1. A method for resizing images, comprising the step of: constructing a grid graph from an input image, the grid graph includes one node for each pixel in the input image, wherein adjacent nodes in the grid graph are connected by arcs, and each arc is directed and associated with a cost; applying a cut to the arcs of the grid graph using a cost function; determining a seam of pixels from the cut, in which the pixels in the seam correspond to nodes in the grid graph immediately adjacent to one side of the cut, and wherein coordinates of the pixels in the seam enforce monotonicity and connectivity constraints; and resizing the input image according to the seam to produce an output image while minimizing a change of energy in the output image when compared with the input image.