1. A video encoding/decoding apparatus comprising: a video encoder for generating an intra-predicted block by predicting pixels of a current block based on pixels of a neighboring block, generating a predicted block by selectively performing filtering on the intra-predicted block based on a correlation among the pixels of the neighboring block or a correlation among pixels of the intra-predicted blocks, generating a residual block by subtracting the predicted block from the current block, generating a transformed and quantized residual block by transforming and quantizing the residual block, and encoding the transformed and quantized residual block; and a video decoder for reconstructing a transformed and quantized residual block from encoded data received, reconstructing a residual block by inverse-quantizing and inverse-transforming the reconstructed transformed and quantized residual block, generating an intra-predicted block by predicting pixels of a current block based on pixels of a neighboring block, generating a predicted block by selectively performing filtering on the intra-predicted block based on a correlation among the pixels of the neighboring block or a correlation among pixels of the intra-predicted block, and reconstructing the current block by adding the reconstructed residual block and the predicted block.