Disclosed are methods, apparatuses, and systems for encoding and decoding an image. The present invention provides an intra prediction unit receives an input image, removes high frequency ingredients by low pass filtering an encoded luma pixel value in the input image during intra prediction, and generates a prediction block by predicting a chroma pixel value by using a low pass filter (LPF) LM chroma mode for applying an LM chroma mode, which is an extended chroma mode technique for generating a prediction block by predicting the chroma pixel value by applying a correlation between color planes to the luma pixel value having removed therefrom the high frequency ingredients.