Generating developable depth images using rank minimization

A computerized method comprising:

• receiving an input depth image having a height value for each pixel;
• identifying boundary pixels and interior pixels for an object in the input depth image;
• using an optimization problem that balances data fidelity with developability, determining a new height value for each pixel of an output depth image corresponding to each interior pixel of the input depth image, the data fidelity based on differences between the new height values of pixels in the output depth image and the height values of corresponding pixels in the input depth image, the developability based on minimizing a rank of Hessians computed for pixels of the output depth image using the new height values;
• determining a new height value for each pixel of the output depth image corresponding to each boundary pixel of the input depth image based on the new height values of pixels in the output depth image corresponding to interior pixels of the input depth image;
• and
• providing the output depth image.

A computer system comprising:

• a processor;
• and
• a computer storage medium storing computer-useable instructions that, when used by the processor, causes the computer system to:
• convert an input depth image with a square pixel grid arrangement to a hexagonal pixel grid arrangement with each pixel having a height value;
• determine a new height value for pixels in an output depth image using an optimization problem that minimize differences between the new height values of pixels in the output depth image and the height values of corresponding pixels in the input depth image and minimizes a rank of Hessians computed for pixels of the output depth image using the new height values of neighboring pixels in the hexagonal pixel arrangement;
• and
• provide the output depth image.