Original image:
Fill pattern:
Introduction
The purpose of this article is to describe how to design an efficient flood fill algorithm.
In order to show the strengths of a good design, I must first: describe the basic types of flood filling and their individual strengths and weaknesses.
Note: By efficient, I mean creating an algorithm that reads as few pixels as possible and uses the least amount of memory allocations. Although we are now talking about flood filling a bitmap, historically speaking, flood fills read and wrote directly to the video, which was very slow. Therefore, it was a must to reduce the number of reads and writes; also the amount of memory was limited, so a reduction in memory usage was also a big plus.
What is the QuickFill Algorithm?
The QuickFill
algorithm is a non-recursive (seed fill) method of filling a 2D graphics image using a scan line search method and doubly linked to lists of nodes to reduce the amount of memory required. The scan line method used in combination with the linked lists, greatly increases the speed at which an image can be filled and allows for multiple fill types to be implemented: background, border, and pattern fills.
Note: The original QuickFill
algorithm was written, as part of my personal DOS graphics library, to fill images displayed on a video monitor.
Basic 4 Way Recursive Method
This is the most basic of all flood filling methods, as well as the simplest.
Its strength: simple to implement by even a beginner programmer.
Its weaknesses: repeated sampling of pixels and recursion (may overflow stack).
The diagram above shows how the flooding of a 3x3 image progresses. As you can see: each pixel was visited 2 or more times, and the depth of recursion was 10.
void SeedFill_1(int x, int y, COLORREF fill_color)
{
if( fill_color != GetPixel(x,y) ) {
SeedFill_1(x,y,fill_color);
SeedFill_1(x-1,y,fill_color);
SeedFill_1(x+1,y,fill_color);
SeedFill_1(x,y-1,fill_color);
SeedFill_1(x,y+1,fill_color);
}
}
void SeedFill_2(int x, int y, COLORREF fill_color, COLORREF border_color)
{
if( border_color != GetPixel(x,y) ) {
SeedFill_2(x,y,fill_color,border_color);
SeedFill_2(x-1,y,fill_color,border_color);
SeedFill_2(x+1,y,fill_color,border_color);
SeedFill_2(x,y-1,fill_color,border_color);
SeedFill_2(x,y+1,fill_color,border_color);
}
}
Basic 8 Way Recursive Method
This is similar to the 4 way method, except that it is even more inefficient.
Its strength: simple to implement by even a beginner programmer.
Its weaknesses: repeated sampling of pixels, recursion (may overflow stack), and it is designed to leak on the diagonals.
Note: This is what I call an abnormal flood fill method. Since it is designed to leak on the diagonals, it has very limited use.
The diagram above shows how the flooding of a 3x3 image progresses. As you can see: each pixel was visited 3 or more times, and the depth of recursion was 10.
void SeedFill_1(int x, int y, COLORREF fill_color)
{
if( fill_color != GetPixel(x,y) ) {
SeedFill_1(x,y,fill_color);
SeedFill_1(x-1,y,fill_color);
SeedFill_1(x+1,y,fill_color);
SeedFill_1(x,y-1,fill_color);
SeedFill_1(x,y+1,fill_color);
SeedFill_1(x-1,y+1,fill_color);
SeedFill_1(x+1,y-1,fill_color);
SeedFill_1(x+1,y+1,fill_color);
SeedFill_1(x-1,y-1,fill_color);
}
}
void SeedFill_2(int x, int y, COLORREF fill_color, COLORREF border_color)
{
if( border_color != GetPixel(x,y) ) {
SeedFill_2(x,y,fill_color,border_color);
SeedFill_2(x-1,y,fill_color,border_color);
SeedFill_2(x+1,y,fill_color,border_color);
SeedFill_2(x,y-1,fill_color,border_color);
SeedFill_2(x,y+1,fill_color,border_color);
SeedFill_2(x-1,y+1,fill_color,border_color);
SeedFill_2(x+1,y-1,fill_color,border_color);
SeedFill_2(x+1,y+1,fill_color,border_color);
SeedFill_2(x-1,y-1,fill_color,border_color);
}
}
Recursive Scan Line Method
The recursive scan line method is a type of 4 way method, but is more efficient than the 4 or 8 way single pixel recursive methods.
