Synthesis of ProgressivelyVariant Textures on Arbitra ry Surfaces SIGGRAPH 2003 Jingdan Zhang, Kun Zhou, Luiz Velho, Baining Guo, Heung-Yeung Shum Introduction We present an approach for decorating surfaces with progressi vely variant textures Can model local texture variations Scale, orientation, color, shape variation
For 2D texture modeling, our feature-based warping technique allows the user to control the shape variations of texture eleme nts Our feature-based blending technique can create a smooth tra nsition between two given homogeneous textures
We propose an algorithm based on texton masks To prevent texture elements breaking apart as they progressively vary Introduction Most of the previous wo rk on surface texture sy nthesis concentrated on homogeneous textures However, many textures, i ncluding the coating patte
rns of various animals suc h as the tiger, cannot be d escribed by stationary sto chastic models Intuitively, their texture el ements change in a progr essive fashion Related work Exemplar-based surface texture synthesis
Gorla et al. 2001, Turk 2001, Wei and Levoy 2001, Ying et al. 2001, Dischler et al. 2002 Only for homogeneous texture synthesis Related work Reaction-diffusion te xtures Procedural Turk , Witkin and Kass  Parameter tweaking aff
ects the result heavily Only a few kind of mat erials can be synthesiz ed Related work Integrating Shap e and Pattern in Mammalian Mod els Walter et al. SIGGRA
PH 2001 By biological simulat ion Sequential Pixel-based Garber 1981, Popat & Picard 1993, Efros & Leung 1999, Wei & Levoy 2000, As hikhmin 2001, Hertzmann et al 2001, Tong et al 2002 Exemplar
Synthesized Overview We represent a progressively-variant texture by a tuple (T,M,F,V) Texture image T Texton mask M Marks which type of texture elements pixel p belongs to
Transition function F Scalar function whose gradient determines how fast t he texture T is changing Orientation field V A unit vector field Overview A progressively-variant 2D texture can be created by our field distortion or feature-based techniques
The field distortion algorithm generates a texture b y scaling and rotating the local coordinate frame at each pixel Using F, V The feature-based techniques create texton masks first first, which then guide the synthesis of the tar get textures Feature-based warping & blending
Overview To synthesize a progressively-variant texture on a mes h, we start with a 2D progressively-variant texture sam ple (To,Mo,Fo,Vo) User needs to specify Fs and Vs over the target mesh The synthesis algorithm controls the scale and orienta tion variation of texture elements by matching Fs and
Vs with their 2D counterparts Our algorithm synthesizes a texton mask Ms in conjunc tion with the target texture Ts and uses Ms to prevent t he breaking of texture elements Overview Field Distortion Synthesis
Synthesizes a progressively-variant texture To User specifies scale and orientation vectors at a fe w locations Interpolates these key scales and orientations to genera te the entire Fo and Vo by using radial basis functions Extends [Wei and Levoy 2000] by incorporating sca le and orientation variations controlled Fo and Vo
Pyramid-based sequential neighborhood matching algorith m Field Distortion Synthesis Fo and Vo control the target texture through the construction of the neighborhood N(p) N(p) is scaled using Fo(p) and rotated using Vo(p) Pixels in N(p) is resampled from To using bilinear i nterpolation Does not consider pixel coverage
The synthesis order has a large effect on th e synthesis quality Field Distortion Synthesis Texton Mask Specification To apply feature-based techniques, the user must specify a te xton mask on a given texture
Our user interface is based on color thresholding The user picks one or two pixel colors Provide dilation and erosion for refining texton masks Our experiences suggest that a texton mask indicating one or two types of the most prominent texture elements is sufficien t
Work well for most textures More sophisticated segmentation methods can be used to generate b etter texton masks Feature-Based Warping With input Texture Ti and texton mask Mi Produce new mask Mo Use Fo to control the parameters in the editing operat ions
