Flood fill

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Flood fill, also called seed fill, is an algorithm that determines the area connected to a given node in a multi-dimensional array. It is used in the "bucket" fill tool of paint programs to determine which parts of a bitmap to fill with color, and in puzzle games such as Minesweeper, Puyo Puyo, Lumines, and Magical Drop for determining which pieces are cleared.

Contents 1 The algorithm 1.1 Alternative implementations 2 Scanline Fill 3 Vector implementations 4 See also 5 External links

[edit] The algorithm

The flood fill algorithm takes three parameters: a start node, a target color, and a replacement color. The algorithm looks for all nodes in the array which are connected to the start node by a path of the target color, and changes them to the replacement color. There are many ways in which the flood-fill algorithm can be structured, but they all make use of a queue or stack data structure, explicitly or implicitly. One implicitly stack-based (recursive) flood-fill implementation (for a two-dimensional array) goes as follows:

Flood-fill (node, target-color, replacement-color):
 1. If the color of node is not equal to target-color, return.
 2. Set the color of node to replacement-color.
 3. Perform Flood-fill (one step to the west of node, target-color, replacement-color).
    Perform Flood-fill (one step to the east of node, target-color, replacement-color).
    Perform Flood-fill (one step to the north of node, target-color, replacement-color).
    Perform Flood-fill (one step to the south of node, target-color, replacement-color).
 4. Return.

[edit] Alternative implementations

Though easy to understand, the implementation of the algorithm used above is impractical in languages and environments where stack space is severely constrained (e.g. Java applets).

An explicitly queue-based implementation might resemble the pseudo-code below. This implementation is not very efficient, but can be easily done without using the stack, and it is easy to debug:

Flood-fill (node, target-color, replacement-color):
 1. Set Q to the empty queue.
 2. If the color of node is not equal to target-color, return.
 3. Add node to the end of Q.
 4. While "Q" is not empty: 
 5.     Set "n" equal to the first element of "Q"
 6.     If the color of n is equal to target-color, set the color of n to replacement-color.
 7.     Remove first element from "Q"
 7.     If the color of the node to the west of n is target-color, set the color of that node to replacement-color, add that node to the end of Q.
        If the color of the node to the east of n is target-color, set the color of that node to replacement-color, add that node to the end of Q.
        If the color of the node to the north of n is target-color, set the color of that node to replacement-color, add that node to the end of Q.
        If the color of the node to the south of n is target-color, set the color of that node to replacement-color, add that node to the end of Q.
 8. Return.

Most practical implementations use a loop for the west and east directions as an optimization to avoid the overhead of stack or queue management:

Flood-fill (node, target-color, replacement-color):
 1. Set Q to the empty queue.
 2. If the color of node is not equal to target-color, return.
 3. Add node to Q.
 4. For each element n of Q:
 5.  If the color of n is equal to target-color:
 6.   Set w and e equal to n.
 7.   Move w to the west until the color of the node to the west of w no longer matches target-color.
 8.   Move e to the east until the color of the node to the east of e no longer matches target-color.
 9.   Set the color of nodes between w and e to replacement-color.
10.   For each node n between w and e:
11.    If the color of the node to the north of n is target-color, add that node to Q.
       If the color of the node to the south of n is target-color, add that node to Q.
12. Continue looping until Q is exhausted.
13. Return.

Adapting the algorithm to use an additional array to store the shape of the region allows generalization to cover "fuzzy" flood filling, where an element can differ by up to a specified threshold from the source symbol. Using this additional array as an alpha channel allows the edges of the filled region to blend somewhat smoothly with the not-filled region.

[edit] Scanline Fill

The algorithm can be sped up by filling lines. Instead of pushing each potential future pixel coordinate into the stack, it inspects the neighbour lines (previous and next) to find adjacent segments that may be filled in a future pass; the coordinates (either the start or the end) of the line segment are pushed on the stack. In most cases this scanline algorithm is at least an order of magnitude faster than the per-pixel one.

[edit] Vector implementations

The current development version of Inkscape (which is now version 0.46) includes a bucket fill tool, giving output similar to ordinary bitmap operations and indeed using one: the canvas is rendered, a flood fill operation is performed on the selected area and the result is then traced back to a path. It uses concept of a boundary condition.

[edit] See also

• Boundary fill is an algorithm used for the similar purposes as Flood fill
• Connected Component Labeling

[edit] External links

• Source code for implementing the flood fill algorithm in Java, C, and OCaml.
• Sample implementations for recursive and non-recursive, classic and scanline flood fill, by Lode Vandevenn.
• C implementation of Flood/Seed Fill Algorithm from Graphics Gems; BSD(ish) license, by Paul Heckbert.
• Flash flood fill implementation, by Emanuele Feronato.