This paper provides a novel signal processing for detecting defects based on the spatio-temporal gradient analysis over the Lamb-wave field. The proposed processing classifies the wave field through the rank of the covariance matrix which is defined by the four-dimensional vector with following components: a vertical displacement, its vertical velocity, and a pair of out-of-plane shearing strains. The covariance matrix provides the information about defects. Its determinant, therefore, is proposed as the inhomogeneity-index of the object surface. In this study, the physical meanings of the proposed index are shown, the computational process in the Lamb-wave field near the defects is discussed and their behaviors are investigated through FDTD-simulations and acoustic experiments.