Batik Presentation
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The Batik Trick
a Physically Plausible Simulation of Traditional Batik Painting
using
Distance Transforms, Distance Transforms, and Distance Transforms
by
Brian Wyvill and Kees van Overveld
contents
1. The Art of Batik Painting
2. The Visual Effects and their Causes
3. Distance Transforms
4. A Batik Simulator
5. Results, Conclusions and Summary
1.The Art of Batik Painting
Batik (American: ba-teek’; Correct: bah’-tik)
•origins unknown; 2000 years old; Middle-east, India or
Central Asia?
•most prevalent: Indonesian island of Java; since 14th or
15th century
• http://www.story-of-batik.com/html/history_of_batik.html
1.The Art of Batik Painting
1.The Art of Batik Painting
the wax-gorithm:
while (not ready){
dye entire cloth with color C;
for(p in uncovered region) p.color *= C;
wash off color on wax-covered areas (if any);
cover part of exposed region with wax;
if(expensive || just for fun) remove wax from
some regions;
}
correct mistakes or add painted details;
sell;
// you should be rich now
!!!
1.The Art of Batik Painting
example
2.The Visual Effects and their Cause
(the phenomenology of dye absorption and wax cracking)
2.The Visual Effects and their Cause
(the phenomenology of dye absorption and wax cracking)
non-homogenous cloth absorption rates:
2.The Visual Effects and their Cause
(the phenomenology of dye absorption and wax cracking)
non-homogenous cloth absorption rates:
cracks occur in time-order
... because crack-propagation
is a causal process: cracks run
until they encounter another
(earlier) crack or the bound of
the wax
instead of all-at-once
so there are few crack
crossings but most Tjunctions
2.The Visual Effects and their Cause
(the phenomenology of dye absorption and wax cracking)
non-homogenous cloth absorption rates:
cracks occur in time-order
cracks often end in maximally concave regions of wax borders
..instead of...
...because it is energetically cheap to have shorter cracks
2.The Visual Effects and their Cause
(the phenomenology of dye absorption and wax cracking)
non-homogenous cloth absorption rates:
cracks occur in time-order
cracks often end in maximally concave regions of wax borders
cracks erode, so older cracks result in wider dye traces than younger cracks
2.The Visual Effects and their Cause
(the phenomenology of dye absorption and wax cracking)
non-homogenous cloth absorption rates:
cracks occur in time-order
cracks often end in maximally concave regions of wax borders
cracks erode, so older cracks result in wider dye traces than younger cracks
junction regions are fragile, so wax breaks off, leaving widened ‘younger’
crack ends
2.The Visual Effects and their Cause
(the phenomenology of dye absorption and wax cracking)
non-homogenous cloth absorption rates
cracks occur in time-order
cracks often end in maximally concave regions of wax borders
cracks erode, so older cracks result in wider dye traces than younger cracks
junction regions are fragile, so wax breaks off, leaving widened ‘younger’
crack ends
...this will be achieved by an appropriate noise function
2.The Visual Effects and their Cause
(the phenomenology of dye absorption and wax cracking)
