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Non-standard
gradient fills
When I'm writing
"advanced math", I mean all, what is at least slightly more
sophisticate than "bicubic interpolation". Looking at what the most
popular progs for image processing do, I always try to understand,
which algorithms they use. In fact, I didn't find something really
intricate. There are lots of really sophisticated methods, used in
science: computer tomography, holography and so on. I believe, that
some of such methods could be used in common progs for image processing
with a great benefit. Raster to vector conversion of photorealistic
images is just the same case. It is traditionally considered as a
rather difficult task. Methods, what one is using, trying to solve some
problem, must be adequate to this problem. What actually presents in
some raster? Set of contours and areas, painted with non-constant, but
relatively slowly changing color (to say nothing about hi-frequency
texture). Therefore, one must have tools for describing curves and
regions with gradient fills. Meanwhile using of Bezier curves is enough
efficient way to convert an edge between differently colored regions to
vector object, situation with gradient fills is lots worse. I know none
of vectorizers with gradient fills support. All of what I've seen makes
the same thing- they decrease number of colors, actually presents in a
source raster image, create edges, enclosing each constantly colored
part of the source image. It means numerous contours, what are absent
in a source raster. This is why all existing vectorizers offer
alternative: either ugly looking image, reminds of a cheap Japanese
cartoon, or a huge file repeatedly surpassing an initial raster in the
sizes. In result the vector file similar to the raster prototype,
deserves only one thing: "Exit without saving". On the other hand,
tools for creation vector images support gradient fills. They offer
gradient meshes for it. Not the best variant, I dare to say. This
situation can be compared to drawing curves with the aid of only
polylines. Really, they provide better control to drawing line than
Bezier curves and are simpler. But if one wants to draw a circle with
the same predeterminated quality, this one must use much more control
points, if he choses polylines. For manual drawing and editing small
number of control points is crucial. Therefore, using gradient meshes
for gradient fills one meets at least two problems. This one must
create these gradient meshes, and, be created, gradient meshes forces
him to set color at each node- wants he do it or not. I think, that
gradient meshes are used so widely only because programmers know math
not enough well. There are more efficient methods for describing
non-constantly colored areas using as few info as possible. Here two
different methods for gradient fills are presented, borrowed from the
theory of elasticity, and results of raster to vector conversion, based
on them. No gradient meshes at all. I'm trying to incorporate them into
vector graphic. Look at what could be done, using non-standard gradient
fills.
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 Warping
You can warp images without meshes at all. Put some
control points onto an image to be distorted and move them. No problem
at all. The only thing, what should be kept in mind, is that if one
control point is moved, the whole image will be distorted. This fact
could be treated as a defect, in comparison with mesh-based methods, or
as an advantage. On the other hand, if you want to restrict distortion
of some area of an image, put there some anchor points and do not move
them. Or select a rectangular part of the whole image and warp it,
leaving the rest untouched. Fix result of warping inside this
rectangular area, select another area, warp it and so on. You may
repeat it as much times as you need. One can put a lot of control
points, hundreds in fact, but for demo its number is limited to six.
Load photo of your beloved boss and go ahead.
Download
WarperDemo.zip(454 Kb) Download WarperDemo.7z(316 Kb)
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Outliner
This program detects edges, separating differently
colored regions of an image and converts them to scalable vector
curves. It takes a raster and transforms it to contour vector image.
Output
can be saved as vector (AI, EMF, SVG) or raster (PNG) graphic (For demo
output image can be saved only as EMF- Enhanced Meta File.). This
program is designed mostly for photorealistic true color rasters, not
for technical illustration. It can convert them too, but for such kind
of images another converters are better. One may set contour width,
change size and proportions of an output and delete short lines. Try
demo. Compare this prog with its analogues. My goal was to write a
prog, what makes small and accurate vector images. Try and check by
youself, if I did it. (A mountain above has been drawn with outliner
too.)
Download
Outliner.zip(433 Kb) Download Outliner.7z(336 Kb)
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Vectorization
Here the first method of raster to vector
conversion is presented. Let's name it "method A".
This method is based on one not well known (otherwise it would be
widely used) method for 2D interpolation. Let's try to imagine a flat
table with set of nails, hammered into it. Each nail's head has its own
elevation above table's surface. Let's take thin flexible sheet of
steel (tinfoil) and press it to these nails. After this op each point
of curved tinfoil will have some elevation above table's surface. This
elevation may be treated as one of color components. Therefore, this
method require only bounding curve for each area to be painted and set
of vertices. To make computations as simple as possible, the whole
image should be parted for set of pieces. This is the problem: not all
edges between differently colored regions a closed curves, many of them
are open arcs. Thus, here some additional contours are necessary too.
