Image Description and 3D Interpretation From Image Trajectories Under

WE PROPOSE THAT CONSTRUCTING GLOBAL SPATIAL ORGANIZATIONS FROM INDIVI- DUAL TOKEN TRAJECTORIES IS A POWERFUL TECHNIQUE FOR MOTION AND STRUCTURE INTERPRETATION. RECOVERING 3D MOTION AND STRUCTURE FROM GROUPED TRAJECTOR- IES HAS MANY ANALOGIES WITH 3D STRUCTURE-FROM-CONTOURS IN STATIC IMAGERY, WHICH HAVE NOT BEEN MADE EXPLICIT IN THE 3D SCENE INTERPRETATION AND MOTION VISION LITERATURE. OUR PROPOSAL IS ALSO SIMILAR TO STEVEN''S [25] IDEA OF STRONGLY SUGGESTED GEOMETRIC GROUPINGS IN GLASS PATTERNS. ADDITIONALLY, FOR OUR MOTION MODEL, THE GROUPED TRAJECTORIES EXPLOIT THE SYMMETRY INHERENT IN THE MOTION. WE DEMONSTRATE OUR APPROACH THROUGH A TWO-STAGE PROCESS OF IMAGE DESCRIPTION OF THE MOTION OF TRACKED POINTS AND THEIR 3D INTERPRETA- TION FROM THE RESULTING IMAGE TRAJECTORIES. WE SOLVE FOR THE SCENE MOTION AND STRUCTURE PARAMETERS FOR A SET OF 3D POINTS ROTATING RIGIDLY AROUND AN ARBITRARY AXIS. INSTEAD OF USING INDIVIDUAL POINT CORRESPONDENCES AND COMPUTE, IN CLOSED FORM, THE 3D MOTION AND STRUCTURE PARAMETERS USING THE QUADRATIC FORM MATRIX REPRESENTING EACH CONIC. WE ALSO PRESENT AN ALGORITHM TO OBTAIN STABLE AND ROBUST CONIC FITS TO SPATIALLY PROXIMAL GROUPED POINT SETS CONSTRAINED LOCALLY BY SIMILARITY OF SOME PARAMETERS. IN CONTRAST, THE DESCRIPTIONS FROM INDIVIDUAL FITS ARE HIGHLY UNSTABLE AND PRACTICALLY USELESS FOR ANY 3D INTERPRETATION.