Using forward and backward kernels to filter images

A computer-implemented method for depth of field filtering an image including a plurality of pixels, the method comprising:

• specifying a plurality of forward kernels, each of the forward kernels being centered at a corresponding center pixel in the plurality of pixels and being based on a depth value assigned to the corresponding center pixel;
• for each of the forward kernels, determining convolution weights of neighborhood pixels within a neighborhood surrounding the center pixel of the forward kernel, each neighborhood pixel's convolution weight being determined based on the forward kernel and a backward kernel that is centered at the neighborhood pixel and is based on a depth value assigned to the neighborhood pixel;
• and
• blurring the image at each center pixel of the forward kernels using the convolution weights and pixel values of the neighborhood pixels within the neighborhood surrounding the center pixel.

A software product tangibly embodied in a computer-readable medium, for filtering an image including a plurality of pixels, the software product comprising instructions operable to cause one or more data processing apparatus to perform operations comprising:

• receiving a forward kernel centered at a first pixel in the image, the forward kernel assigning forward weights to pixels in a neighborhood surrounding the first pixel;
• specifying a backward kernel centered at a second pixel within the neighborhood surrounding the first pixel based on a local attribute of the image at the second pixel, the backward kernel assigning backward weights to pixels in a neighborhood surrounding the second pixel;
• determining a first convolution weight of the second pixel based on the backward kernel and forward kernel, wherein determining the convolution weight of the second pixel includes,
• determining a forward weight assigned to the second pixel by the forward kernel,
• determining a backward weight assigned to the first pixel by the backward kernel, and
• using the forward weight and the backward weight to determine the first convolution weight of the second pixel by multiplying the forward weight and the backward weight;
• and
• using the first convolution weight and a pixel value of the second pixel to generate a new value of the first pixel.

A software product tangibly embodied in a machine-readable medium, for depth of field filtering an image including a plurality of pixels, the software product comprising instructions operable to cause one or more data processing apparatus to perform operations comprising:

• specifying a plurality of forward kernels, each of the forward kernels being centered at a corresponding center pixel in the plurality of pixels and being based on a depth value assigned to the corresponding center pixel;
• for each of the forward kernels, determining convolution weights of neighborhood pixels within a neighborhood surrounding the center pixel of the forward kernel, each neighborhood pixel's convolution weight being determined based on the forward kernel and a backward kernel that is centered at the neighborhood pixel and is based on a depth value assigned to the neighborhood pixel;
• and
• blurring the image at each center pixel of the forward kernels using the convolution weights and pixel values of the neighborhood pixels within the neighborhood surrounding the center pixel.

A system for filtering an image including a plurality of pixels, the system comprising:

• a filter configured to:
• receive a forward kernel centered at a first pixel in the image, the forward kernel assigning forward weights to pixels in a neighborhood surrounding the first pixel;
• specify a backward kernel centered at a second pixel within the neighborhood surrounding the first pixel based on a local attribute of the image at the second pixel, the backward kernel assigning backward weights to pixels in a neighborhood surrounding the second pixel;
• determine a first convolution weight of the second pixel based on the backward kernel and the forward kernel, wherein to determine the first convolution weight of the second pixel, the filter is further configured to,
• determine a forward weight assigned to the second pixel by the forward kernel,
• determine a backward weight assigned to the first pixel by the backward kernel, and
• use the forward weight and the backward weight to determine the first convolution weight of the second pixel by multiplying the forward weight and the backward weight;
• and
• use the first convolution weight and a pixel value of the second pixel to generate a new value of the first pixel.