Three-dimensional image space transformation
A three-dimensional image transformation, executing on one or more computer systems, can mathematically transform a first two-dimensional image space onto a second two-dimensional image space using a three-dimensional image space. The three-dimensional image transformation can project the three-dimensional image space onto the first two-dimensional image space to map the first two-dimensional image space to the three-dimensional image space. Thereafter, the three-dimensional image transformation can project the second two-dimensional image space onto the three-dimensional image space to map the three-dimensional image space to the second two-dimensional image space.
1. A computer system for transforming an input image among a plurality of two-dimensional image spaces, the computer system comprising:
a memory configured to store the input image in a first two-dimensional image space from among the plurality of two-dimensional image spaces; and
a processor, configured to execute instructions stored in the memory, the instructions, when executed by the processor, configuring the processor to:
transform the input image from the first two-dimensional image space to a three-dimensional image space,
transform the three-dimensional image space to a second two-dimensional image space from among the plurality of two-dimensional image spaces to generate an output image, and
visualize the output image in the second two-dimensional image space.
2. The computer system of claim 1 , wherein the instructions, when executed by the processor, configure the processor to:
transform a first plurality of two-dimensional coordinates of the input image from the first two-dimensional image space to a plurality of three-dimensional coordinates of the three-dimensional image space; and
transform the plurality of three-dimensional coordinates of the three-dimensional image space to a second plurality of two-dimensional coordinates of the second two-dimensional image space to generate the output image.
3. The computer system of claim 2 , wherein the instructions, when executed by the processor, configure the processor to:
project the plurality of three-dimensional coordinates onto the first plurality of two-dimensional coordinates to map the input image from the first two-dimensional image space to the three-dimensional image space; and
project the second plurality of two-dimensional coordinates onto the plurality of three-dimensional coordinates to map the output image from the three-dimensional image space to the second two-dimensional image space.
4. The computer system of claim 3 , wherein the instructions, when executed by the processor, configure the processor to project the plurality of three-dimensional coordinates onto the first plurality of two-dimensional coordinates using a mathematical forward projection function.
5. The computer system of claim 4 , wherein the mathematical forward projection function comprises an equirectangular projection function, an equidistant fisheye projection function, an equisolid fisheye projection function, a stereographic fisheye projection function, an equiangular cubemap projection function, or a latitude/longitude projection function.
6. The computer system of claim 3 , wherein the instructions, when executed by the processor, configure the processor to project the second plurality of two-dimensional coordinates onto the plurality of three-dimensional coordinates using a mathematical reverse projection function.
7. The computer system of claim 6 , wherein the mathematical reverse projection function comprises an equirectangular projection function or a fisheye projection function.
8. The computer system of claim 1 , wherein the instructions, when executed by the processor, configure the processor to color or to texturize the output image in the second two-dimensional image space in accordance with a plurality of intensity values of the input image in the first two-dimensional image space.
9. The computer system of claim 8 , wherein the instructions, when executed by the processor, configure the processor to map the plurality of intensity values of a first plurality of pixels of the input image in the first two-dimensional image space onto corresponding pixels from among a second plurality of pixels of the output image in the second two-dimensional image space.
10. A method for transforming an input image among a plurality of two-dimensional image spaces, the method comprising:
retrieving, by a computer system, the input image in a first two-dimensional image space from among the plurality of two-dimensional image spaces;
transforming, by the computer system, a first plurality of two-dimensional coordinates of the input image from the first two-dimensional image space to a plurality of three-dimensional coordinates of a three-dimensional image space;
transforming, by the computer system, the plurality of three-dimensional coordinates of the three-dimensional image space to a second plurality of two-dimensional coordinates of a second two-dimensional image space from among the plurality of two-dimensional image spaces to generate an output image; and
mapping, by the computer system, one or more intensity values of the input image in the first two-dimensional image space onto the output image in the second two-dimensional image space to visualize the output image in the second two-dimensional image space.
11. The method of claim 10 , wherein the transforming the first plurality of two-dimensional coordinates of the input image comprises projecting the plurality of three-dimensional coordinates onto the first plurality of two-dimensional coordinates to map the input image from the first two-dimensional image space to the three-dimensional image space, and
wherein the transforming the plurality of three-dimensional coordinates of the three-dimensional image space comprises projecting the second plurality of two-dimensional coordinates onto the plurality of three-dimensional coordinates to map the output image from the three-dimensional image space to the second two-dimensional image space.
12. The method of claim 11 , wherein the projecting the plurality of three-dimensional coordinates comprises projecting the plurality of three-dimensional coordinates onto the first plurality of two-dimensional coordinates using a mathematical forward projection function.
13. The method of claim 12 , wherein the mathematical forward projection function comprises an equirectangular projection function, an equidistant fisheye projection function, an equisolid fisheye projection function, a stereographic fisheye projection function, an equiangular cubemap projection function, or a latitude/longitude projection function.
14. The method of claim 11 , wherein the projecting the second plurality of two-dimensional coordinates comprises projecting the second plurality of two-dimensional coordinates onto the plurality of three-dimensional coordinates using a mathematical reverse projection function.
15. The method of claim 14 , wherein the mathematical reverse projection function comprises an equirectangular projection function or a fisheye projection function.
16. A computer system for transforming an input image among a plurality of two-dimensional image spaces, the computer system comprising:
a memory configured to store the input image in a first two-dimensional image space from among the plurality of two-dimensional image spaces; and
a processor, configured to execute instructions stored in the memory, the instructions, when executed by the processor, configuring the processor to:
project a plurality of three-dimensional coordinates of a three-dimensional image space onto a first plurality of two-dimensional coordinates of the input image from the first two-dimensional image space,
project a second plurality of two-dimensional coordinates of a second two-dimensional image space from among the plurality of two-dimensional image spaces onto the plurality of three-dimensional coordinates of the three-dimensional image space to generate an output image, and
map a plurality of intensity values of a first plurality of pixels of the input image in the first two-dimensional image space onto corresponding pixels from among a second plurality of pixels of the output image in the second two-dimensional image space.
17. The computer system of claim 16 , wherein the instructions, when executed by the processor, configure the processor to project the plurality of three-dimensional coordinates onto the first plurality of two-dimensional coordinates using a mathematical forward projection function.
18. The computer system of claim 17 , wherein the mathematical forward projection function comprises an equirectangular projection function, an equidistant fisheye projection function, an equisolid fisheye projection function, a stereographic fisheye projection function, an equiangular cubemap projection function, or a latitude/longitude projection function.
19. The computer system of claim 16 , wherein the instructions, when executed by the processor, configure the processor to project the second plurality of two-dimensional coordinates onto the plurality of three-dimensional coordinates using a mathematical reverse projection function.
20. The computer system of claim 19 , wherein the mathematical reverse projection function comprises an equirectangular projection function or a fisheye projection function.