Exact and approximate algorithms for detecting lines in a two-dimensional image space are discussed. For the case of uniformly distributed noise within an image space, transform methods and different notions of probability measures governing the parameters of the transforms are described. It is shown that different quantization schemes of the transformed space are desirable for different probabilistic assumptions. The quantization schemes are evaluated and compared. For one of the procedures that uses a generalized Duda-Hart procedure and a mixed quantization scheme, the time complexity to find all m-flats in n-space is shown to be bounded by O(ptm(n-m)2), where p is the number of points and t is a user parameter. For this procedure more true flats in a given orientation have been found and the number of spurious flats is small.