Large intelligent surface-based transceivers (LISBTs), in which a spatially continuous surface is being used for signal transmission and reception, have emerged as a promising solution for improving the coverage and data rate of wireless communication systems. To realize these objectives, the acquisition of accurate channel state information (CSI) in LISBT-assisted wireless communication systems is crucial. In this paper, we propose a channel estimation scheme based on a parametric physical channel model for line-of-sight dominated communication in millimeter and terahertz wave bands. The proposed estimation scheme requires only five pilot signals to perfectly estimate the channel parameters assuming there is no noise at the receiver. In the presence of noise, we propose an iterative estimation algorithm that decreases the channel estimation error due to noise. The training overhead and computational cost of the proposed scheme do not scale with the number of antennas. The simulation results demonstrate that the proposed estimation scheme significantly outperforms other benchmark schemes.