We study the problem of rounding a real-valued matrix into an integer-valued matrix to minimize an Lp-discrepancy measure between them. To define the Lp-discrepancy measure, we introduce a family ℱ of regions (rigid submatrices) of the matrix and consider a hypergraph defined by the family. The difficulty of the problem depends on the choice of the region family ℱ. We first investigate the rounding problem by using integer programming problems with convex piecewise-linear objective functions and give some nontrivial upper bounds for the Lp discrepancy. We propose "laminar family" for constructing a practical and well-solvable class of ℱ. Indeed, we show that the problem is solvable in polynomial time if ℱ is the union of two laminar families. Finally, we show that the matrix rounding using L1 discrepancy for the union of two laminar families is suitable for developing a high-quality digital-halftoning software.