1. An image processing apparatus, comprising: a first memory, for storing an original image having a first width; a second memory; a buffer, having a second width smaller than the first width; a fetching module, for fetching a sub-image of the original image from the first memory and storing the sub-image into the buffer; wherein a width of the sub-image is smaller than or equal to the second width, the fetching module configured to operate with predefined rules for fetching the sub-image of the original image from the first memory; and a processing module, for performing an image processing process on the sub-image image to generate a processed sub-image, and storing the processed sub-image into the second memory, wherein the original image comprises N number of sub-images, each of the sub-images having the width smaller than the second width, and N is an integer greater than 1; and the fetching module sequentially fetches the N sub-images from the first memory to the buffer for processing by the processing module, wherein each sub-image comprises a main part and a border part, the border part of a first sub-image is also the main part of a second sub-image, and the border part is selected to prevent image discontinuity of processed sub-images, wherein the border part is used to perform the image processing process on the main part of the first sub-image to generate a processed sub-image, while the border part of the first sub-image itself is not processed.