Method And Apparatus For Rendering An Image Impinging Upon A Non-Planar Surface

• US 20080088526A1
• Filed: 10/17/2006
• Published: 04/17/2008
• Est. Priority Date: 10/17/2006
• Status: Active Grant

• Current Assignee: Seiko Epson Corporation (Seiko Group)
• Original Assignee: Seiko Epson Corporation (Seiko Group)
• Inventors: McFadyen, Doug, Kadantseva, Tatiana Pavlovna
• Granted Patent: US 7,873,233 B2
• Time in Patent Office: Days
• US Class Current: 345/1.1
• CPC Class Codes: G02B 2027/011 comprising device for correcting geometrical aberrations, distortion
• CPC Class Codes: G02B 2027/014 comprising information/image processing systems
• CPC Class Codes: G02B 27/01 Head-up displays

Abstract

The present invention is directed to a method and system to render an image that impinges upon a non-planar surface to attenuate, if not abrogate, distortions introduced by the surface that features mapping the image as a plurality of spaced-apart planar cells to coordinates of the non-planar surface to produce a plurality of the inverted planar cells, with each of the cells including multiple pixels of the image, minimizing a distance between the cells while minimizing a change in the distance of each of the plurality of cells with respect to the surface coordinates; and impinging the plurality of planar cells upon the non-planar surface.

Claims

1. A method of rendering an image that impinges upon a non-planar surface, said method comprising:

mapping said image as a plurality of spaced-apart planar cells to surface coordinates of said non-planar surface, with each of said plurality of planar cells including multiple pixels of said image; and

minimizing a distance between said plurality of planar cells while minimizing a change in distance between each of said plurality of planar cells with respect to said surface coordinates; and

impinging said plurality of planar cells upon said non-planar surface.

2. The method as recited in claim 1 wherein mapping further includes associating pixels of said image with a plurality of polygons, each of which corresponds to one of said plurality of spaced-apart planar cells and includes multiple vertices having an initial spatial relationship and mapping said vertices to coordinates of said non-planar surface, producing mapped polygons and generating a matrix of distortions coefficients from the vertices of said mapped polygons, with said distortion coefficients defining a relative spatial relationship among said pixels upon said non-planar surface;

producing, from said distortion matrix, an inverse matrix having a plurality of inverting coefficients associated therewith.

3. The method as recited in claim 1 wherein minimizing further includes fitting edges of adjacent planar cells of said plurality of planar cells to a linear function, located between said edges, employing least-squares fit.

4. The method as recited in claim 2 wherein mapping further include filtering said distortion coefficients through a cubic filter to minimize the presence of noise.

5. The method as recited in claim 1 wherein said image includes a plurality of pixels each of which has an initial relative position with respect to the remaining pixels of said image and mapping further includes obtaining a calibration matrix that defines an offset in said initial relative position between first and second subgroups of pixels and generating an inverse of said calibration matrix, defining an inverse matrix having a plurality of inverting coefficients associated, with impinging further including defining a relative spatial relationship among said pixels of each of said plurality of planar cells being defined by said inverting coefficients.

6. The method as recited in claim 1 further including impinging said image upon said non-planar surface and rendering said image spaced-apart from said non-planar surface.

7. The method as recited in claim 1 further including impinging said image upon said non-planar surface and rendering said image upon said non-planar surface.

8. The method as recited in claim 1 further including transmitting said image through said non-planar surface.

9. The method as recited in claim 1 further including reflecting said image from said non-planar surface.

10. A method of rendering an image spaced-apart from a non-planar surface, said method comprising:

associating pixels of said image with a plurality of polygons each of which includes multiple vertices having an initial spatial relationship;

mapping said vertices to coordinates of said non-planar surface, producing mapped polygons;

generating a matrix of distortion coefficients from the vertices of said mapped polygons, with said distortion coefficients defining a relative spatial relationship among said pixels upon said non-planar surface;

producing, from said distortion matrix, an inverse matrix having a plurality of inverting coefficients associated therewith;

impinging pixels of said mapped polygons upon said non-planar surface with the relative spatial relationship among said pixels of each of said mapped polygons being defined by said inverting coefficients, producing inverted polygons.