non-homogenous cloth absorption rates
cracks occur in time-order
cracks often end in maximally concave regions of wax borders
cracks erode, so older cracks result in wider dye traces than younger cracks
junction regions are fragile, so wax breaks off, leaving widened ‘younger’
crack ends
...whereas various Distance Transforms will be used for these
3.Distance Transforms
(Jack-of-all-trades in image processing)
3.Distance Transforms
(Jack-of-all-trades in image processing)
formal definition:
for a set S, and a metric | , |: S S
and a subset VS, we define
s, sS: D(s)=MIN(v:v V:|s-v|)
3.Distance Transforms
(examples)
in geometry: for small distance D:
L1 -metric
arb. shape V
for large distance D:
L2 -metric
L -metric
small D: V’s border
small D: V’s border
small D: V’s border
large D: diamond
large D: circle
large D: square
3.Distance Transforms
(observations)
•distance transform models decreasing influence at larger D: shape
details are lost (Huygens’ principle)
•shape of (D=const)-contour dominates for large D
•distance transform is related to
•
Minkowsky sum
•
Voronoi diagram
•
low-pass filtering & multi-scale
•
implicit surfaces
•
Dijsktra’s shortest path (discrete S)
•most preferred metric: L2 (independent of coordinate system)
•brute force calculation requires O(|S||V|) calculations
•approximations require O(n |S|) calculations
3.Distance Transforms
(fast approximation)
a two-pass algorithm for the Distance Transform:
for(pixel p in V) D(p)=0;
for(pixel p in S\V) D(p)=infinity;
for(pixel p: scan from top left to bottom right){
for(pixel n in upper left half Neighborhood(p))
if(D(n)+|n-p|>D(p))D(p)=D(n)+|n-p|;
}
for(pixel p: scan from bottom right to top left){
for(pixel n in lower right half Neighborhood(p))
if(D(n)+|n-p|>D(p))D(p)=D(n)+|n-p|;
}
(optionally, smooth D(p) with a suitable relaxation)
3.Distance Transforms
(fast approximation)
0
0
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3.Distance Transforms
(fast approximation)
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3.Distance Transforms
(fast approximation)
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0
3.Distance Transforms
(fast approximation)
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0
0
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3.Distance Transforms
(fast approximation)
0
1
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3.Distance Transforms
(fast approximation)
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1
1.41
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3.Distance Transforms
(fast approximation)
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1.41
2.41
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3.Distance Transforms
(fast approximation)
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1
1.41
2.41
3.41
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0
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0
3.Distance Transforms
(fast approximation)
0
1
1.41
2.41
3.41
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1
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0
3.Distance Transforms
(fast approximation)
0
1
1.41
2.41
3.41
0
0
1
1.41
0
0
3.Distance Transforms
