Seam-carving is a content-aware image resizing technique where the image is reduced in size by one pixel of height (or width) at a time. A vertical seam in an image is a path of pixels connected from the top to the bottom with one pixel in each row; a horizontal seam is a path of pixels connected from the left to the right with one pixel in each column. Below left is the original 505-by-287 pixel image; below right is the result after removing 150 vertical seams, resulting in a 30% narrower image. Unlike standard content-agnostic resizing techniques (such as cropping and scaling), seam carving preserves the most interest features (aspect ratio, set of objects present, etc.) of the image.

Although the underlying algorithm is simple and elegant, it was not discovered until 2007. Now, it is now a core feature in Adobe Photoshop and other computer graphics applications.

Dr. Hug in the ocean Dr. Hug in the ocean

In this assignment, you will create a data type that resizes a W-by-H image using the seam-carving technique.

Finding and removing a seam involves three parts and a tiny bit of notation:

  1. Notation. In image processing, pixel (x, y) refers to the pixel in column x and row y, with pixel (0, 0) at the upper left corner and pixel (W − 1, H − 1) at the bottom right corner. This is consistent with the Picture data type in algs4.jar. Warning: this is the opposite of the standard mathematical notation used in linear algebra where (i, j) refers to row i and column j and with Cartesian coordinates where (0, 0) is at the lower left corner.

    a 3-by-4 image
      (0, 0)     (1, 0)     (2, 0)  
      (0, 1)     (1, 1)     (2, 1)  
      (0, 2)     (1, 2)     (2, 2)  
      (0, 3)     (1, 3)     (2, 3)  

    We also assume that the color of a pixel is represented in RGB space, using three integers between 0 and 255. This is consistent with the java.awt.Color data type.

  2. Energy calculation. The first step is to calculate the energy of each pixel, which is a measure of the importance of each pixel—the higher the energy, the less likely that the pixel will be included as part of a seam (as we'll see in the next step). In this assignment, you will implement the dual-gradient energy function, which is described below. Here is the dual-gradient energy function of the surfing image above:

    Dr. Hug as energy

    The energy is high (white) for pixels in the image where there is a rapid color gradient (such as the boundary between the sea and sky and the boundary between the surfing Josh Hug on the left and the ocean behind him). The seam-carving technique avoids removing such high-energy pixels.

  3. Seam identification. The next step is to find a vertical seam of minimum total energy. This is similar to the classic shortest path problem in an edge-weighted digraph except for the following:

    Vertical Seam
  4. Seam removal. The final step is to remove from the image all of the pixels along the seam.

The SeamCarver API. Your task is to implement the following mutable data type:

public class SeamCarver {

   // create a seam carver object based on the given picture
   public SeamCarver(Picture picture)

   // current picture
   public Picture picture()

   // width of current picture
   public int width()

   // height of current picture
   public int height()

   // energy of pixel at column x and row y
   public double energy(int x, int y)

   // sequence of indices for horizontal seam
   public int[] findHorizontalSeam()

   // sequence of indices for vertical seam
   public int[] findVerticalSeam()

   // remove horizontal seam from current picture
   public void removeHorizontalSeam(int[] seam)

   // remove vertical seam from current picture
   public void removeVerticalSeam(int[] seam)

   //  unit testing (optional)
   public static void main(String[] args)


Analysis of running time (optional and not graded). 

Web submission. Submit a .zip file containing and any other supporting files (excluding algs4.jar and You may not call any library functions except those in java.lang, java.util, java.awt.Color, and algs4.jar.

This assignment was developed by Josh Hug, Maia Ginsburg, and Kevin Wayne.
Copyright © 2013.