations results in least squares estimates which are different for both the positions and their quality. Corresponding photogrammetric techniques based on point and line features, on the other hand, provide unique estimates and covariances for both non-redundant and redundant cases. A refined least squares approach, for which the linear invariance equations become non-linear, appears to alleviate the non- uniqueness problem. Point-based image invariance is investigated for 3D objects in multiple images. The concepts of the essential and fundamental matrices for use with calibrated and uncalibrated cameras, respectively, are presented. The use of the fundamental matrix to transfer images from two photographs to a third is described and early results summarized. Introducing a constraint on the fundamental matrix stabilizes the solution, which otherwise leads to widely varying results. Preliminary results from linear invariance based object point transfer suggest that the uniqueness problem arising from point sequences also exists in this task. Research is continuing to resolve this issue and to provide photogrammetric equivalent and complimentary methods to invariance.