Disclosed are methods, apparatuses, and systems for encoding and decoding an image. The present invention provides an intra prediction unit that receives an input image, calculates a correlation between a Luma area block and Chroma area block in the input image in intra prediction, removes high frequency ingredients by low-pass filtering an encoded luma pixel based on the calculated correlation, and generates a prediction block by applying an LM chroma mode, which is an extended chroma mode technique, to the luma pixel removed therefrom the high frequency ingredients.