NAPSAC: High Noise, High Dimensional Robust Estimation - it’s in the Bag. An umber of the most powerful robust estimation algorithms, such as RANSAC, MINPRAN and LMS ,h ave their basis in selecting random minimal sets of data to instantiate hypotheses. However, their perfor- mance degrades in higher dimensional spaces due to the exponentially decreasing probability of sampling a set that is composed entirely of inliers. In order to overcome this, rather than picking sets at random, a new strategy is proposed that alters the way samples are taken, under the assumption that inliers will tend to be closer to one another than outliers. Based on this premise, the NAPSAC (N Adjacent Points SAmple Consensus) algorithm is derived and its performance is shown to be superior to RANSAC in both high noise and high dimensional spaces.