Our system synthesizes a progressively-vari ant texture To using two texton masks, Mi an d Mo, and known texture Ti As an application of image analogies [Hertzman n et al. 2001] Refer to the step as Texton mask filtering Feature-Based Warping Feature-Based Warping
Feature-Based Warping All masks used in this paper have fewer tha n four colors and usually the mask is binary Can easily apply morphological operations such a s dilation, erosion Can also apply image warping techniques s uch as mesh warping, field warping, and wa rping using radial basis functions
Require feature points and feature lines Feature-Based Blending Takes two homogeneous textures T0 and T1 and gene rates a progressively-variant texture Tb We assume T0, T1, and Tb are all of the same size and are de fined on a unit square Also use simple linear transition function and texton mask M 0, M1 Fb(x, y) = x
Tb can be obtained by color blending T0` and T1` T0` and T1` can be obtained by synthesizing T0 and T1 using Mb T0` and T1` have their features aligned thus does not cause ghosting when color blended Feature-Based Blending The key to generating T0` and T1` is the con struction of Mb
We want Mb(x, y) to be like M0 when x 0 a nd like M1 when x 1 M(x, y) = xM1(x, y) + (1x)M0(x, y) Gaussian blur M(x, y) to reduce discontinuity Convert M(x, y) to Mb using user provided threshol d Feature-Based Blending Surface Texture Synthesis
With (To,Mo,Fo,Vo), synthesize Ts over the mesh surface User needs to specify Vs and Fs at some key locations Interpolates over the entire surface Standard L2-norm is a poor perceptual meas ure for neighborhood similarity Synthesis without texton mask may break apart text ure elements
Surface Texture Synthesis Our algorithm synthesizes a texton mask Ms in conjunction with the texture Ts Texton masks are resistant to damage caused by deficiencies in the L2-norm Surface Texture Synthesis Surface Texture Synthesis
Candidate pool C(v,) is constructed for eac) is constructed for eac h vertex v in mesh A candidate pixel p from To must satisfy a conditio n |Fo(p)Fs(v)| < ) is constructed for eac, ) is constructed for eac = 0.1 Neighborhood Nm(v) and Nc(v) is in the tang ent plane of the surface at v, with same orie ntation as Vs(v) Nm(p) and Nc(p) is from To, with same orientation a
s Vo(p) Surface Texture Synthesis We use larger neighborhoods when searching for texton mask value, while smaller for color value Texton masks determine the layout of texture elements whereas the synthesis of pixel colors is simply a step to fill in the details Nc(p) should really be Nc(p, s) where s = Fo(p) is the scal
e at p Nc(p, smin) be the smallest neighborhood and N c(p, smax) be the lar gest We determine the size of N c(p, s) by linearly interpolating betwe en that of Nc(p, smin) and Nc(p, smax) and rounding the result up t o the nearest integer Applies to all type of neighborhoods Surface Texture Synthesis We populate C(v,) is constructed for eac) using k-coherence techn ique
With an additional check for the transition functio n condition We pre-compute k-nearest neighbors for ea ch pixels We use k = 20 Surface Texture Synthesis Surface Texture Synthesis
An alternative approach to handle transition functions is to put the function values in the alpha channel However, this may not satisfy the condition from e qu. 1 We need a orientation field for input texture as well Discussion
Texton masks are also useful for homogeneo us texture synthesis Previous methods would break some texture elem ents due to insufficient texture measurement Results Results Although color thresholding may not always
generate a good segmentation in the traditi onal sense, the resulting texton masks are u sually good enough We hand painted a texton mask when color thresholding fails Our algorithm was still able to produce good resul ts Conclusion
Our main contribution in this paper is a framework for progressi vely variant textures on arbitrary surfaces Feature-based warping and blending The general framework we propose should be applicable to most textures One area of future work is to add more user control to feature b ased blending User may want more control over the way texture changes
Another topic is to explore the multi-way transition among more than two textures Finally, we are interested in other ways to control the local varia tions of textures
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