This paper first presents novel approximate reverse carry full adder (ARFA) circuits where the weight of the input carry is more than that of the output carry. Using the proposed ARFAs and conventional full adders, new approximate reverse carry propagate adder (ARCAs) architectures are presented where the carry propagates in a counter manner. The proposed ARCA provides trade-off in accuracy and performance depending on the number of ARFAs used. Further, novel accuracy reconfigurable reverse carry propagate adders are proposed that provide approximate sum with high energy efficiency and can also deliver 100% accurate sum with small performance penalty. For comparative analysis, the proposed and existing adders are modeled in Verilog and synthesized via Synopsys Design Compiler with 65 nm PDK. The synthesis results of the proposed 16-bit ARCA-II show 9.93% reduced energy consumption over the existing. Finally, the Gaussian smoothing filter (GSF) embedded with the proposed adder shows 12.15% reduced energy consumption with an acceptable image quality (1.64 dB loss in PSNR) over the GSFs with the existing adder.