Anisometric texture synthesis

A computer-readable storage medium having stored and encoded thereon computer-executable instructions for synthesizing texture on a surface using an exemplar, comprising:

• specifying a Jacobian field at a pixel;
• selecting a direction to examine based on a direction component;
• defining a synthesis-space inverse-Jacobian-transformed neighbor offset vector using an exemplar-space neighbor offset and an inverse Jacobian at the pixel;
• normalizing the synthesis-space inverse-Jacobian-transformed neighbor offset vector to have a length of one;
• determining which of eight immediate neighbors of the pixel to access based on the normalized synthesis-space inverse-Jacobian-transformed neighbor offset vector;
• accessing one of the eight immediate pixel neighbors that is closest in the selected direction to the pixel being processed, where the synthesized pixel coordinate image does not directly contain pixel colors but instead contains pixel coordinates where the pixel colors are fetched in an exemplar texture;
• warping upsampled pixel coordinates of the pixel and its immediate pixel neighbors using the Jacobian field;
• correcting the warped, upsampled pixel coordinates using the Jacobian field to allow rotation and scaling of the coordinates of the pixel and neighboring pixels;
• and
• parameterizing the surface over a parametric domain by mapping the parametric domain onto the surface.

A computer-implemented process for synthesizing anisometric synthesized texture from an exemplar, comprising:

• using the computer having a processor to perform the following:
• inputting a Jacobian field J(p) at a pixel (p) and an initialization image at a previous resolution level;
• upsampling pixel coordinates at the previous resolution level to generate a current resolution level having a finer resolution than the previous resolution level;
• defining φ as a synthesis-space inverse-Jacobian-transformed neighbor offset vector, where φ=J−1(p)Δ and where Δ is an exemplar-space neighbor offset and J−1(p) is an inverse Jacobian at pixel (p);
• normalizing the synthesis-space inverse-Jacobian-transformed neighbor offset vector to have a length of one;
• determining which one of the eight immediate neighbors of the pixel forming a pixel neighborhood to access based on the normalized synthesis-space inverse-Jacobian-transformed neighbor offset vector;
• accessing one of the eight immediate pixel neighbors of the pixel that is closest in a selected direction to the pixel being processed;
• warping the upsampled pixel coordinates of the pixel neighborhood using the Jacobian field;
• and
• using the exemplar and the warped upsampled pixel coordinates to obtain the anisometric synthesized texture.