Given a pair of left-right views of a calibrated stereo rig at two different poses, we have previously proposed two robust and efficient feature matching methods. These so-called quadruplet feature matching schemes use RANSAC for outlier rejection in establishing spatio-temporal matches in four views, and computing the motion of the stereo rig from one pose to the next . However, a significant number of valid quadruplet matches may be missed in part due to the inherent difficulties of temporal feature matching/tracking, and in part because of the conservative nature of the applied epipolar mutual-enforcing quadruplet matching technique in exchange for increased robustness. Having determined some initial quadruplet matches, an optimum motion is then determined by applying all the constraints embedded in the geometry of the two stereo pairs . In this paper, we exploit the estimated motion to identify a larger number of valid quadruplet features under the so-called Epiflow Quadruplet Matching framework. Here, local matching dissimilarities of the left and right views individually and in the left-right views at the second stereo pose are expressed in terms of an energy function of discrepancies between optimal and estimated feature locations. The deviations of the feature locations in the second stereo views are defined as 4-D vectors that are constrained by quadratic constraints arising from the stereo epipolar geometry. Experiments with two sets of real data are presented to show the performance from the proposed energy minimization framework. Subsequent improvement in motion estimation, accommodated by utilizing more correct quadruplets matches, leads to a a natural framework for iterative motion estimation and feature matching.