Methods and systems to pre-warp an image

1. A method comprising:

generating a first pre-warped spatial coordinate associated with a first initial spatial coordinate of a set of initial spatial coordinates of a pixel of an image to be projected using a first function, the first function comprising a sum of:

a value of a first warp path function at the first spatial coordinate, the first warp path function being selected based on a value of a second initial spatial coordinate of the set of initial spatial coordinates; and

a first delta; and

outputting the first pre-warped spatial coordinate.

2. The method of claim 1 , wherein the outputting the first pre-warped spatial coordinate comprises communicating the first pre-warped spatial coordinate to an image projection device to project the pixel.

3. The method of claim 1 , further comprising:

projecting the pixel using the first pre-warped spatial coordinate.

4. The method of claim 1 , further comprising:

obtaining the first warp path function associated with an image projection device, comprising:

operating the image projection device to project the pixel on a display element using the first initial spatial coordinate to form a projected pixel;

determining a displayed spatial coordinate of the projected pixel on the display element;

determining a deviation of the displayed spatial coordinate from the first initial spatial coordinate; and

generating the first warp path function to describe an inverse of the deviation.

5. The method of claim 1 , wherein the first warp path function comprises a piecewise polynomial.

6. The method of claim 1 , wherein the first delta is a constant.

7. The method of claim 1 , wherein the first delta comprises a corresponding function of the first initial spatial coordinate.

8. The method of claim 1 , further comprising:

selecting the first warp path function based on one or more of:

a wavelength of a light to be used to project the pixel; and

a temperature of an image projection device to project the pixel.

9. The method of claim 1 , further comprising:

selecting a second function based on a second value of the first initial spatial coordinate;

generating a second pre-warped spatial coordinate associated with the second initial spatial coordinate using the second function, the second function comprising a sum of:

a corresponding value of a second warp path function at the second initial spatial coordinate; and

a second delta; and

outputting the second pre-warped spatial coordinate.

10. A method comprising:

obtaining an initial spatial coordinate of a pixel of an image to be projected, the initial spatial coordinate associated with a first temperature associated with an image projection device to project the pixel;

obtaining a second temperature associated with the image projection device;

generating a pre-warped spatial coordinate of the pixel associated with the initial spatial coordinate, the pre-warped spatial coordinate calculated based on a temperature change between the second temperature and the first temperature and a temperature deviation function; and

outputting the pre-warped spatial coordinate.

11. The method of claim 10 , wherein the outputting the pre-warped spatial coordinate comprises communicating the pre-warped spatial coordinate to the image projection device to project the pixel.

12. The method of claim 10 , further comprising:

projecting the pixel using the pre-warped spatial coordinate.

13. The method of claim 10 , further comprising:

obtaining the temperature deviation function, comprising:

operating the image projection device to project the pixel on a display element using the initial spatial coordinate at the first temperature to form a first projected pixel;

determining a first displayed spatial coordinate of the first projected pixel on the display element;

operating the image projection device to project the pixel on the display element using the initial spatial coordinate at the second temperature to form a second projected pixel;

determining a second displayed spatial coordinate of the second projected pixel on the display element;

determining a deviation of the second displayed spatial coordinate from the first displayed spatial coordinate; and

generating the temperature deviation function to describe an inverse of the deviation.

14. A system comprising:

a controller in communication with a light source and a spatial modulator, the controller to:

obtain a set of spatial coordinates of a pixel of an image to be projected;

generate a first pre-warped spatial coordinate associated with a first spatial coordinate of the set of spatial coordinates, the first pre-warped spatial coordinate calculated as a sum of:

a value of a first warp path function at the first spatial coordinate, the first warp path function selected based on a second spatial coordinate of the set of spatial coordinates; and

a first delta; and

control the spatial modulator to project the pixel using the first pre-warped spatial coordinate.

15. The system of claim 14 , wherein the controller is further to:

obtain the first warp path function associated with the system, wherein to obtain the first warp path function the controller is to:

control the light source and the spatial modulator to project the pixel on a display element using the set of spatial coordinates to form a projected pixel;

determine a displayed set of spatial coordinates of the projected pixel on the display element;

determine a deviation of the displayed set of spatial coordinates from the set of spatial coordinates; and

generate the first warp path function to describe an inverse of the deviation.

16. The system of claim 14 , wherein the first warp path function comprises a piecewise polynomial.

17. The system of claim 14 , wherein the first delta is a constant.

18. The system of claim 14 , wherein the first delta comprises a corresponding function of the first spatial coordinate.

19. The system of claim 14 , wherein the controller is further to:

select the first warp path function based on one or more of:

a wavelength of the light source to be used to project the pixel; and

a temperature of the system.

20. The system of claim 14 , wherein the controller is further to:

generate a second pre-warped spatial coordinate associated with the second spatial coordinate, the second pre-warped spatial coordinate calculated as a corresponding sum of:

a corresponding value of a second warp path function at the second spatial coordinate; and

a second delta; and

control the spatial modulator to project the pixel using the first pre-warped spatial coordinate and the second pre-warped spatial coordinate.