Synthesis of advecting texture using adaptive regeneration

1. A method for synthesizing advecting texture on a surface, comprising:

using a computing device having a processor to generate a synthesized texture image on the surface resembling a user given exemplar image;

measuring a distortion of the synthesized texture image by measuring a Frobenius error norm of the synthesized texture image; and

selectively regenerating the synthesized texture image based on the measured distortion to cause the synthesized texture to flow over the surface while preserving an appearance similar to the exemplar:

wherein the Frobenius error norm is given by:

ξ=∥ J S −J∥ 2 ,

where ξ is the Frobenius norm, J is a desired anisometric Jacobian, J S is a Jacobian of a current synthesized texture, S, given by J S =(ddx(S) ddy(S)), where (ddx(S)) is an estimate of a derivative of synthesized coordinates along an x-axis, and (ddy(S)) is an estimate of a derivative of the synthesized coordinates along a y-axis.

2. The method of claim 1 , wherein the surface is a planar image domain.

3. The method of claim 1 , wherein the surface is a polyhedral mesh in 3D.

4. The method of claim 1 , further comprising:

defining a velocity field that specifies the flow over the surface; and

predicting the synthesized texture image by advecting pixel coordinates of a synthesized texture image at a previous time frame according to the velocity field.

5. The method of claim 1 , further comprising:

defining a distortion threshold; and

regenerating the synthesized texture image if the measured distortion is greater than the distortion threshold.

6. The method of claim 5 , further comprising causing a user to input the distortion threshold.

7. The method of claim 1 , further comprising performing the selective regeneration on finest levels of a multi-level texture synthesis technique.

8. A computer-readable storage medium having stored and encoded thereon computer-executable instructions for adaptively regenerating synthesized texture on a surface, comprising:

predicting what the synthesized texture will look like on the surface at a current time frame;

measuring a Jacobian J S , of the synthesized texture, S, given by J S =(ddx(S) ddy(S)), where (ddx(S)) is an estimate of a derivative of synthesized coordinates along an x-axis and (ddy(S)) is an estimate of a derivative of the synthesized coordinates along a y-axis;

determining a desired Jacobian, J, of the synthesized texture;

comparing the measured Jacobian, J S , and the desired Jacobian, J, to measure a distortion of the synthesized texture using a Frobenius error norm given by:

ξ=∥ J S −J∥ 2 ; and

regenerating the synthesized texture on the surface based on the comparison between the measured Jacobian and the desired Jacobian.

9. The computer-readable storage medium of claim 8 , further comprising:

comparing the measure distortion to a threshold; and

regenerating the synthesized texture on the surface if the measured distortion is greater than the threshold.

10. The computer-readable storage medium of claim 9 , wherein the threshold is defined by a user.

11. A computer-implemented process for synthesizing a synthesized advecting texture on a surface at a current time frame, comprising:

inputting an exemplar, which is a small example image from which larger textures are automatically generated, and a velocity field, which specifies a flow over the surface;

using the computer having a processor to measure a distortion of the synthesized advecting texture at a pixel at a current resolution level in a previous time frame using a Frobenius error norm that is a measure of a magnitude of a matrix, wherein the Frobenius error norm is given by:

ξ=∥ J S −J∥ 2 ,

where ξ is the Frobenius norm, J is a desired anisometric Jacobian, J S is a Jacobian of a current synthesized texture, S, given by J S =(ddx(S) ddy(S)), where (ddx(S)) is an estimate of a derivative of synthesized coordinates along an x-axis, and (ddy(S)) is an estimate of a derivative of the synthesized coordinates along a y-axis;

comparing the measured distortion to a distortion threshold; and

outputting the synthesized texture on the surface the current time frame based on the comparison.

12. The computer-implemented process of claim 11 , further comprising:

determining that the measured distortion is greater than the distortion threshold; and

predicting the selected pixel in a current resolution level of the current time frame by upsampling the synthesized advecting texture in a previous resolution level of the current time frame.

13. The computer-implemented process of claim 11 , further comprising:

determining that the measured distortion is less than the distortion threshold; and

predicting the selected pixel in a current resolution level of the current time frame by advecting pixel coordinates of the current resolution level of the previous time frame according to the velocity field.

14. The computer-implemented process of claim 11 , further comprising:

determining that there are additional pixels to be processed at the current resolution level and the current time frame; and

selecting another pixel in the current level of the current time frame to obtain a selected pixel; and

processing the selected pixel according to the process set forth above in claim 11 .

15. The computer-implemented process of claim 11 , further comprising:

determining that there are no additional pixels to be processed at the current resolution level and the current time frame; and

performing synthesis correction that involves comparing pixel neighborhoods of candidates with a neighborhood computed for a current pixel;

wherein the neighborhoods are in undistorted exemplar space.