3D Computer Vision by Shape-from-Motion

par Adrien Bartoli (Université de Clermont-Ferrand - ISIT - CENTI - Faculté de Médecine)

mercredi 5 juin 2013, 16:30 → 17:30 Europe/Paris

Salle de conférence (XLIM)

3D Computer Vision researches the problem of computing the observed environment’s 3D shape from 2D images. The currently most successful approach uses as inputs several 2D images taken by a moving camera. This is the so-called Shape-from-Motion paradigm, where ‘motion’ refers to the camera motion. One of the cornerstones of Shape-from-Motion is the projective camera. This model is based on perspective projection, which best trades-off simplicity and closeness to physics. In Shape-from-Motion, there is a fundamental distinction to be made between rigid and deformable environments. In other words, time-independent versus time-dependent 3D shape. In the former case, the shape observed in each of the input 2D images remains the same. In the latter case however, the environment deforms through time and the relationship that holds between the 3D shape’s different states may be extremely complicated. The deformable case obviously leads to more challenging theoretical and algorithmic problems than the rigid case. Rigid Shape-from-Motion has been studied over the past few decades and has been extremely successful. I will describe its main results. Projective geometry comes into the play with the concept of projective 3D Computer Vision, where the recovered 3D shape is only projectively equivalent to the real observed 3D shape. Interestingly, the projective 3D shape is recoverable without knowing the camera’s internal parameters in advance (such as the focal length). Interestingly as well, the camera’s internal parameters may be recovered while upgrading the projective to a Euclidean 3D shape, equivalent to the real 3D shape up to a similarity transform. Deformable Shape-from-Motion has been studied over the past decade and is yet an open challenge. I will describe its main results and successes with an emphasize on the concept of shape template and the problem of shape deformation modeling. I will raise the issues and potential interest of introducing projective geometry into the modeling. Finally, I will present the application of Shape-from-Motion in medical endoscopy with an emphasis on computer-aided laparosurgery in gynecology.