This article presents the master-slave time-delayed competitive neural networks in space-time discretized frames(STD-CNNs) with the heterogeneous structure, induced by the design of an adaptive learning parameter in the slave STD-CNNs. This article addresses the issue of exponential synchronization for the time-delayed STD-CNNs with the heterogeneous structure via the controls at the boundaries, based on the learning law setting for the parameter in the slave STD-CNNs. In a corresponding manner, the exponential synchronization for time-delayed STD-CNNs with the homogeneous structure can be achieved via boundary controls. This study demonstrates that the problem of exponential synchronization for time-delayed heterogeneous STD-CNNs can be modeled by designating a time-varying learning parameter in the slave STD-CNNs, which can then be solved by means of calculative linear matrix inequalities(LMIs). To illustrate the feasibility of the current work, a numerical example is presented.