Its strength: complete lines are scanned.
Its weaknesses: repeated sampling of some lines and recursion (may overflow stack).
The diagram above shows how the flooding of a 3x3 image progresses. As you can see: each line was visited 1 to 3 times, and the depth of recursion was 2.
The line fill method below may be inefficient, but it reduces the number of times that a pixel is revisited and reduces the number of recursive calls made. It also has the advantage of being optimizable, that is it can be improved through optimization techniques.
Some techniques that can be applied are:
- write scan and search line functions that read and write the image data directly
- rewrite the function to remove recursion
extern int nMinX, nMaxX, nMinY, nMaxY;
void LineFill_3(int x1, int x2, int y,
COLORREF fill_color, COLORREF seed_color)
{
int xL,xR;
if( y < nMinY || nMaxY < y )
return;
for( xL = x1; xL >= nMinX; --xL ) {
if( GetPixel(xL,y) != seed_color )
break;
SetPixel(xL,y,fill_color);
}
if( xL < x1 ) {
LineFill_3(xL, x1, y-1, fill_color, seed_color);
LineFill_3(xL, x1, y+1, fill_color, seed_color);
++x1;
}
for( xR = x2; xR <= nMaxX; ++xR ) {
if( GetPixel(xR,y) != seed_color )
break;
SetPixel(xR,y,fill_color);
}
if( xR > x2 ) {
LineFill_3(x2, xR, y-1, fill_color, seed_color);
LineFill_3(x2, xR, y+1, fill_color, seed_color);
--x2;
}
for( xR = x1; xR <= x2 && xR <= nMaxX; ++xR ) {
if( GetPixel(xR,y) == seed_color )
SetPixel(xR,y,fill_color);
else {
if( x1 < xR ) {
LineFill_3(x1, xR-1, y-1, fill_color, seed_color);
LineFill_3(x1, xR-1, y+1, fill_color, seed_color);
x1 = xR;
}
for( ; xR <= x2 && xR <= nMaxX; ++xR) {
if( GetPixel(xR,y) == seed_color ) {
x1 = xR--;
break;
}
}
}
}
}
void SeedFill_3(int x, int y, COLORREF fill_color)
{
COLORREF seed_color = GetPixel(x,y);
if( fill_color != seed_color )
LineFill_3(x,x,y,fill_color,seed_color);
}
A Simple Non-recursive Scan Line Method
The non-recursive scan line method is a type of 4 way method, but is more efficient than the recursive method.
Its strengths: complete lines are scanned, and no recursion.
Its weaknesses: repeated sampling of some lines, and limited stack size.
The line fill method below is more inefficient than the recursive method. It also has the advantage of being optimizable, that is it can be improved through optimization techniques.
Some techniques that can be applied are:
- write scan and search line functions that, read the image data directly
- rewrite the code so that it uses a linked list for stack
The second, so called, optimization technique, appears as if it would slow down the filling process. If it was used in the same way as the stack array in the following code, then you would be correct. The fact is, a linked list allows us to apply other optimization techniques that more than compensate for the slight loss in efficiency. For example: we could pop items off the stack based on their line number, which reduces the number of items on the stack.
Note: Since most programmers now work with bitmaps, instead of reading and writing directly to video, the first optimization above may be all that is required to make this a truly fast solid flood fill algorithm.
