A Digital Airbrushing Algorithm

A Digital Airbrushing Algorithm

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A Digital Airbrushing Algorithm
Don Lancaster Synergetics, Box 809, Thatcher, AZ 85552 copyright c2008 pub 3/08 as GuruGram #87 http://www.tinaja.com don@tinaja.com (928) 428-4073

lassic airbrushing was a technique of using elaborate masks and a miniature paint sprayer to cover up and improve portions of a photo. So they looked better or eliminated perceived defects. We can instead define digital airbrushing as...
DIGITAL AIRBRUSHING -- Given four points on a bitmap image p0, p1, p2, and p3, match the color at those points and linearly gradient blend all intermediate points inside that defined area.


You might want to do this because there is a bad lighting burn. Or dirt to get removed. Or are doing historical retouching. Or want to improve the top cover on a test equipment image. Or are preparing eBay resale images . We looked at some fundamental new image manipulation tools in BMP2PSA.PDF as GuruGram #84. As our first application example, we will expand these tools into a set of digital airbrushing utilities. As additional features, we will allow the airbrushing to be any quadrilateral shape and not a simple aligned rectangle. We will further allow adding randomized texture of arbitrary depth to improve the "interest" and "match" of the corrected area. While the algorithms we will look at can be adapted to any language that can access host disk files, easily manipulate data arrays, handle the HSB and RGB conversions, and cleanly detect path insidedness, we'll focus on using PostScript arrays of strings and its superb infill operator as a preferred solution. A preliminary algorithm study appears here with its results here. The working utilities are found as our file AIRBRUT1.PSL. An example demo appears here. A bad lighting burn has been partially eliminated lower right and some speckle upper left. Mild texture has been added to match the image areas.
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The Algorithm
There is some subtlety and sneakiness that makes digital airbrushing nontrivial. Here is a useful approach...
A DIGITAL AIRBRUSHING ALGORITHM -- (1) Establish four points x0,y0 x1,y1, x2,y2, and x3,y3 CLOCKWISE FROM THE LOWER LEFT in the area to be airbrushed. (2) Calculate a bounding box that will contain all of the control points. (3) Find the HSB values at the corners of the bounding box that would be needed to create a linear two dimensional gradient that matches the four control HSB values. This will involve solving four linear equations in four unknowns. (4) Establish the quadrilateral path and make corrections to only those inside pixels. (5) Normalize the bounding box to a unit square. Then use bilineal interpolation to determine all needed internal pixel values. (6) Optionally randomize each pixel RGB value to add a desired depth of textural interest.

It is very important to note that you normally will want to work in HSB ( huesaturation-brightness ) space rather than RGB ( red-green-blue ). The reason is that a linear RGB transition from red to green goes through gray, while a similar HSB transition goes from the more expected red to orange to yellow to green.
PostScript is especially adept at converting between these two color standards...

HSB to RGB: hue sat bright setHSBcolor currentRGBcolor RGB to HSB red blue green setRGBcolor currentHSBcolor

Several minor points before continuing: Our PostScript examples optionally use our Gonzo Utilities. Our provided .BMP image airbrushing utility textfile is
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first modified and then gets run by Using Acrobat Distiller as a General Purpose PostScript Computer. Which will pick up a selected .BMP image, modify it, and save it to a new filename. No knowledge of PostScript is needed for this utility.
Distiller versions newer than 8.1 prevent diskfile access as a default. To use

these, enter Distiller from your command line using "acrodist -F". This application expands upon our Bitmap to PS Array Conversions tutorial and utility from our GuruGram library. Other enhancements and expansions are planned in a continuing series. The .BMP Data Format may demand one, two, or three padding bytes to make each new row start on a 32 bit boundary. While the math to do this is somewhat obtuse, the needed count apparently simplifies to xpixels 4 mod. This detail may not yet be picked up in some of the earlier material.

A Preliminary Study
A simplified preliminary study was first done to explore the airbrushing algorithm. It is found here with its results here. Our usual approach to bitmap adjustments is to convert the bitmap to a PostScript array of strings. Those strings are then modified and then either saved as a new bitmap or as a PostScript image. Only a single array of strings is used in the study. This could represent one plane of HSB or RGB color space. The data values were first set to 46 which will appear as an ASCII period. Quadrilateral control points of 97, 104, 112, and 122 were then selected clockwise from lower left. In the output log reports of the demo, these will appear as lower case a, h, p, and z. A rectangular bounding box is next found that will exactly contain all of the quadrilateral control points. A lower boundary can be found by comparing two points and discarding the larger one; comparing another two points and again discarding the larger one; and then comparing and discarding the larger of the two remaining points...
/bbxmin llx ulx 2 copy gt {exch} if pop urx urx 2 copy gt {exch} if pop 2 copy gt {exch} if pop store

The upper boundary is found by discarding the smaller of each pair, and the y max and min values are handled similarly. These four corners are placed in the demo log as lower case ASCII "o" characters of 111. A bilineal interpolation is a suitable tool to generate gradients in most images. Assume you have a unit square and a new sought after point fractional distances x and y from the corners. The general bilineal interpolation will be...
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newvalue = (1-x)(1-y) * ( llvalue ) + (1-x)(y) * ( ulvalue ) + (x)(y) * ( urvalue ) + (x)(1-y) * ( lrvalue )

