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in the previous lecture we have seen a concrete example of how to calculate the Delta value for a given hard feature and the closer the value to one the more likely we have found a hard feature but we have to sum up lots of lots of values because a hard feature usually contains lots of lots of pixels so not just eight pixels but for example thousands of pixels so we have to sum up lots of lots of values and thats why we have to talk about integral images okay so the problem is that we have to calculate the average of a given region several times and calculating the average has the running time complexity although N squared which is a quadratic running time algorithm so we can use integral image approach to achieve or do one so constant running time complexity you may post the question that why are there so many operations because we have to use hard features with all possible sizes and locations okay so we have been talking about the edge feature and the line feature but of course we