Flood fill, also called seed fill, is an algorithm

Algorithm

In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...

 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

Bitmap

In computer graphics, a bitmap or pixmap is a type of memory organization or image file format used to store digital images. The term bitmap comes from the computer programming terminology, meaning just a map of bits, a spatially mapped array of bits. Now, along with pixmap, it commonly refers to...

 to fill with color, and in games such as Go and Minesweeper for determining which pieces are cleared. When applied on an image to fill a particular bounded area with color, it is also known as boundary fill.

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

Stack (data structure)

In computer science, a stack is a last in, first out abstract data type and linear data structure. A stack can have any abstract data type as an element, but is characterized by only three fundamental operations: push, pop and stack top. The push operation adds a new item to the top of the stack,...

 data structure, explicitly or implicitly. One implicitly stack-based (recursive

Recursion

Recursion is the process of repeating items in a self-similar way. For instance, when the surfaces of two mirrors are exactly parallel with each other the nested images that occur are a form of infinite recursion. The term has a variety of meanings specific to a variety of disciplines ranging from...

) 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.

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 applet

Java applet

A Java applet is an applet delivered to users in the form of Java bytecode. Java applets can run in a Web browser using a Java Virtual Machine , or in Sun's AppletViewer, a stand-alone tool for testing applets...

s).

An explicitly queue-based implementation is shown in the pseudo-code below. This implementation is not very efficient, but can be coded quickly, does not use a stack, and it is easy to debug:

Flood-fill (node, target-colour, replacement-colour):
1. Set Q to the empty queue.
2. If the colour of node is not equal to target-colour, 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 colour of n is equal to target-colour:
7. Set the colour of n to replacement-colour.
8. If the colour of the node to the west of n is target-colour:
9. Add that node to the end of Q
10. If the colour of the node to the east of n is target-colour:
11. Add that node to the end of Q
12. If the colour of the node to the north of n is target-colour:
13. Add that node to the end of Q
14. If the colour of the node to the south of n is target-colour:
15. Add that node to the end of Q
16. Remove first element from Q
17. 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.
12. If the color of the node to the south of n is target-color, add that node to Q.
13. Continue looping until Q is exhausted.
14. 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

Alpha compositing

In computer graphics, alpha compositing is the process of combining an image with a background to create the appearance of partial or full transparency. It is often useful to render image elements in separate passes, and then combine the resulting multiple 2D images into a single, final image in a...

 allows the edges of the filled region to blend somewhat smoothly with the not-filled region.

Fixed memory method (right-hand fill method)

A method exists that uses essentially no memory for four-connected

Pixel connectivity

In image processing and image recognition, pixel connectivity is the way in which pixels in 2- or 3-dimensional images relate to their neighbors.-4-connected:...

 regions by pretending to be a painter trying to paint the region without painting himself into a corner. This is also a method for solving mazes. The four pixels making the primary boundary are examined to see what action should be taken. The painter could find themselves in one of several conditions:

1. All four boundary pixels are filled.
2. Three of the boundary pixels are filled.
3. Two of the boundary pixels are filled.
4. One boundary pixel is filled.
5. Zero boundary pixels are filled.

Where a path or boundary is to be followed, the right-hand rule is used. The painter follows the region by placing their right-hand on the wall (the boundary of the region) and progressing around the edge of the region without removing their hand.

For case #1, the painter paints (fills) the pixel the painter is standing upon and stops the algorithm.

For case #2, a path leading out of the area exists. Paint the pixel the painter is standing upon and move in the direction of the open path.

For case #3, the two boundary pixels define a path which, if we painted the current pixel, may block us from ever getting back to the other side of the path. We need a "mark" to define where we are and which direction we are heading to see if we ever get back to exactly the same pixel. If we already created such a "mark", then we preserve our previous mark and move to the next pixel following the right-hand rule.

A mark is used for the first 2-pixel boundary that is encountered to remember where the passage started and in what direction the painter was moving. If the mark is encountered again and the painter is traveling in the same direction, then the painter knows that it is safe to paint the square with the mark and to continue in the same direction. This is because (through some unknown path) the pixels on the other side of the mark can be reached and painted in the future. The mark is removed for future use.

If the painter encounters the mark but is going in a different direction, then some sort of loop has occurred which caused the painter to return to the mark. This loop must be eliminated. The mark is picked up and the painter then proceeds in the direction indicated previously by the mark using a left-hand rule for the boundary (similar to the right-hand rule but using the painter's left hand). This continues until an intersection is found (with three or more open boundary pixels). Still using the left-hand rule the painter now searches for a simple passage (made by two boundary pixels). Upon finding this two-pixel boundary path, that pixel is painted. This breaks the loop and allows the algorithm to continue.

For case #4, we need to check the opposite 8-connected corners to see if they are filled or not. If either or both are filled, then this creates a many-path intersection and cannot be filled. If both are empty, then the current pixel can be painted and the painter can move following the right-hand rule.

The algorithm trades time for memory. For simple shapes it is very efficient. However, if the shape is complex with many features, the algorithm spends a large amount of time tracing the edges of the region trying to ensure that all can be painted.

This algorithm was first available commercially in 1981 on a Vicom Image Processing system manufactured by Vicom Systems, Inc. The classic recursive flood fill algorithm was available on this system as well.

Scanline fill

The algorithm can be sped up by filling lines. Instead of pushing each potential future pixel coordinate on 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.

Efficiency : each pixel is checked once.

Vector implementations

Version 0.46 of Inkscape

Inkscape

Inkscape is a free software vector graphics editor, licensed under the GNU General Public License. Its goal is to implement full support for the Scalable Vector Graphics 1.1 standard....

 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 the concept of a boundary condition

Boundary value problem

In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional restraints, called the boundary conditions...

.

Large scale behaviour

The primary technique used to control a flood fill will either be data-centric or process-centric. A data-centric approach can use either a stack or a queue to keep track of seed pixels that need to be checked. A process-centric algorithm must necessarily use a stack.

A 4-way floodfill algorithm that uses the adjacency technique and a queue as its seed pixel store yields an expanding lozenge-shaped fill.

Efficiency : 4 pixels checked for each pixel filled (8 for an 8-way fill).

A 4-way floodfill algorithm that use the adjacency technique and a stack as its seed pixel store yields a linear fill with "gaps filled later" behaviour. This approach can be particularly seen in older 8-bit computer games.

Efficiency : 4 pixels checked for each pixel filled (8 for an 8-way fill).

External links

• Didactical Javascript implementation of scanline polygon fill, by Guilherme Polo.
• Sample implementations for recursive and non-recursive, classic and scanline flood fill, by Lode Vandevenne.
• C implementation of Flood/Seed Fill Algorithm from Graphics Gems; BSD(ish) license, by Paul Heckbert.
• Flash flood fill implementation, by Emanuele Feronato.
• QuickFill: An efficient flood fill algorithm., by John R. Shaw.