The fundamental matrix (FM) represents the perspective transform between two or more uncalibrated images of a stationary scene, and is traditionally estimated based on 2- parameter point-to-point correspondences between image pairs. Recent invariant correspondence techniques however, provide robust correspondences in terms of 4 to 6- parameter invariant regions. Such correspondences contain important information regarding scene geometry, information which is lost in FM estimation techniques based solely on 2-parameter point translation. In this article, we present a method of incorporating this additional information into point-based FM estimation routines, entitled TIP (transfer of invariant parameters). The TIP method transforms invariant correspondence parameters into additional point correspondences, which can be used with FM estimation routines. Experimentation shows that the TIP methods result in more robust FM estimates in the case of sparse correspondence, and allows estimation based on as few as 3 correspondences in the case of affine-invariant features.