11. The method as recited in claim 10 further including fitting edges of adjacent inverted polygons to a linear function, located between said edges, employing a least-squares fit.

12. The method as recited in claim 10 wherein associating further includes associating pixels of said image with a plurality of squares and mapping further includes mapping said vertices to coordinates of said non-planar surface so as to associate pixels of each of said plurality of squares to a quadrilateral.

13. The method as recited in claim 10 filtering said distortion coefficients through a cubic filter to minimize the presence of noise.

14. The method as recited in claim 10 wherein impinging further includes reflecting said image from said non-planar surface to render said image in a region spaced-apart from said non-planar surface.

15. The method as recited in claim 10 wherein associating further includes associating pixels of said image with a plurality of squares and mapping further includes mapping said vertices to coordinates of said non-planar surface so as to associate pixels of each of said plurality of squares to a quadrilateral, with said non-planar surface having a radius of curvature associated therewith and said quadrilaterals being mapped to areas of said non-planar surface, upon which a portion of said image associated with each of said quadrilaterals is to impinge, having minimal variations in said radius of curvature over said portion, with impinging further including defining the relative spatial relationship among said pixels of each of said quadrilaterals by said inverting coefficients, producing inverted quadrilaterals, and further including fitting edges of adjacent inverted quadrilaterals to a linear function, located between said edges, employing a least-squares fit.

16. A system to render an image spaced-apart from a non-planar surface, said system comprising:

an image rendering device;

a processor in data communication with said image rendering device;

a memory in data communication with said processor, said memory storing computer-readable instruction to be operated on by said processor, said computer-readable instructions including code to associate pixels of said image with a plurality of polygons each of which includes multiple vertices having an initial spatial relationship, code to map said vertices to coordinates of said non-planar surface, producing mapped polygons, code to generate a matrix of distortion coefficients from the vertices of said mapped polygons, with said distortion coefficients defining a relative spatial relationship among said pixels upon said non-planar surface, code to produce, from said distortion matrix, an inverse matrix having a plurality of inverting coefficients associated therewith, and code to impinge pixels of said mapped polygons upon said non-planar surface with the relative spatial relationship among said pixels of each of said mapped polygons being defined by said inverting coefficients, producing inverted polygons.

17. The system as recited in claim 16 wherein said computer-readable instructions further includes code to fit edges of adjacent inverted polygons to a linear function, located between said edges, employing a least-squares fit.

18. The system as recited in claim 16 wherein said code to associate further includes a first sub-routine to associate pixels of said image with a plurality of squares and said code to map further includes a second sub-routine to map said vertices to coordinates of said non-planar surface so as to associate pixels of each of said plurality of squares to a quadrilateral.

19. The system as recited in claim 16 further including a cubic filter to filter said distortion coefficients to minimize the presence of noise.

20. The system as recited in claim 16 wherein said code to associate further includes a first sub-routine to associate pixels of said image with a plurality of squares and said code to map further includes a second sub-routine to map said vertices to coordinates of said non-planar surface so as to associate pixels of each of said plurality of squares to a quadrilateral, with non-planar surface having a radius of curvature associated therewith and said quadrilaterals being mapped to areas of said non-planar surface, upon which a portion of said image associated with each of said quadrilaterals is to impinge, having minimal variations in said radius of curvature over said portion, with said code to impinge further including a third sub-routine to define the relative spatial relationship among said pixels of each of said quadrilaterals by said inverting coefficients, producing inverted quadrilaterals, and said computer-readable instructions further includes code to fit edges of adjacent inverted quadrilaterals to a linear function, located between said edges, employing a least-squares fit.