(fast approximation)
0
1
1.41
2.41
3.41
0
0
1
1.41
2.41
0
0
3.Distance Transforms
(fast approximation)
0
1
1.41
2.41
3.41
0
0
1
1.41
2.41
0
0
3.Distance Transforms
(fast approximation)
0
1
1.41
2.41
3.41
0
0
1
1.41
2.41
0
0
1
3.Distance Transforms
(fast approximation)
0
1
1.41
2.41
3.41
0
0
1
1.41
2.41
0
0
1
2
3.Distance Transforms
(fast approximation)
0
1
1.41
2.41
3.41
0
0
1
1.41
2.41
0
0
1
2
1.41
3.Distance Transforms
(fast approximation)
0
1
1.41
2.41
3.41
0
0
1
1.41
2.41
0
0
1
2
1.41
1
3.Distance Transforms
(fast approximation)
0
1
1.41
2.41
3.41
0
0
1
1.41
2.41
0
0
1
2
1.41
1
1
3.Distance Transforms
(fast approximation)
0
1
1.41
2.41
3.41
0
0
1
1.41
2.41
0
0
1
2
1.41
1
1
1.41
3.Distance Transforms
(fast approximation)
0
1
1.41
2.41
3.41
0
0
1
1.41
2.41
0
0
1
2
1.41
1
1
1.41
2.41
3.Distance Transforms
(fast approximation)
0
1
1.41
2.41
3.41
0
0
1
1.41
2.41
0
0
1
2
1.41
1
1
1.41
2.41
2.82
3.Distance Transforms
(fast approximation)
0
1
1.41
2.41
3.41
0
0
1
1.41
2.41
0
0
1
2
1.41
1
1
1.41
2.41
2.82
2.41
3.Distance Transforms
(fast approximation)
0
1
1.41
2.41
3.41
0
0
1
1.41
2.41
0
0
1
2
1.41
1
1
1.41
2.41
2.82
2.41
2
3.Distance Transforms
(fast approximation)
0
1
1.41
2.41
3.41
0
0
1
1.41
2.41
0
0
1
2
1.41
1
1
1.41
2.41
2.82
2.41
2
2
3.Distance Transforms
(fast approximation)
0
1
1.41
2.41
3.41
0
0
1
1.41
2.41
0
0
1
2
1.41
1
1
1.41
2.41
2.82
2.41
2
2
2.41
3.Distance Transforms
(fast approximation)
0
1
1.41
2.41
3.41
0
0
1
1.41
2.41
0
0
1
2
1.41
1
1
1.41
2.41
2.82
2.41
2
2
2.41
2.82
3.Distance Transforms
(fast approximation)
0
1
1.41
2.41
3.41
0
0
1
1.41
2.41
0
0
1
2
1.41
1
1
1.41
2.41
2.82
2.41
2
2
2.41
2.82
next we revert the scanning direction
3.Distance Transforms
(fast approximation)
0
1
1.41
2.41
3.41
0
0
1
1.41
2.42
0
0
1
2
1.41
1
1
1.41
2.41
3.82
2.82
2.41
2
2
2.41
2.82
3.Distance Transforms
(fast approximation)
0
1
1.41
2.41
3.41
0
0
1
1.41
2.41
0
0
1
2
2.41
1.41
1
1
1.41
2.41
3.82
2.82
2.41
2
2
2.41
2.82
3.Distance Transforms
(fast approximation)
0
1
1.41
2.41
3.41
0
0
1
1.41
2.41
0
0
1
2
3.41
2.41
1.41
1
1
1.41
2.41
3.82
2.82
2.41
2
2
2.41
2.82
3.Distance Transforms
(fast approximation)
0
1
1.41
2.41
3.41
0
0
1
1.41
2.41
1
0
0
1
2
3.41
2.41
1.41
1
1
1.41
2.41
3.82
2.82
2.41
2
2
2.41
2.82
3.Distance Transforms
(fast approximation)
0
1
1.41
2.41
3.41
0
0
1
1.41
2.41
2
1
0
0
1
2
3.41
2.41
1.41
1
1
1.41
2.41
3.82
2.82
2.41
2
2
2.41
2.82
3.Distance Transforms
(fast approximation)
0
1
1.41
2.41
3.41
0
0
1
1.41
2.41
3
2
1
0
0
1
2
3.41
2.41
1.41
1
1
1.41
2.41
3.82
2.82
2.41
2
2
2.41
2.82
3.Distance Transforms
(fast approximation)
0
1
1.41
2.41
3.41
1
0
0
1
1.41
2.41
3
2
1
0
0
1
2
3.41
2.41
1.41
1
1
1.41
2.41
3.82
2.82
2.41
2
2
2.41
2.82
3.Distance Transforms
(fast approximation)
0
1
1.41
2.41
3.41
2
1
0
0
1
1.41
2.41
3
2
1
0
0
1
2
3.41
2.41
1.41
1
1
1.41
2.41
3.82
2.82
2.41
2
2
2.41
2.82
3.Distance Transforms
(fast approximation)
0
1
1.41
2.41
3.41
2
1
0
0
1
1.41
2.41
3
2
1
0
0
1
2
3.41
2.41
1.41
1
1
1.41
2.41
3.82
2.82
2.41
2
2
2.41
2.82
3.Distance Transforms
(fast approximation)
0
1
1.41
2.41
2.82
2
1
0
0
1
1.41
2.41
3
2
1
0
0
1
2
3.41
2.41
1.41
1
1
1.41
2.41
3.82
2.82
2.41
2
2
2.41
2.82
3.Distance Transforms
(fast approximation)
1