extern int nMinX, nMaxX, nMinY, nMaxY;
typedef struct { int x1, x2, y, dy; } LINESEGMENT;
#define MAXDEPTH 10000
#define PUSH(XL, XR, Y, DY) \
if( sp < stack+MAXDEPTH && Y+(DY) >= nMinX && Y+(DY) <= nMaxY ) \
{ sp->xl = XL; sp->xr = XR; sp->y = Y; sp->dy = DY; ++sp; }
#define POP(XL, XR, Y, DY) \
{ --sp; XL = sp->xl; XR = sp->xr; Y = sp->y+(DY = sp->dy); }
void SeedFill_4(int x, int y, COLORREF new_color)
{
int left, x1, x2, dy;
COLORREF old_color;
LINESEGMENT stack[MAXDEPTH], *sp = stack;
old_color = GetPixel(x, y);
if( old_color == new_color )
return;
if( x < nMinX || x > nMaxX || y < nMinX || y > nMaxY )
return;
PUSH(x, x, y, 1);
PUSH(x, x, y+1, -1);
while( sp > stack ) {
POP(x1, x2, y, dy);
for( x = x1; x >= nMinX && GetPixel(x, y) == old_color; --x )
SetPixel(x, y, new_color);
if( x >= x1 )
goto SKIP;
left = x+1;
if( left < x1 )
PUSH(y, left, x1-1, -dy);
x = x1+1;
do {
for( ; x<=nMaxX && GetPixel(x, y) == old_color; ++x )
SetPixel(x, y, new_color);
PUSH(left, x-1, y, dy);
if( x > x2+1 )
PUSH(x2+1, x-1, y, -dy);
SKIP: for( ++x; x <= x2 && GetPixel(x, y) != old_color; ++x ) {;}
left = x;
} while( x<=x2 );
}
}
The QuickFill Algorithm
Finally, we get to the QuickFill
method of flood filling, which is a type of 4 way method, but is more efficient than the simple non-recursive method (believe it or not).
Note: For the purposes of this article, I will be describing (mostly) the original QuickFill
algorithm, since the included code does not use optimized scan, search, and line drawing functions (remember, the original code directly accessed the video).
Its strengths are:
- supports 3 types of fills: background, border and pattern
- optimized scan, search and drawing functions
- no recursion
- use of doubly linked list, to allow for efficiently removing items from list based on line number
- efficient use of list for reverse line splitting, when pattern filling is required
Its weakness: repeated sampling of some lines, during solid fills.
As you can see from the code below, this is the most complicated method of flood filling. It was derived, indirectly, from the ideas presented in the simple non-recursive method.
The steps taken to create the original code were as follows:
- Wrote
QuickFill
function based on what I could remember about scan line filling. - Replaced stack array with two singly linked lists.
- Modified
PopLine
function, so that lines would be removed based on line number. - Added
SearchLeft
, SearchRight
, ScanLeft
, ScanRight
functions; in order to allow for optimization of searching and scanning. - Added the
PushOpposite
function, which reverse splits lines, in order to reduce the number of lines revisited. This required that the list be changed to a doubly linked list and that the list be x-sorted. The reason behind this function was to eliminate all line revisits, but instead, it just reduced the number of visits (at a cost). - Optimization of all of the above.
Note: While testing the port of the code to Windows, I discovered a gapping hole in the single visit code, patterns and masks could not be empty or the code would get stuck looping for ever (hence the following).
In order to make this function more useful to Windows programmers, I added code to support flooding of image with a bitmap pattern. Since PushOpposite
only reduces the number of lines revisited and does not prevent revisits, I had to add another linked list to keep track of which lines had already been visited. The PushOpposite
function is still required as it still reduces the number of line revisits and, as a bonus, it reduces the number of items placed in the visited list. To optimize the visited list, I decided to use visited blocks (rectangles) instead of visited lines, this serves to reduce the number of items needed in the list, which means less memory allocations.
