Pixel Approximation Errors in Common Watershed Algorithms

The exact, subpixel watershed algorithm delivers very accurate watershed boundaries based on a spline interpolation, but is slow and only works in 2D. On the other hand, there are very fast pixel watershed algorithms, but they produce errors not only in certain exotic cases, but also in real-world images and even in the most simple scenarios. In this work, we examine closely the source of these errors and propose a new algorithm that is fast, approximates the exact watersheds (with pixel resolution), and can be extended to 3D.