0
1
1.41
2.41
2.82
2
1
0
0
1
1.41
2.41
3
2
1
0
0
1
2
3.41
2.41
1.41
1
1
1.41
2.41
3.82
2.82
2.41
2
2
2.41
2.82
3.Distance Transforms
(fast approximation)
2
1
0
1
1.41
2.41
2.82
2
1
0
0
1
1.41
2.41
3
2
1
0
0
1
2
3.41
2.41
1.41
1
1
1.41
2.41
3.82
2.82
2.41
2
2
2.41
2.82
3.Distance Transforms
(fast approximation)
3.82
2
1
0
1
1.41
2.41
2.82
2
1
0
0
1
1.41
2.41
3
2
1
0
0
1
2
3.41
2.41
1.41
1
1
1.41
2.41
3.82
2.82
2.41
2
2
2.41
2.82
3.Distance Transforms
(fast approximation)
2.82
3.82
2
1
0
1
1.41
2.41
2.82
2
1
0
0
1
1.41
2.41
3
2
1
0
0
1
2
3.41
2.41
1.41
1
1
1.41
2.41
3.82
2.82
2.41
2
2
2.41
2.82
3.Distance Transforms
(fast approximation)
2.41
2.82
3.82
2
1
0
1
1.41
2.41
2.82
2
1
0
0
1
1.41
2.41
3
2
1
0
0
1
2
3.41
2.41
1.41
1
1
1.41
2.41
3.82
2.82
2.41
2
2
2.41
2.82
3.Distance Transforms
(fast approximation)
2
2.41
2.82
3.82
2
1
0
1
1.41
2.41
2.82
2
1
0
0
1
1.41
2.41
3
2
1
0
0
1
2
3.41
2.41
1.41
1
1
1.41
2.41
3.82
2.82
2.41
2
2
2.41
2.82
3.Distance Transforms
(fast approximation)
1
2
2.41
2.82
3.82
2
1
0
1
1.41
2.41
2.82
2
1
0
0
1
1.41
2.41
3
2
1
0
0
1
2
3.41
2.41
1.41
1
1
1.41
2.41
3.82
2.82
2.41
2
2
2.41
2.82
3.Distance Transforms
(fast approximation)
1.41
1
2
2.41
2.82
3.82
2
1
0
1
1.41
2.41
2.82
2
1
0
0
1
1.41
2.41
3
2
1
0
0
1
2
3.41
2.41
1.41
1
1
1.41
2.41
3.82
2.82
2.41
2
2
2.41
2.82
3.Distance Transforms
(fast approximation)
2.41
1.41
1
2
2.41
2.82
3.82
2
1
0
1
1.41
2.41
2.82
2
1
0
0
1
1.41
2.41
3
2
1
0
0
1
2
3.41
2.41
1.41
1
1
1.41
2.41
3.82
2.82
2.41
2
2
2.41
2.82
3.Distance Transforms
(fast approximation)
4.23
2.41
1.41
1
2
2.41
2.82
3.82
2
1
0
1
1.41
2.41
2.82
2
1
0
0
1
1.41
2.41
3
2
1
0
0
1
2
3.41
2.41
1.41
1
1
1.41
2.41
3.82
2.82
2.41
2
2
2.41
2.82
3.Distance Transforms
(fast approximation)
3.82
4.23
2.41
1.41
1
2
2.41
2.82
3.82
2
1
0
1
1.41
2.41
2.82
2
1
0
0
1
1.41
2.41
3
2
1
0
0
1
2
3.41
2.41
1.41
1
1
1.41
2.41
3.82
2.82
2.41
2
2
2.41
2.82
3.Distance Transforms
(fast approximation)
3.41
3.82
4.23
2.41
1.41
1
2
2.41
2.82
3.82
2
1
0
1
1.41
2.41
2.82
2
1
0
0
1
1.41
2.41
3
2
1
0
0
1
2
3.41
2.41
1.41
1
1
1.41
2.41
3.82
2.82
2.41
2
2
2.41
2.82
3.Distance Transforms
(fast approximation)
3
3.41
3.82
4.23
2.41
1.41
1
2
2.41
2.82
3.82
2
1
0
1
1.41
2.41
2.82
2
1
0
0
1
1.41
2.41
3
2
1
0
0
1
2
3.41
2.41
1.41
1
1
1.41
2.41
3.82
2.82
2.41
2
2
2.41
2.82
3.Distance Transforms
(fast approximation)
2
3
3.41
3.82
4.23
2.41
1.41
1
2
2.41
2.82
3.82
2
1
0
1
1.41
2.41
2.82
2
1
0
0
1
1.41
2.41
3
2
1
0
0
1
2
3.41
2.41
1.41
1
1
1.41
2.41
3.82
2.82
2.41
2
2
2.41
2.82
3.Distance Transforms
(fast approximation)
2.41
2
3
3.41
3.82
4.23
2.41
1.41
1
2
2.41
2.82
3.82
2
1
0
1
1.41
2.41
2.82
2
1
0
0
1
1.41
2.41
3
2
1
0
0
1
2
3.41
2.41
1.41
1
1
1.41
2.41
3.82
2.82
2.41
2
2
2.41
2.82
3.Distance Transforms
(fast approximation)
2.82
2.41
2
3
3.41
3.82
4.23
2.41
1.41
1
2
2.41
2.82
3.82
2
1
0
1
1.41
2.41
2.82
2
1
0
0
1
1.41
2.41
3
2
1
0
0
1
2
3.41
2.41
1.41
1
1
1.41
2.41
3.82
2.82
2.41
2
2
2.41
2.82
3.Distance Transforms
(related algorithms)
•the distance transform can be turned into an identity+distance
transform (IDT) by also keeping track of the identity of the closest
object Vi: this is a discrete approximation to the Voronoi diagram
with arbitrary initial objects.
