CHAPTER 4 Stroke Generation
4.2 Contour Sketching on Fins
4.3.2 Apply Brush Model
After control points of all fins are generated, we apply the side stroke brush model.
The system draws lines inside fins randomly, as shown in Figure 4.26.
Figure 4.26 The result of sketching
CHAPTER 5 Washing
In this chapter, we discuss the dyeing effect in our system. First, we get the information about color from input image. Then we simulate pigments which move above and inside the paper. Finally, we blend the washing image and sketching image.
Figure 5.1 shows the flowchart of washing.
In Lingnan School Painting, washing is an important skill to show stereo and gradational feeling. Painters put a cushion under the paper when washing. Then they moisten the paper, and use “a row of brushes” to wash layer by layer gradually.
Because there is oil that does not absorb water on the surface of cushion, water flows above the paper. The water diffusion happens above and inside the paper.
In section 5.1, we talk about the generation of washing region. Then we explain our proposed washing model in section 5.2. It consists of the paper model, Layer model, the moving of water flow, and pigment diffusion process. Then we use
“Subtractive Color Mixture” to model the overlapping of mixture in section 5.3.
Figure 5.1 Flowchart of washing
5.1 Washing Region
We scan image in raster-scan order, and find out the range of color which we want to wash. The range of color is defined in advance, but users can modify it. After finding out regions which we want to wash, user can determine to use gradational color or the same color in washing region.
5.2 Washing Model
This section introduces how we simulate the washing of Lingnan School Painting. Our model simulates the water flowing above and inside paper. Because painters put a cushion under the paper when washing, there is oil that does not absorb water on the surface of cushion. Water flows above the paper. After a while, water is absorbed into the paper, and diffused by capillary phenomenon. Curtis [17] proposed
“Shallow-water layer” to simulate water and pigment flow above the surface of the paper. Yu [24] proposed a layer model which represents the movement of water and pigment between neighboring cells into the paper. In paper modeling, we reference Curtis’s and Yu’s model. In water flowing, we reference Navier-Stoke Equation and Local Equilibrium Model (LEM) to simulate but make some modifications.
Paper Model
In paper model, paper is composed of paper cells. Each paper cell is called a papel[14]. Each papel has eight neighboring papels which are connected by fiber. The number of fibers which connect two neighboring papels is determined randomly [13].
Figure 5.2 shows an example for the relationship among neighboring papels inside the paper.
1 , 1 −
− j
pi pi,j−1 pi+ j1, −1
j
pi−1, pi,j pi+1,j
1 , 1 +
− j
pi pi,j+1 pi+ j1, +1 Papel
fiber
Figure 5.2 The relationship among neighboring papels inside the paper
To represent the diffusion phenomenon, the layer model is proposed. In the layer model, each papel inside the paper is divided into three layers: surface layer, absorption layer, and deposition layer. Besides there is a “shallow-water layer” above the paper. Figure 5.3 shows the layer model.
Shallow-Water Layer
Figure 5.3 The layer structure of papel.
Simulate Diffusion Phenomena
First, the initial water (pigment) quantity is W (P). When water particles flow, pigment particles move with it simultaneously. In hydrodynamics, Navier-Stoke Equation describes fluid motion which considers viscous fluid. Eq.(5.1) is 2D Navier-Stokes Equation.
: the velocity in y direction where
p v u μ
: the velocity in x direction
: viscosity (In all of our example, we set 0.3)
The water (pigment) quantity move to neighboring papel of x direction is : water pressure
)
We use Navier-Stokes Equation to simulate water flowing above the paper. At the same time, water and pigment also are absorbed by surface layer, and quantity absorbed in the surface layer is determined by the constant ratio (We set 0.4).
where ( ) denotes the quantity of water (pigment) absorbed by surface layer, and ( ) denotes the quantity of water (pigment) in Shallow-water layer.
s
In surface layer, water flows to neighboring papels if . denotes the water quantity of k’th neighboring papel. The quanity of and are determined by the following equations.
k
where denotes the total number of neighboring fibers which is connected to the papel and the water quantity is smaller than . denotes the number of fibers which connects and .
∑
=adjusting parameter(In our system, we setα1 =0.2,α2 =0.8,ε =0.4). is the unit
The water and pigment absorbed by absorption layer is determined by the following equation. denote the maximum and minimum absorption ratio, respectively. denotes the
maximum quantity of water which could be deposited in the deposition layer and denotes the remaining water quantity in the deposition layer. (In our system, we set
The absorbed water and pigment is desorbed to the surface layer or deposition layer in the next time. The desorbed quantity to the surface layer is determined as following.
The quantity deposited in the deposition layer is determined by the constant deposited ratiod.
where ( ) denotes the quantity of water (pigment) deposited, and is maximum capacious quantity of water in the deposition layer.
,
In Huang’s [11] ink diffusion process, the whole process includes skeleton finding, initial area pipelining and propagation process. Since diffusion which we simulate is regions, there is no need to find the skeleton and initial area pipelining. Water particles in the most outer region in initial area diffuse first. Water particles in the second most outer region then diffuse right after the former diffusion. In other words, water particles in the second largest number of region index of papels diffuse right after water diffusion in the largest number of region index finished, as shown in Figure 5.4. Although each of the processes of water diffusion in diffused region seems discrete, it is actually a continuous diffusion process in a global view.
