Response function determination by rank minimization

1. A method comprising:

under control of one or more processors configured with executable instructions:

receiving a request to determine a response function of an image capture device;

transforming a problem of determining the response function of the image capture device into a framework of a rank minimization problem; and

determining the response function of the image capture device based on the framework of the rank minimization problem.

2. The method of claim 1 , further comprising receiving one or more images that are obtained by the image capture device under a predetermined condition.

3. The method of claim 2 , wherein the predetermined condition comprises at least one of:

capturing the one or more images each with a different exposure time;

capturing the one or more images each with a different illumination; or

capturing the one or more images that include irradiance mixtures around respective image edges.

4. The method of claim 2 , wherein the transforming comprises arranging intensity values of each image into an observation matrix.

5. The method of claim 4 , wherein the determining the response function comprises:

determining an inverse function that, when applied to the observation matrix, minimizes a rank of the observation matrix; and

obtaining the response function of the image capture device from the determined inverse function.

6. The method of claim 5 , wherein the determining the response function further comprises eliminating outliers in the observation matrix.

7. The method of claim 6 , wherein the outliers comprise outliers due to at least one of a misalignment of the one or more images, a motion in a scene displayed in the one or more images, or a shadow displayed in the one or more images.

8. The method of claim 6 , wherein the eliminating comprises:

decomposing the observation matrix into a rank-one matrix and a high-rank matrix having a rank higher than one; and

applying a predetermined threshold to the high-rank matrix to eliminate the outliers.

9. The method of claim 8 , wherein the eliminating comprises determining the predetermined threshold based on statistics of the high-rank matrix, the statistics of the high-rank matrix being calculated based on Gaussian distribution of rank deviations from a rank-one approximation.

10. The method of claim 5 , wherein the obtaining is based on properties of monotonicity and continuity of the response function of the image capture device.

11. The method of claim 4 , wherein the arranging comprises inputting the intensity values of each image into a respective vector of the observation matrix.

12. The method of claim 11 , wherein the transforming further comprises arranging the respective vector of each image in the observation matrix to exhibit a linear dependence with one another after an inverse function is applied to the observation matrix.

13. One or more computer-readable storage device comprising a memory storing computer-executable instructions that, when executed by one or more processors, configure the one or more processors to perform acts comprising:

receiving input data that is obtained by a device under a predetermined condition; and

determining a response function of the device within a framework of a rank minimization problem based on the received input data.

14. The one or more computer-readable storage device of claim 13 , wherein the input data comprises one or more images or one or more image frames of a video.

15. The one or more computer-readable storage device of claim 14 , wherein the determining comprises:

arranging intensity values of each image or image frame into an observation matrix;

determining an inverse function that minimizes a rank of the observation matrix; and

obtaining the response function of the device from the determined inverse function.

16. The one or more computer-readable storage device of claim 15 , wherein the obtaining is based on properties of monotonicity and continuity of the response function of the device.

17. The one or more computer-readable storage device of claim 15 , wherein the arranging further comprises inputting the intensity values of each image or image frame into a respective vector of the observation matrix.

18. The one or more computer-readable storage device of claim 17 , wherein the arranging further comprises arranging the respective vector of each image or image frame in the observation matrix to exhibit a linear dependence with one another after the inverse function is applied to the observation matrix.

19. The one or more computer-readable storage device of claim 14 , wherein the predetermined condition comprises at least one of:

capturing the one or more images or the one or more image frames each with a different exposure time;

capturing the one or more images or the one or more image frames each with a different illumination; or

capturing the one or more images or the one or more image frames that include irradiance mixtures around respective image or image frame edges.

20. A method comprising:

under control of one or more processors configured with executable instructions:

receiving a request to determine a radiometric response function of an optical device;

receiving one or more images that are obtained by the optical device under a predetermined condition;

arranging intensity values of each image into an observation matrix;

determining an inverse function that minimizes a rank of the observation matrix; and

determining the radiometric response function of the optical device from the determined inverse function.