In this paper we study the problem of rounding a real-valued matrix into an integer-valued matrix to rmmmize 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 J-. 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. Then, we propose "laminar family" for constructing a practical and well-solvable class of T. Indeed, we show that the problem is solvable in polynomial time if T is a union of two laminar families. Finally, we show that the matrix rounding using Li-discrepancy for a union of two laminar families is suitable for developing a high-quality digital-halftoning software.