remember:
for(pixel p in V ) D(p)=0;
for(pixel p in S\ V ) D(p)=infinity;
for(pixel p: scan from top left to bottom right){
for(pixel n in upper left half Neighborhood(p))
if(D(n)+|n-p|>D(p)) D(p)=D(n)+|n-p|;
}
(and similar for other half)
3.Distance Transforms
(related algorithms)
•the distance transform can be turned into an identity+distance
transform (IDT) by also keeping track of the identity of the closest
object Vi: this is a discrete approximation to the Voronoi diagram
with arbitrary initial objects.
remember:
for(pixel p in Vi) {D(p)=0;Id(p)=Vi; }
for(pixel p in S\{Vi}) {D(p)=infinity; Id(p)= ‘none’;}
for(pixel p: scan from top left to bottom right){
for(pixel n in upper left half Neighborhood(p))
if(D(n)+|n-p|>D(p)) {D(p)=D(n)+|n-p|;
Id(p) = Id(n);
}
}
(and similar for other half)
3.Distance Transforms
(related algorithms)
•the distance transform can be turned into an identity+distance
transform (IDT) by also keeping track of the identity of the closest
object Vi: this is a discrete approximation to the Voronoi diagram
with arbitrary initial objects.
•after D(s) is computed, it tells the shortest distance to the border of V. D(s)
allows local updating in case of local modifications of V.
•larger neighborhoods give better approximation to circular (D(s)=const)contours
3 x 3, 4-connected: square;
3 x 3, 8-connected: 8-gon,
5 x 5, 24-connected: 16-gon,
7 x 7, 48-connected: 32-gon, etc.
4.A Batik Simulator
(architecture)
4.A Batik Simulator
(architecture)
•the Batik process simulation consists of two phases:
•generating cracks
•applying a next dye bath, taking the recent cracks
into account
4.A Batik Simulator
(crack generation)
•crack initialization
•crack propagation
•crack tuning
4.A Batik Simulator
(crack generation: crack initialization)
V = current wax distribution;
generate D(s);
while(not enough cracks){
pick random point p V;
// The chance to pick a cell is proportional to the area
// of the cell. This results in uniform average cell areas.
while (n Neighbors(p), D(n)>D(p))p=n;
// D(p) is local maximum of the Distance Transform (DT)
find direction d of steepest descent;
propagateCrack(p,d,-d);
// Every crack ends at the border of the cell it started in.
