Our main contribution is a rather general lemma that can be used to obtain upper bounds on the expected number of extreme points for a large class of noise distributions. We then apply this lemma to obtain explicit bounds for random noise coming from the Gaussian normal distribution of variance σ² and the uniform distribution in a hypercube of side length &epsilon. For these noise distributions we show upper bounds of O( (1/ σ )^d * log^3/2 * d - 1 n ) and O( ( (n log n) / ε )^d/(d+1) ), respectively. Besides its theoretical motivation our model is also motivated by the observation that in many applications of convex hull algorithms the input data is inherently noisy, e.g. when the data comes from physical measurement or imprecise arithmetic is used.}, author = {Damerow, Valentina and Sohler, Christian}, booktitle = {Proceedings of the 12th European Symposium on Algorithms (ESA'04)}, isbn = {9783540230250}, issn = {0302-9743}, title = {{Extreme Points Under Random Noise}}, doi = {10.1007/978-3-540-30140-0_25}, year = {2004}, }