1. A medical image processing apparatus which performs image processing on a medical input image, comprising: a pixel extraction portion for extracting an inappropriate pixel satisfying a predetermined condition in the input image; a replacing pixel information calculation portion for calculating replacing information with which pixel information of the inappropriate pixel is to be replaced, based on pixel information of a predetermined region including the extracted inappropriate pixel or adjacent to the extracted inappropriate pixel; and a replaced image generation portion for replacing the pixel information of the inappropriate pixel in the input image with the replacing information and generating a replaced image.