1. abstract
2. privous work
   1. physical
      1. Norton et al. [Norton et al. 1991]
      2. Terzopoulos and Fleischer [Terzopoulos and Fleischer 1988b]
      3. finite element method
         1. Metaxas and Terzopoulos [Metaxas and Terzopoulos 1992]
         2. O’Brien and Hodgins[O’Brien and Hodgins 1999]
         3. Koichi Hirota et al, [Hirota et al. 2000],[Hirota et al. 1998]
         4. Federl and Prusinkiewicz [Federl and Prusinkiewicz2002]
      4. a larger finite element mesh can take considerable compute time
   2. non-physical
      1. [Raghavachary 2002]
      2. [Gobron and Chiba 2001]
      3. our method
         1. the Distance Transform [Jain 1989] algorithm
3. Visual Characteristics of Batik
   1. the dye(颜料)
      1. is absorbed non-homogenously by the cloth
      2. Introducing some noise can simulate it
         1. a variation on Perlin noise [Wyvill and Novins 1999]
   2. Cracks
      1. are formed in time order
      2. will run until meeting the edge of the wax or another crack
      3. often end in maximally concave regions
      4. The number of cracks generated is chosen by the user
   3. Cracks erode
      1. older cracks are wider than younger cracks
      2. tends to break off at T-junctions
   4. types of wax
      1. e.g. more paraffin gives more cracking
   5. our process
      1. first generates one or more wax images
         1. digital images
      2. 1. A wax image is loaded into the batik program
      3. 2. cracks are produced
      4. 3. a colour is chosen and applied as a dye
      5. 4. create the final image
4. Distance Transforms
   1. definitions
      1. Ω defines the image domain
      2. W defines the part of Ω that is covered with wax
      3. the set V consists of the border of W together with all the cracks
   2. observations
      1. (1) newer cracks run from one older crack to another older crack
      2. (2) cracks serve to alleviate the tension in the wax
         1. distance transform
            1. The Jain algorithm[Jain 1989]
         2. identity of feature
            1. the Identity Distance Transform (IDT)
5. The Crack Algorithm
   1. algorithm
   2. two boundary conditions
      1. a crack should pass through a point that is at (locally) maximal distance from any earlier crack
      2. a crack should propagate as fast as possible to the nearest feature
   3. noice
      1. a filtered Brownian motion noise
   4. the widening of the T-junction
6. Controlling The Process
   1. several controls
      1. crack width (d(p))
      2. crack density (ρ (p))
      3. crack randomness (wigglyness w(p))
      4. functions of the location p
      5. users can set the red (d(p)), green (ρ (p)), and blue (w(p)) distributions in the input image
7. Applying the Dye
   1. A Multiplicative Colour Model for Dye Application
   2. Geometrical Aspects of the Dye Distribution