Single image photometric stereo for colored objects
Techniques are disclosed for reconstructing the surface geometry of an object using a single image. A computing device is configured to reconstruct a surface for a colored object from a single image using surface integrability as an additional constraint. The image is captured under an illumination of three fixed colored lights that correspond to three color channels, such as red, green and blue (RGB). The RGB image can be separated into three grayscale images, with different lighting for each image, and the geometry can be reconstructed by computing the surface normals of these separate images. Depth can be estimated by integrating the surface normals.
1. A computer-implemented method comprising:
receiving a single input image of an object illuminated by at least three differently colored light sources, the object having at least one of a non-white surface and a multicolored surface;
separating the single input image into a plurality of grayscale images each corresponding to a color channel associated with one of the differently colored light sources;
calculating a first single constant albedo and normal vectors with respect to the surface of the object based on an intensity of pixels and light direction in a first cluster of pixels having a first substantially constant albedo in at least one of the separate grayscale images;
calculating a second single constant albedo and normal vectors with respect to the surface of the object based on an intensity of pixels and light direction in a second cluster of pixels having a second substantially constant albedo in at least one of the separate grayscale images; and
determining a surface geometry of the object as a function of:
the first single constant albedo and the corresponding normal vectors, and
the second single constant albedo and the corresponding normal vectors.
2. The method of claim 1 , wherein the color channels include red, green and blue.
3. The method of claim 1 , wherein the determining of the surface geometry is constrained by a surface integrability constraint.
4. The method of claim 3 , wherein the surface integrability constraint is expressed by the following equation:
∂
∂
x
(
n
2
n
3
)
=
∂
∂
y
(
n
1
n
3
)
wherein x and y represent pixel coordinate axes, and wherein n 1 , n 2 and n 3 together represent the three-dimensional surface normal vectors, respectively.
5. The method of claim 1 , wherein a region of the single input image is missing light from one of the differently colored light sources, and wherein the method further includes inpainting the missing light into the region.
6. The method of claim 1 , further comprising displaying, via a display device, a graphical representation of the surface of the object based on the surface geometry.
7. An image processing system, comprising:
a storage comprising at least one memory; and
one or more processors each operatively coupled to the storage, the one or more processors configured to carry out a process comprising:
receiving a single input image of an object illuminated by at least three differently colored light sources, the object having at least one of a non-white surface and a multicolored surface;
separating the single input image into a plurality of grayscale images each corresponding to a color channel associated with one of the differently colored light sources;
calculating a first single constant albedo and normal vectors with respect to the surface of the object based on an intensity of pixels and light direction in a first cluster of pixels having a first substantially constant albedo in at least one of the separate grayscale images;
calculating a second single constant albedo and normal vectors with respect to the surface of the object based on an intensity of pixels and light direction in a second cluster of pixels having a second substantially constant albedo in at least one of the separate grayscale images; and
determining a surface geometry of the object as a function of:
the first single constant albedo and the corresponding normal vectors, and
the second single constant albedo and the corresponding normal vectors.
8. The system of claim 7 , further comprising red, green and blue light sources for illuminating the object from different directions.
9. The system of claim 7 , wherein the determining of the surface geometry is constrained by a surface integrability constraint.
10. The system of claim 9 , wherein the surface integrability constraint is expressed by the following equation:
∂
∂
x
(
n
2
n
3
)
=
∂
∂
y
(
n
1
n
3
)
wherein x and y represent pixel coordinate axes, and wherein n 1 , n 2 and n 3 together represent the three-dimensional surface normal vectors, respectively.
11. The system of claim 7 , wherein a region of the single input image is missing light from one of the differently colored light sources, and wherein the process includes inpainting the missing light into the region.
12. The system of claim 7 , further comprising a display device operatively coupled to the processor, wherein the process includes displaying, via a display device, a graphical representation of the surface of the object based on the surface geometry.
13. A non-transitory computer readable medium having instructions encoded thereon that when executed by one or more processors cause a process to be carried out, the process comprising:
receiving a single input image of an object illuminated by at least three differently colored light sources, the object having at least one of a non-white surface and a multicolored surface;
separating the single input image into a plurality of grayscale images each corresponding to a color channel associated with one of the differently colored light sources;
calculating a first single constant albedo and normal vectors with respect to the surface of the object based on an intensity of pixels and light direction in a first cluster of pixels having a first substantially constant albedo in at least one of the separate grayscale images;
calculating a second single constant albedo and normal vectors with respect to the surface of the object based on an intensity of pixels and light direction in a second cluster of pixels having a second substantially constant albedo in at least one of the separate grayscale images; and
determining a surface geometry of the object as a function of:
the first single constant albedo and the corresponding normal vectors, and
the second single constant albedo and the corresponding normal vectors.
14. The non-transitory computer readable medium of claim 13 , wherein the color channels include red, green and blue.
15. The non-transitory computer readable medium of claim 13 , wherein the determining of the surface geometry is constrained by a surface integrability constraint.
16. The non-transitory computer readable medium of claim 15 , wherein the surface integrability constraint is expressed by the following equation:
∂
∂
x
(
n
2
n
3
)
=
∂
∂
y
(
n
1
n
3
)
wherein x and y represent pixel coordinate axes, and wherein n 1 , n 2 and n 3 together represent the three-dimensional surface normal vectors, respectively.
17. The non-transitory computer readable medium of claim 13 , wherein a region of the single input image is missing light from one of the differently colored light sources, and wherein the process includes inpainting the missing light into the region.