// Rationale: cracks start far from border where stress
// is high
update DT (only in the environment of recent crack)
}
4.A Batik Simulator
(crack generation: crack propagation)
propagateCrack(p,d[0],d[1]){
// have two halves of the crack run simultaneously
p[0]=p[1]=p;
while(not ready){
for(j=0;j<2;j++)if(p[j] in wax (=not on a crack or off wax)){
step p[j] in direction d[j];
estimate d[j] based on local distance gradient;
// rationale: this ensures shortest way to the border of the cell,
// therefore to maximally curved local concavities (if any)
perturb d[j] with IIR-filtered noise
}
}
}
4.A Batik Simulator
(crack generation: crack propagation; cont.-d)
p[0]
the pixels labeled with
black squares are labeled
as ‘on a crack’;
their distance values D(s)
are sub-pixel accurate;
the formed crack is the
red polyline with subpixel coordinates;
the blue squares indicate
pixels used for computing
D(s) and the next
positions of p[j]
4.A Batik Simulator
(crack generation: crack propagation; cont.-d)
the pixels labeled with
black squares are labeled
as ‘on a crack’;
their distance values D(s)
are sub-pixel accurate;
the formed crack is the
red polyline with subpixel coordinates;
the blue squares indicate
pixels used for computing
D(s) and the next
positions of p[j]
4.A Batik Simulator
(crack generation: crack propagation; cont.-d)
the pixels labeled with
black squares are labeled
as ‘on a crack’;
their distance values D(s)
are sub-pixel accurate;
the formed crack is the
red polyline with subpixel coordinates;
the blue squares indicate
pixels used for computing
D(s) and the next
positions of p[j]
4.A Batik Simulator
(crack generation: crack propagation; cont.-d)
the pixels labeled with
black squares are labeled
as ‘on a crack’;
their distance values D(s)
are sub-pixel accurate;
the formed crack is the
red polyline with subpixel coordinates;
the blue squares indicate
pixels used for computing
D(s) and the next
positions of p[j]
4.A Batik Simulator
(crack generation: crack propagation; cont.-d)
the pixels labeled with
black squares are labeled
as ‘on a crack’;
their distance values D(s)
are sub-pixel accurate;
the formed crack is the
red polyline with subpixel coordinates;
the blue squares indicate
pixels used for computing
D(s) and the next
positions of p[j]
4.A Batik Simulator
(crack generation: crack propagation; cont.-d)
the pixels labeled with
black squares are labeled
as ‘on a crack’;
their distance values D(s)
are sub-pixel accurate;
the formed crack is the
red polyline with subpixel coordinates;
the blue squares indicate
pixels used for computing
D(s) and the next
positions of p[j]
4.A Batik Simulator
(crack generation: crack propagation; cont.-d)
the pixels labeled with
black squares are labeled
as ‘on a crack’;
their distance values D(s)
are sub-pixel accurate;
the formed crack is the
red polyline with subpixel coordinates;
the blue squares indicate
pixels used for computing
D(s) and the next
positions of p[j]
4.A Batik Simulator
(crack generation: crack propagation; cont.-d)
...etcetera
until we reach a pixel
that is already on a
crack or off the wax
4.A Batik Simulator
(crack generation: crack tuning)
we account for two additional effects:
•the age of a crack for age-dependent
width of the dye track
•widening the junction between a crack
and an older crack
4.A Batik Simulator
(crack generation: crack tuning; age administration)
During crack propagation, store ‘age of the crack’(=inverse of crack
counter) as an identification tag in all ‘crack’ pixels.
After all cracks are generated, use identity+distance transform to
attribute, to each pixel p, the age of the crack C to which p is closest,
together with the distance to C.
prior to IDT:
pixels are
labeled as
‘wax’ or
‘crack’; only
‘crack’-pixels
know their age
after IDT: all
pixels have an
‘age’ label set.
‘wax’-pixels
know both the
distance to the
closest crack
and the age of
that crack.
4.A Batik Simulator
(crack generation: crack tuning; age administration)
And now it’s time for some serendipity:
the wedge-shaped generalized Voronoi shapes
look just like typical batik-type irregularities in
dye-absorption near the wax cracks!
prior to IDT:
pixels are
labeled as
‘wax’ or
‘crack’; only
‘crack’-pixels
know their age
after IDT: all
pixels have an
‘age’ label set.
‘wax’-pixels
know both the
distance to the
closest crack
and the age of
that crack.
4.A Batik Simulator
(crack generation: crack tuning; junction administration)
D(s) tells how far s lies from the nearest junction with the border or
the nearest older crack: there, D( )=0.