But, their number is much fewer than for usual methods of raster to
vector conversion is required. And pieces of an image are much larger.
This is why vectors, created with this kind of gradient fills are much
smaller and have better quality than all what can produce another
vectorizers. The girl on a picture does not look like a vector, does
she? But, she is. Corresponding vector file even as a text is four
times smaller than the source bitmap. Unfortunately, an opportunity of
qualitative conversion a raster in a vector isn't the finish. This
operation has only a sense if one is going in future to edit the
received vector file. For manual editing the small size of the file is
critical. More shortly, the editor is necessary, and it is not presents
now. If you want to know, how can vector graphic with support
of an advanced gradient fills be, load SVSDemo. This program represents
viewer and some vector files. These files are similar to SVG files, but
only with some non-standard types of records. Therefore, they could be
opened with any text editor, if you want to see their structure.
Download
SVSViewer.zip(306 Kb) Download SVSViewer.7z(259 Kb)
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Painting
Certainly, I'm trying to use this kind of gradient
fills, to realize at least a subset of ops, what are necessary for
full-functional editor. My goal was to create a tool for painting
regions with non-constant color, a tool, more efficient and convenient
than gradient meshes. Try to play with PaintingTool and realize
yourself, whether I really did it. This prog offers a possibility to
create a vector image «from zero level». It means,
drawing curves, changing its shapes, if you need, and painting obtained
regions. You may do these ops in any sequence. You may paint without
contours at all, in such case the whole image will be painted. To paint
some region you need put some control points (vertices) on it and set
color (RGB triplet) of each vertex. A region, bounded by curves, what
you have drawn, will be painted. Free tails of these curves will be
ignored. There are some restrictions. One vertex cannot be put too
close to others ones and on a curve. I'm in doubt, whether this last
restriction has a sense. May be, I'll cancel it later. Well, more
detailed info you'll find in menu's help topic. What is the most
interesting for me is if this method is as efficient, as I think and
which enhancements should be added. This image is what I created with
my PaintingTool. Sorry I'm not a painter to show you something
more impressive made by myself, but, thanks to V.Kovaleff., you can see
some images, created with PaintingTool. Yeah, this boy is obviously no
Velaskes, but these images are much better than all of what I can
produce myself. I've added some results of vectorization too. These
ones differs from original painting, and I see no need to explain which
image in particular is result of original painting. But both kind of
these images illustrate, I hope, potentiality of advanced vector
graphic.
Download
PaintingToolDemo.zip(497 Kb) Download
PaintingToolDemo.7z(377 Kb)
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Painting
Pen
There are another methods of painting, and
really efficient ones. Look at what one can do without vertices nor
enclosed regions at all. Let's try to imagine thin sheet of tinfoil.
You may make a slash by an axe or knife. In such case both sides of
this slash moves at the same direction: both up or both down. Scissors
are the other case: one side of a slash moves up, the other down. Let's
name this method for gradient fills Method B. This way to realize
gradient fills and converter, based on it, doesn't require additional
contours at all. There is a program, what illustrates Method B. I named
this tool Painting pen: one need to draw lines, but the whole image is
painted simultaneously. Now this is a draft, which is intended only to
demonstrate method. One may try raster to vector conversion too: this
op is included. Actually, vector is buried deep inside my prog and an
user sees only raster image. There is one nuance: raster to vector
conversion, based on described here method of gradient fills, isn't
complete. Some additional info must be included into resulting vector.
Complete method must be based on Method A plus Method B. Program, what
is presented here, PaintingPen is intended for tablet's input, so one
may set intensity of a line (the difference in brightness of sides of a
slash) by pressing to tablet's surface with mutable force. In any
event, serious drawing should be done with a tablet, not with a mouse.
Grayscale images, placed at Gallery, could be created so. They are in
fact result of raster to vector conversion, but all info, necessary to
reproduce them, is set of contours and one parameter (intensity),
distributed along theses lines. PaintingPenDemo is an simulator, what
demonstrates you process of creation such images as if someone is
drawing on a tablet.
Download
PaintingPen2.0.zip(763 Kb) Download
PaintingPenDemo.zip(687 Kb)
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Gallery. Here results of raster to vector conversion
are presented as well as original painting. Click to enlarge.
     
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Downloads.
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Contact
If
you want to tell something, go ahead.
Andrew Matseevsky, Kluchi-1, Kamchatka, Russia.
+79147864061 ;Copyright © 2007 All rights reserved.
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