Note: The following is the QuickFill function taken from version 1.0 of the code.
int CQuickFill::QuickFill(
CBitmap* pBitmap,int x,int y,
COLORREF fill_color,COLORREF border_color)
{
COLORREF ThisColor;
int MaxY,MaxX,dy;
int ChildLeft,ChildRight;
int ParentLeft,ParentRight;
#ifdef QUICKFILL_SLOW
HWND hWnd;
if( m_bSlowMode )
hWnd = ::GetActiveWindow();
#endif
if( !m_DibData.CreateDIB(pBitmap) )
return -3;
#ifdef QUICKFILL_TEST
SHORT nKeyState;
m_CurStackSize = m_MaxStackSize = m_VisitSize = 0U;
m_CurrentLine = 0;
#endif
m_bXSortOn = m_bMemError = FALSE;
m_LastY = -1;
if( CLR_INVALID != border_color ) {
ThisColor = GetPixel(x,y);
if( ThisColor == border_color )
return -1;
ThisColor = border_color;
m_bXSortOn = TRUE;
}
else {
ThisColor = GetPixel(x,y);
if( ThisColor == fill_color && !m_DibPattern.GetDibPtr() )
return -1;
if( m_DibPattern.GetDibPtr() || memcmp(m_FillMask,_SolidMask,8) )
m_bXSortOn = TRUE;
}
#define FindLeft(x,y,xmin,color) \
((CLR_INVALID != border_color) \
? SearchLeft(x,y,xmin,color) : ScanLeft(x,y,xmin,color))
#define FindRight(x,y,xmax,color) \
((CLR_INVALID != border_color) \
? SearchRight(x,y,xmax,color) : ScanRight(x,y,xmax,color))
#define SkipRight(x,y,xmax,color) \
((CLR_INVALID != border_color) \
? ScanRight(x,y,xmax,color) : SearchRight(x,y,xmax,color))
if( MakeList() )
return -2;
MaxX = m_DibData.GetWidth()-1;
MaxY = m_DibData.GetHeight()-1;
PushLine(x,x,y,+1);
PushLine(x,x,y+1,-1);
while( m_pLineList ) {
PopLine(&ParentLeft,&ParentRight,&y,&dy);
y += dy;
if( y < 0 || MaxY < y )
continue;
if( m_bMemError )
continue;
if( m_bXSortOn && IsRevisit(ParentLeft,ParentRight,y) )
continue;
#ifdef QUICKFILL_SLOW
if( m_bSlowMode ) {
nKeyState = ::GetAsyncKeyState(VK_ESCAPE);
if( nKeyState < 0 )
break;
}
m_CurrentLine = y;
#endif
ChildLeft = FindLeft(ParentLeft,y,0,ThisColor)+1;
if( ChildLeft<=ParentLeft ) {
ChildRight = FindRight(ParentLeft,y,MaxX,ThisColor)-1;
if( ChildLeft == ChildRight )
SetPixel(ChildRight,y,fill_color);
else
DrawHorizontalLine(ChildLeft,ChildRight,y,fill_color);
#ifdef QUICKFILL_SLOW
if( m_bSlowMode && hWnd ) {
m_DibData.SetDIBits(pBitmap);
::InvalidateRect(hWnd,NULL,FALSE);
::UpdateWindow(hWnd);
}
#endif
if( ParentLeft-1<=ChildLeft && ChildRight<=ParentRight+1 ) {
PushLine(ChildLeft,ChildRight,y,dy);
}
else {
if( m_bXSortOn )
PushOpposite(ParentLeft,ParentRight,
ChildLeft,ChildRight,y,dy);
else
PushLine(ChildLeft,ChildRight,y,-dy);
PushLine(ChildLeft,ChildRight,y,dy);
}
++ChildRight;
}
else ChildRight = ParentLeft;
while( ChildRight < ParentRight ) {
ChildRight = SkipRight(ChildRight,y,ParentRight,ThisColor);
if( ChildRight<=ParentRight ) {
ChildLeft = ChildRight;
ChildRight = FindRight(ChildLeft,y,MaxX,ThisColor)-1;
if( ChildLeft == ChildRight )
SetPixel(ChildRight,y,fill_color);
else
DrawHorizontalLine(ChildLeft,ChildRight,y,fill_color);
#ifdef QUICKFILL_SLOW
if( m_bSlowMode && hWnd ) {
m_DibData.SetDIBits(pBitmap);
::InvalidateRect(hWnd,NULL,FALSE);
::UpdateWindow(hWnd);
}
#endif
if( ChildRight <= ParentRight+1 )
PushLine(ChildLeft,ChildRight,y,dy);
else {
if( m_bXSortOn )
PushOpposite(ParentLeft,ParentRight,
ChildLeft,ChildRight,y,dy);
else
PushLine(ChildLeft,ChildRight,y,-dy);
PushLine(ChildLeft,ChildRight,y,dy);
}
++ChildRight;
}
}
if( m_bXSortOn )
PushVisitedLine(ParentLeft,ParentRight,y);
}
FreeList();
m_DibData.SetDIBits(pBitmap);
m_DibData.DeleteObject();
return( m_bMemError?-2:0 );
}
Parent/Child Line Relationship
Basic Line Pushing
Note: In the following diagram, "Scanned" implies next line to be scanned, when line being pushed is popped off the stack.
