We discuss applications of quantum computation to geometric data processing. Especially, we give efficient algorithms for intersection problems and proximity problems. Our algorithms are based on Brassard et al. 's amplitude amplification method, and analogous to Buhrman et al. 's algorithm for element distinctness. Revealing these applications is useful for classifying geometric problems, and also emphasizing potential usefulness of quantum computation in geometric data processing. Thus, the results will promote research and development of quantum computers and algorithms.