Abstract Mixed‐integer optimal control problems (MIOCPs) are often solved using a decomposition approach, consisting of solving partial outer convexified relaxed problem and rounding scheme to obtain discrete‐valued control. We show that even in the presence Vanishing Constraints (VCs) binary with linearly bounded integrated deviation exists, if grid is equidistant. note this can be computed ef...

This paper shows that the semantic labelling of line drawings of curved objects with piecewise C3 surfaces is solvable in linear time. This result is robust to changes in the assumptions on object shape. When all vanishing points are known, a different linear-time algorithm exists to solve the labelling problem. Furthermore, in both cases, all legally labelled line drawings of curved objects ar...

Camera calibration from a single image is of importance in computer vision. It requires a priori scene information. In recent years, some methods have been studied to solve this problem. One approach is to adopt the idea of using vanishing points and vanishing lines. Circles and balls are also introduced for the calibration target. Besides, symmetry and coplanar points and lines can be applied ...

A man-made environment is characterized by a lot of parallel lines and a lot of orthogonal edges. In this article, a new method for detecting the three mutual orthogonal directions of such an environment is presented. Since realtime performance is not necessary for architectural application, like building reconstruction, a computationally more intensive approach was chosen. On the other hand, o...

Commencing with a review of methods for vanishing point (VP) detection, a new approach is suggested. The proposed approach estimates the location of candidate vanishing points and provides probability measures which reflect the likelihood of those points being the VPs. This new approach allows VPs to be identified in less structured environments compared with its conventional counterparts.

We establish a straightforward estimate for the number of open sets with fundamental group constraints needed to cover total space fibrations. This leads vanishing results simplicial volume and minimal entropy, e.g., certain mapping tori.

Unit quaternion is an ideal parameterization for joint rotations. However, due to the complexity of the geometry of S group, it’s hard to specify meaningful joint constraints with unit quaternion. In this paper, we have proposed an effective and accurate method to specify the rotation limits for joints parameterized with the unit quaternion. Joint constrains constructed with our method are adeq...

We study the necessary and sufficient conditions on Abelianizable first class constraints. The necessary condition is derived from topological considerations on the structure of gauge group. The sufficient condition is obtained by applying the theorem of implicit function in calculus and studying the local structure of gauge orbits. Since the sufficient condition is necessary for existence of p...