In real world, the wet region will dry out gradually. This phenomenon is called
evaporation. The evaporation of water is a complicated process in which many factors
play a role. One important factor is the contact area with atmosphere [17]. When other
Figure 5.4 The Diffusion process
factors are almost fixed, larger contact area results in higher rate of water evaporation.
In Huang’s [11] thesis, the contact area of each papel with atmosphere is equal. Based on the equality of the contact area of all papels, the rate of water evaporation in each papel of the paper is approximately equal. There is another important factor which is in opposite to the evaporation of water, called humidity [17]. For the simplicity and the demand of our theorem, we assume that the number of water particles evaporated in papel p at step t-th, Etp, depends on the humidity H (0≤ H ≤1 ) and is
expressed by the equation,
p t
p h H Water
E = (1− )× (5.8)
where Waterp is the number of water particles in papel p , and function yields a coefficient for the evaporation of water, where
) (x h
1
0≤ x≤ . Figure 5.5 shows an example of the function . The less the humidity, the greater is the amount of water evaporated.
h
Figure 5.5 Function h(x) for determining the quantity of water evaporated (Courtesy of Huang)
Figure 5.6 show the result of washing, and we moisten the whole paper in these cases. Figure5.6 (a), (b), and (c) show the region of coloration. The results which only use a layer model are shown in Figure5.6 (d), (e), and (f). Moreover, the results of our proposed model are shown in Figure5.6 (g), (h), and (i).
(the same color)
(a) pigment P= 8 (b) pigment P= 5 (c) pigment P= 5 (the same color) (the gradational color)
(d) washing result of (a) (only use a layer model)
(e) washing result of (b) (only use a layer model)
(f) washing result of (c) (only use a layer model)
(g) washing result of (a) (our proposed method)
(h) washing result of (b) (our proposed method)
(i) washing result of (c) (our proposed method) Figure 5.6 Samples results of washing
5.3 Color Mixture
Every time after simulating the effect of washing, we will start to do the color mixture. We take Subtractive Color Mixture to model the overlapping of color in our system. When our system washes next color, we set the result which already washed is background. Then foreground and background are combined to next result.
Figures 5.7 and 5.8 show some examples of washing and the result of combining with contour sketching.
Composition
initial gradational color initial the same color
the quantity of pigment = 7 the quantity of pigment = 5.5
washing result washing result
final washing result
Figure 5.7 Result of washing and combined image
Composition
initial the same color initial the same color
the quantity of pigment = 4 the quantity of pigment = 4.5
washing result washing result
final washing result
Figure 5.8 Result of washing and combined image
CHAPTER 6 Implementation and Results
In this chapter, the implementation and results are presented. The input sources are reference image and labeling image. The background of reference image is removed beforehand, and the labeling image indicates the place of fins. The algorithm is implemented in C# language with an Intel 1.6GHz CPU and 768MB RAM.
After our system combines results of contour sketching and of washing, we apply a background. Background is generated according to the position of fishes. The pixel near fish body is deep green color, and color change thin gradually as the distance from fish changes far.
Example 1 is a 1200×700 image as shown in Figure 6.1. Figure 6.2 shows the results of contour sketching. Figure 6.3 shows the result of washing. The final result of this example which already applies background is shown in Figure 6.4.
Figure 6.1 The original image of example 1
Figure 6.2 The contour sketching of example 1
Figure 6.3 The washing result of example 1
Figure 6.4 The final result of example 1
Example 2 is a 1000×580 image as shown in Figure 6.5. Figure 6.6 shows the results of contour sketching. Figure 6.7 shows the result of washing. The final result of this example which already applies background is shown in Figure 6.8.
Figure 6.5 The original image of example 2
Figure 6.6 The contour sketching of example 2
Figure 6.7 The washing result of example 2
Figure 6.8 The final result of example 2
Example 3 is an 800×800 image as shown in Figure 6.9. Figure 6.10 shows the results of contour sketching. Figure 6.11 shows the result of washing. The final result of this example which already applies background is shown in Figure 6.12.
Figure 6.9 The original image of example 3
Figure 6.10 The contour sketching of example 3
Figure 6.11 The washing result of example 3
Figure 6.12 The final result of example 3
CHAPTER 7 Conclusion and Future Works
In this thesis, we propose a method to synthesize Lingnan School Painting on Embroidered Fish. We simulate this style by two processes: contour sketching and coloring. In the former process, we design a brush model to simulate Horse Hair Brush. In coloring, we propose a washing model to simulate the effect of dyeing. The whole process is semi-automatic. Users just input several parameters and draw the fish spine. The rest of work is done by the computer. Therefore, users my generate Lingnan style Painting easily by using our proposed system without any painting skill.
However, there are still some issues left to be solved in the future.
1. The extracted region of washing is not fine. The border of fishes is darker than the rest part. Our system decides it as the part of black. So we hope to use better algorithm to find out the region.
2. Our proposed system uses the basic Subtractive Color Mixture method. This
method simulates the traditional Chinese color mixture roughly but not exactly.
Moreover, the other advanced methods focus on the color mixture of Western Painting, such as KM model. We hope to find a suitable or integrate several color mixture methods for traditional Chinese colors.
3. Our system is not entirely automatic, users still need to draw a spine. Although it is not difficult to draw, the produced results could be different. So we hope our system generate spine stroke automatically in the future.
4. Fish belly and scales would be further processed to emphasize three-dimensional effect. And we recommend that contour sketching should be more similar to the style of painters.
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