Background

Seam carving is a technique for image resizing, where the size of an image is reduced by one pixel in height (by removing a horizontal seam) or width (by removing a vertical seam) at a time. Unlike cropping pixels from the edges or scaling the entire image, seam carving is content-aware, because it attempts to identify and preserve the most important content in an image by inferring the “importance” of each pixel from the surrounding pixels.

Say for example that you want to crop this image¹ of Broadway Tower into a square:

Original image	Simple cropping	Seam carving
Original image.	The cropping is done from the edges, and the tower has to be cropped out to make it square.	The width is reduced by removing repetitive grass deemed “unimportant” from the middle.

This video from the algorithm’s original inventors explains the algorithm visually, although we will not implement the image enlargement part of the algorithm:

Seam carving works by using an energy function to find the lowest energy-connected pixels either horizontally or vertically across an image and then removing it. The word “energy” seems scary, but it is the same concept as finding derivatives in calculus. The energy of a pixel is the magnitude of the rate of change of colors at that pixel, and that rate of change in turn is defined by the difference in color between the pixel and its neighbors. A high energy pixel is one that has a large change from its neighbors while a low energy pixel has very little change between itself and its neighbors.

Our implementation uses a DualGradientEnergyFunction helper class, already implemented for you. The way we calculate this value is by approximating the derivative in the $X$ and $Y$ directions then combine these using the Pythagorean theorem to get the overall change. You will use this as the cost function when you model the image as a graph.

Inside src/seamcarving, you’ll find the SeamCarver class that represents the overall seam carving application. It has methods for removing the least-noticeable horizontal or vertical seams from a picture. The removeHorizontal() method works by:

1. Calling SeamFinder.findHorizontal() to find the least-noticeable horizontal seam.
2. Removing this horizontal seam by creating a new picture with all the pixels except for the ones specified in the horizontal seam.
3. Returning the horizontal seam (primarily to verify that the correct seam was removed).

The removeVertical() method does the same thing except in the vertical orientation.

In this project, you will implement a graph algorithm, a graph representation of a non-graph problem, and optionally, a dynamic programming algorithm for seam carving.

• DjikstraShortestPathFinder: finds the shortest path by using Dijkstra’s Algorithm.
• DjikstraSeamFinder: finds the seam to remove by using a reduction of the shortest path problem.
• DynamicProgrammingSeamFinder: an optimized way to find the seam to remove by using dynamic programming.