This paper introduces the modular cellular neural network (CNN), which is a new CNN structure constructed from nine one-layer modules with intercellular interactions between different modules. The new network is suitable for implementing many image processing operations. Inputting an image into the modules results in nine outputs. The topographic characteristic of the cell interactions allows the outputs to introduce new properties for image processing tasks. The stability of the system is proven and the performance is evaluated in several image processing applications. Experiment results on texture segmentation show the power of the proposed structure. The performance of the structure in a real edge detection application using the Berkeley dataset BSDS300 is also evaluated.