Reverse Line Splitting
Note: In the following diagram, the scanning/pushing starts at the top.
Note: In the following diagram, the blue (arrowed) lines represent the lines being pushed.
Background
At the time that the QuickFill
algorithm was created, I had seen only two types of flood fills used and wanted an algorithm that could handle both types. The first type used a border-color approach, which meant that the area that needed to be filled first had to be outlined with a border of a given color; this approach is the least desirable of the flood fills. The second type used the color at the seed-point, which meant that only pixels of that color were filled; this approach is much more versatile, since it allows for multiple image objects of varying color to be contained in the area being filled. Both of these flood fill types used a horizontal scan-line approach to solve the problem of flood filling an image.
When trying to find information on how to implement a fast flood fill algorithm, I discovered that there was almost no information on the subject. The only algorithms that I found were:
- the basic recursive 4 way flood fill that has been mentioned in many publications (and still is), this is the worst (and slowest) method for filling an image
- a non-recursive scan-line version (ref. 1), that was faster than the 4 way version (still too slow for my purposes), and
- a non-recursive scan-line version (ref. 2) that used two linked lists to implement a flood fill algorithm, faster (but still too slow)
The first two methods had the advantage of being very compact, and very slow. The third method on the other hand, had the potential of being very fast and complicated.
After placing the idea on the back burners for a while, since it was for my own personal graphics library and was not a priority, I had an epiphany. I was having a cup of coffee at the local coffee shop and thinking about how I could solve the problem, when it all came together in my head. I started with the ideas used in the simple scan-line algorithm (ref. 1) and proceeded to expand on the idea using a singly linked list (ref. 2) of nodes, representing a LIFO stack. Over the next nine days, I made incremental changes to the algorithm, each designed to increase the over all speed. When I was finished, I had an algorithm that was not only fast, but faster than every implementation that I could find, except for the one implemented in the Fastgraph
library by Ted Gruber (written in assembly). Five months after the completion of the code, I finally went back and added the code necessary for single line visits so that the QuickFill
function could also handle pattern fills.
References
- A Seed Fill Algorithm by Paul Heckbert from "Graphics Gems", Academic Press, 1990
- An Efficient Flood Visit Algorithm by Anton Treuenfels, C/C++ Users Journal Volume 12, Number 8, August, 1994
Using the Code
Note: When running the demo program in slow mode, you can press the ESC key to stop it.
CDibData Specific
If you have not installed the Windows SDK from Microsoft, you will get some compilation errors when compiling in debug mode. The reason for this is that BITMAPV5HEADER
was not defined in the SDK that came with Visual C++ 6.0. Since BITMAPV5HEADER
is only used for displaying debugging information, it should be easy to comment out the code.