We already know the four input quadrilateral values and their fractional x and y distances. But we do not know the four bounding box values. We can write four linear equations in four unknowns to solve for our needed corner values...
A0 A1 A2 A3 = = = = W0*w W1*w W2*w W3*w + + + + X0*x X1*x X2*x X3*x + + + + Y0*y Y1*y Y2*y Y3*y + + + + Z0*z Z1*z Z2*z Z3*z

Here A0 through A3 are the input values. And W0 through Z3 are the known fractional distance products inside the unit square to be interpolated. And w through z are our sought after corner bounding box values. Note that this is "backwards" from normal and here we are really seeking out an inverse transformation solution. Such equations are easily solved with Gaussian Elimination using this specific 4x4 Utility. We could now scan all pixels inside our bounding box and find their interpolated gradient values. But we will only want to change the pixels that are inside of the original quadrilateral. To decide which pixels to change and which to leave alone, we can first create a new PostScript path. This path will be an analog of the mask used in traditional airbrushing. It represents a 1:1 map of the pixels to be modified...
newpath llx lly moveto ulx uly lineto urx ury lineto lrx lry lineto closepath

The little known and wonderfully enigmatic PostScript infill operator can then be used inside a double loop to decide which pixels to update. infill tests an input point to decide whether it is outside or inside of the path. And returns a true or a false result...
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bbymin 1 bbymax {/cury exch store bbxmin 1 bbxmax {/curx exch store curx cury infill {changepixel} if } for } for

Doing this on the study produces a "gradient alphabet". On our real program, the process gets repeated once for each HSB plane per pixel. Speaking of which...

The Actual Airbrushing Utility
Inputs needed to use AIRBRUT1.PSL are the input and output filenames and paths. Plus an airbrushboundaries array that holds eight x and y data values representing four quadrilateral points clockwise from lower left. The utility then pretty much follows an expanded version of the study. Input data points are grabbed and HSB converted. As a reminder, the HSB color space gives more realistic blends than RGB. The input file is then read and converted to a group of three PostScript arrays of strings, one each for hue, saturation, and brightness. A rectangular bounding box is next found. Its HSB corner values are calculated by repeatedly solving the above four equations in four unknowns. From there, a new PostSript masking path is created, and the infill operator used to selectively alter the chosen pixels. Finally, the three arrays of strings are written to a new output .BMP file of your choosing. Details on all of these operations can be reviewed by studying the comments in the AIRBRUT1.PSL utility code. Extensive printout options can be commented in or out to study each portion of the utility in more detail.

Adding Texture
Most bitmap images will involve some grain or variance. If you try overwriting them with a "pure color" gradient, the results may look too "computer like". Our airbrushing utility has a provision to slightly randomize the actual RGB pixels being placed. This is done by picking a small random number range, such as -4 to +4 and adding the value to each pixel plane. A limit check is performed after addition to make sure results stay in an integer 0-255 range. Minor randomizing in RGB space ends up about the same as HSB would end up. A textdepth lets you adjust your texture to match that of the original image. Because of its speed penalty, a textureflag flag allows you to selectively turn the texturizing on and off.
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Like so...
/texture { textureflag {textdepth random dup 2 div sub add cvi } if

dup 255 gt {pop 255} if dup 0 lt {pop 0 } if } store

The random operator is extracted from our Gonzo Utilities. A 5 random would return a random digit from 0 to 4.

Some Extensions
Speed has not yet been optimized. Present operation is acceptably fast for smaller airbrushing areas. Rates are in the 30,000 pixels per second range. An obvious speedup on multiple airbrushing tasks can be done by converting bitmaps to and from PostScript arrays of strings only once per work session. Another obvious improvement would be to allow mouse point entry instead of typed data coordinates. This possibly could be provided through extensions to GhostScript, Acrobat SDK tools, or a supervisory language linking. One use detail: .BMP Bitmaps and PostScript images normally build from the bottom up. But the y coordinate in Paint builds from the top down. To convert the Paint ( or similar ) data, subtract the needed y coordinate from your total Paint height.

For More Help
Once again, our preliminary airbrushing study appears as AIRSTUDY.PSL and its viewable results file as AIRSTUDY.LOG. The working utilities are AIRBRUT1.PSL A demo is found at AIRDEMO1.JPG. This GuruGram file is named AIRBRUSH.PDF and its source code is AIRBRUSH.PSL. The underlying .BMP to and from PostScript strings utility is AOSUTIL1.PSL and its companion tutorial is BMP2PSA.PDF. A .BMP format tutorial called EXPBMP.PDF is also in our GuruGram library. Our Gonzo utilities are found as GONZOUTILS.PSL and its tutorial as GONZOTUT.PDF. Similar tutorials and additional support materials are found on our PostScript and our GurGram library pages. As always, Custom Consulting is available on a cash and carry or contract basis. As are seminars. For details, you can email don@tinaja.com. Or call (928) 428-4073.

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