Multiway Cut for Stereo and Motion
with Slanted Surfaces

Stan Birchfield and Carlo Tomasi

We have extended the multiway-cut algorithm to handle slanted surfaces. The results of the new algorithm, which segments an image into regions while fitting affine parameters to each region, are shown below. The first three rows show stereo pairs of images, while the last two examples come from image sequences).

The third column contains the displacement map (either disparity or motion vector magnitude), with the segmentation overlaid. In the fourth column, lines are thickened where the change in displacement across the boundary surpasses a threshold, thus distinguishing depth or motion discontinuities (thick lines) from creases (thin lines). The 'factor' in the fifth column is the number by which each pixel in the displacement map should be divided to get the measured value (e.g., if the pixel's value is 23, and the factor is 10, then the displacement at that pixel was calculated to be 2.3 pixels).

Original Images Algorithm Output
Left Image Right Image Displacement Map Segmentation overlaid Factor Comments
10 Very clean results on highly textured images.
30 Similar results. There is little evidence in the original images to separate the parking meter from the bush.
10 Errors occur along the vertical crease, because there is no intensity edge.
15 Basic structure of scene is recovered, including the three planes forming the background.
30 Outline of player is recovered, as well as slight slant of crowd.

For more detail, get the original results (40 KB): segmentations, affine parameters, and scaled displacement maps (without segmentation overlaid).