Convolution widely has been used as the main part of the improvement in digital image processing applications. In convolutional computations, a large number of memory accesses and a huge amount of computations challenge its performance. Many of the related proposed convolvers are based on exact computations. Although exact convolvers keep the accuracy of the convolution operation at the top level, sometimes by missing a negligible amount of accuracy, the performance can be improved. Approximate computing is a new technique for solving computation overhead problems. In this paper, approximate 2D convolvers are presented which minimize the memory access rate and computations by a special factor of Multiply-and-Accumulate (MAC) terms. On the other hand, to preserve the flexibility for supporting different required accuracy, the proposed approximate convolvers are combined with the exact designs with real-time pre-processing stages by exploiting innovative methods which manage the hardware overhead. In comparison to conventional convolvers, the proposed designs improve the number of active resources which causes a significant reduction in power consumption. For 3 × 3 kernel size, the evaluation results on the Xilinx Virtex-7 (XC7V2000t) FPGA device show 34% and 20% power optimization of the proposed approximate and combined convolvers respectively, in comparison to Exact Convolver (EC). Also, this improvement grows by increasing the kernel size. Finally, a comparison based on RMSE and PSNR for different sample images and filters reveals that the error rate and image quality reduction are acceptable for many real-time image processing applications.