During crack propagation, label crack pixels p with info about their
distance to the nearest junction (‘d2j’) iff D(p)<THRESHOLD.
Similar as with ‘age’, distribute the values of d2j also to non’crack’-pixels, using a (modified) distance transform. However, this
time decrease rather than increase the distance attribute.
THRESHOLD-D(p)
D(p)
d2j=Max(0,THRESHOLD-D(p))
THRESHOLD
Border of the cell: D( )=0
Distance along the crack
4.A Batik Simulator
(crack generation: crack tuning; junction administration)
D(s) tells how far s lies from the nearest junction with the border or
the nearest older crack: there, D( )=0.
During crack propagation, label crack pixels p with info about their
distance to the nearest junction (‘d2j’) iff D(p)<THRESHOLD.
Similar as with ‘age’, distribute the values of d2j also to non’crack’-pixels, using a (modified) distance transform. However, this
time decrease rather than increase the distance attribute.
prior to modified distance transform: only
‘crack’-pixels have a valid d2j-attribute
junction
after modified distance transform: all pixels
have a valid d2j-attribute which is
propagated outwards and decreased with
distance to the crack.
4.A Batik Simulator
(summary of crack generation)
•as we saw, the Batik process simulation consists of two phases:
•generating cracks
•crack initiate
•crack propagate
•crack tuning
•age administration
•junction administration
•applying a next dye bath, taking the recent cracks into
account
4.A Batik Simulator
(dye application; color model)
Dyes may be modeled as color filters:
r=100
g=100
b=100
transmit: r *=0.9; g*=0.9; b*=0.4
r=90
g=90
b=40
transmit: r *=1.0; g*=1.0; b*=0.25
reflect: r *=0.9; g*=0.9; b*=0.9
r=0.72
g=0.72
b=0.008
dye 2: yellow
r=0.81
g=0.81
b=0.02
dye 1: dark orange
r=90
r=0.81
g=90
g=0.81
b=10
b=0.09
substrate
So we model color filtering by means of component-wise multiplication of dye colors
4.A Batik Simulator
(dye application; algorithm)
if(p off wax){
col = dyeColor;
} else {
d2c = distanceToNearestCrack;
// using D(p)
aof = ageOfNearestCreack;
// using age(p)
d2j = distanceToNearestJunction
// using d2j(p)
amp = computeIntensityOfColorToBeApplied (d2c,aof,d2j);
// decreases with d2c; increases with aof;
// increases with d2j;
col = dyeColor * clamp(amp, 0%, 100%)
}
modulate col with a bandwith filtered noise function;
apply to pixel p using multiplicative color model;
4.A Batik Simulator
(external controls)
The R,G,B channels in the input images constitute process control
parameters:
•red: R(x,y)=0: no wax; R(x,y)>0: thickness of the wax (crack width is
multiplied with R(x,y))
•green: in the crack initialization, random candidates are taken iff
rand(0...1) > G(x,y). So expected cell size is proportional to G(x,y)
•blue: during crack propagation, the path direction is randomly perturbed
with an IIR-filtered random sequence. The random amplitude is B(x,y)
5.Summary and Conclusions
1.
The batik simulator gives convincing batik-type modification of flatcolored, segmented images
2.
The various mechanisms in the batik process can be modeled in terms of
geometric operations and re-entrant image processing operations
3.
All required algorithms can be straightforwardly derived from the
distance transform
4.
An open question remains as to the methodological soundness of
distance transform-based crack formation compared to finite elements-
enter the issue of
incommensurable sets of
assumptions!
based techniques:
5.Results and Conclusions
the effect of
widening
cracks with age
5.Results and Conclusions (cont)
modulating
crack width:
the red channel
5.Results and Conclusions (cont)
modulating
crack density:
the green
channel
5.Results and Conclusions (cont)
modulating
randomness:
the blue
channel
5.Results and Conclusions (cont)
the process of
building a piece
of batik
5.Results and Conclusions (cont)
Questions?
