A method resizes input images by first constructing a grid graph. The grid graph includes one node for each pixel in the input image, and adjacent nodes in the grid graph are connected by arcs. Each arc is directed and has an associated cost. A cut is applied to the arcs of the grid graph using a cost function. A seam of pixels is determined from the cut so that coordinates of the pixels in the seam enforce monotonicity and connectivity constraints. Then, the input image is resized 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.