#include "QuickFill.h"
QuickFill qf;
qf.QuickFill(&bitmap, x, y, fill_color);
qf.QuickFill(&bitmap, x, y, fill_color, border_color);
#include "QuickFill.h"
QuickFill qf;
qf.SetPatternBitmap(&patternBitmap);
qf.SetPatternClearColor(transparentColor);
qf.QuickFill(&bitmap, x, y, fill_color);
qf.SetPatternBitmap();
#include "QuickFill.h"
QuickFill qf;
BYTE diagMask[8] = {
0x80, 0x80>>1, 0x80>>2, 0x80>>3,
0x80>>4, 0x80>>5, 0x80>>6, 0x80>>6,
};
qf.SetFillMask(diagMask);
qf.QuickFill(&bitmap, x, y, fill_color);
qf.SetFillMask();
Points of Interest
The code included with this article relies on the CDibData class to provide direct access to bitmap pixels.
I see no barrier to rewriting the code for use with GDI+, the only reason I did not do that, is that, I do not know enough about GDI+ usage at this time. Besides, I have a personal paint program written using GDI and would like to add this code to it.
For those who want to compare the various flood fill algorithms, I suggest the following:
- Add some tracking variables and code (like the ones in the
QuickFill
code) - Make the test function or functions
private
members of the QuickFill
class - After the
QuickFill
initialization, but before the first push, add a call to the test function. Then clean up after the test function call and return without entering the main QuickFill
loop.
Note: The above is how I tested the recursive scan line code. Since it was written off the top of my head, I needed to be sure it would work.
If any one knows how to completely eliminate the need for the visited list, I would be very interested. When I discovered that the original method used to reduce revisits did not eliminate them, I felt insulted by my own code. At the time I wrote the QuickFill
algorithm, I may have known of this problem and just forgot about it (doubt that).
Question: How would you optimize the QuickFill
algorithm for bitmaps?
Answer: Modify the CDibData
class so that it has optimized functions for ScanLeft
, ScanRight
, SearchLeft
, SearchRight
and horizontal line drawing. Of course, horizontal line drawing would be the hardest, since it would have to work the same as the DrawHorizontalLine
member function.
History
Version 1.0
- Jan 2004: Converted from C (direct video access) to C++ for use with MS Windows bitmaps and added support for: pattern bitmaps to be used as fill and visit-block-list to eliminate revisiting during pattern & mask fills.
Note: Since the original code had direct video access, it could take advantage (with the correct write mode) of byte block copping and color-bit-mask reading (read mode 1). Both of which were hardware supported (VGA/EGA monitors) and much more efficient than reading/writing single pixels directly from/to a bitmap.
Version 1.1
- Feb. 6, 2004: Added left optimization, eliminates some revisits
- Feb. 8, 2004: Added reverse clip optimization, eliminates some revisits
- Feb. 15, 2004: Found
PushOpposite
special case and corrected it - Feb. 19, 2004: Changed internal scan, search and line drawing routines to use pixel color values, in order to increase overall speed while working with palettized bitmaps (modified
CDibData
) - Mar. 5, 2004: (1) Moved
PushVisitedLine
from QuickFill
to PushOpposite
, this increases the number of revisits and reduces the size of the visit list (8:1). (2) Changed visit list to use HLINE_NODE
, since block checking is no longer required and the number of allocations are reduce because the free list can now be used by all. (Of course HLINE_NODE
is larger than we need, since it is not a visit list specific node type) - Mar. 9, 2004: (1) Added argument to
QuickFill
so that user can specify the rectangular area to be filled. (2) Added the GetInvalidRect
function and associated code so that user can retrieve the rectangular coordinates of the bitmap area that has been modified, since lack of this information forces user to redraw whole bitmap.
Changes to demo program:
- "Fill Mask" selection option.
- "Show Revisits" option. This is used to show which lines were placed in the visit list, when pattern bitmaps or masks are used. Line types: Cyan->line in visit list, Yellow->revisited line direction = -1, Blue->revisited line direction = +1.
- Fill area selection via mouse (left-click and drag to select area). To fill: left-click in selected area and release to fill.
- Added elapsed fill time and revisit count to information displayed to right of bitmap.
Credits
- Andrew J. McCauley for modifying
CDibData
debug code so that header type checking occurs based on WINVER
rather than on header type only. This stopped compilation errors which occurred if the user did not have the new Windows SDK installed.
License
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A list of licenses authors might use can be found here.