3D reconstruction from images taken with a coaxial camera rig

A coaxial camera rig consists of a pair of cameras which acquire images along the same optical axis but at different distances from the scene using different focal length optics. The coaxial geometry permits the acquisition of image pairs through a substantially smaller opening than would be required by a traditional binocular stereo camera rig. This is advantageous in applications where physical space is limited, such as in an endoscope. 3D images acquired through an endoscope are desirable, but the lack of physical space for a traditional stereo baseline is problematic. While image acquisition along a common optical axis has been known for many years; 3D reconstruction from such image pairs has not been possible in the center region due to the very small disparity between corresponding points. This characteristic of coaxial image pairs has been called the unrecoverable point problem. We introduce a novel method to overcome the unrecoverable point problem in coaxial camera rigs, using a variational methods optimization algorithm to map pairs of optical flow fields from different focal length cameras in a coaxial camera rig. Our method uses the ratio of the optical flow fields for 3D reconstruction. This results in accurate image pair alignment and produces accurate dense depth maps. We test our method on synthetic optical flow fields and on real images. We demonstrate our method's accuracy by evaluating against a ground-truth. Accuracy is comparable to a traditional binocular stereo camera rig, but without the traditional stereo baseline and with substantially smaller occlusions.