This paper addresses the problem of camera calibration by exploiting image invariants under camera/object rotation. A novel translation + planar motion is studied here. The 3 × 3 homography mapping corresponding points before and after the motion is exploited to obtain image invariants under perspective projection. The homography is found to form a “rotation conic” under different rotation angl...

We prove that the curvature flow of an embedded planar network of three curves connected through a triple junction, with fixed endpoints on the boundary of a given strictly convex domain, exists smooth as long as the lengths of the three curves stay far from zero. If this is the case for all times, then the evolution exists for all times and the network converges to the Steiner minimal connecti...

A specialized formulation of Azarbayejani and Pentland's framework for recursive recovery of motion, structure and focal length from feature correspondences tracked through an image sequence is presented. The specialized formulation addresses the case where all tracked points lie on a plane. This planarity constraint reduces the dimension of the original state vector, and consequently the numbe...

It has been shown recently that rigid or affine dynamics of curves defined by algebraic equations can be represented in terms of Riccati dynamics of possibly complex lines. In this work, we develop new Riccati equations in real variables for closed-bounded curves and new recursions on multiplicative scalars in the decomposition of the curve. A parameter identification scheme has also been propo...

Designing mechanical devices, called linkages, that draw a given plane curve has been a topic that interested engineers and mathematicians for hundreds of years, and recently also computer scientists. Already in 1876, Kempe proposed a procedure for solving the problem in full generality, but his constructions tend to be extremely complicated. We provide a novel algorithm that produces much simp...

In practice, rigid objects often move on a plane. The object then rotates around a fixed axis and translates in a plane orthogonal to this axis. For a concrete example, think of a car moving on a street. Given multiple static affine cameras which observe such a rigidly moving object and track feature points located on this object, what can be said about the resulting feature point trajectories ...

We report on the development of a planar kangaroo model, which has a tail with two degrees of freedom and a compliant and rolling leg. The full body dynamics of the model are investigated, and it serves as an underlying model for the optimization of leg and tail trajectories. Keywordsmotion optimization, kangaroo, model

Typical tracking algorithms exploit temporal coherence, in the sense of expecting only small object motions. Even without exact knowledge of the scene, additional spatial coherence can be exploited by expecting only a rigid 3d motion. Feature tracking will benefit from knowing about this rigidity of the scene, especially if individual features cannot be tracked by themselves due to occlusions o...

This article presents the kinematic analysis of a new class of mechanical devices called planar Reconfigurable Motion Generators (RMGs) for multi-phase motion generation tasks having only a slight change in the desired motion. The concepts of configuration matrices and state vectors are introduced as a novel way to represent planar RMGs. The kinematic analysis of a planar RMG in it’s initial co...