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We present our novel Adaptive Multi-Affine (AMA) feature-matching algorithm that finds correspondences between two views of the same non-planar object. The proposed method only uses monocular images to robustly match clusters of 2-D features according to their relative position on the object surface; finally, AMA adaptively finds the best number of clusters that maximizes the number of matching features. We use AMA to recover a feature tracker from failure (e.g., loss of points due to occlusions or deformations), by robustly matching the features in the images before and after such events. This is paramount in Augmented-Reality (AR) systems for Minimally-Invasive Surgery (MIS) to cope for frequent occlusions and organ deformations that can cause the tracked image-points to drastically reduce (or even disappear) in the current video. We validated our approach on a large set of MIS videos of partial-nephrectomy surgery; AMA achieves an increased number of matches, as well as a reduced feature-matching error when compared to state-of-the-art method.