1. A method for detecting and removing a false contour, comprising: receiving an input video; verifying whether a pixel of the input video is included in a contour; calculating simplicity of the pixel; determining whether the pixel is included in a false contour based on the simplicity and based on whether the pixel is included in the contour; and removing the false contour from the input video via smoothing with respect to the false contour, wherein the calculating the simplicity of the pixel comprises: verifying whether a difference between the adjacent pixels within a search window, including the pixel in a center thereof, is less than a predetermined difference; and calculating the simplicity of the pixel based on the difference between the adjacent pixels when the difference is less than the predetermined difference.