In a graphical perspective, a vanishing point (VP) is a 2D point (in the image plane) which is the intersection of parallel lines in the 3D world (but not parallel to the image plane). In other words, the vanishing point is the spot to which the receding parallel lines diminish. In principle, there can be more than one vanishing point in the image. VP can commonly be seen in fields, railroads, ...

In Section 4.1 of the main paper, we describe the quadrilateral-based sampling algorithm. Here, we further show in Figure 1 an example of how a quadrillateral is sampled from vanishing lines. First, from all the detected horizontal vanishing directions, we randomly select one of them; and among all the vanishing lines belonging to the selected horizontal vanishing direction, we randomly select ...

We associate to a pair (X, D), consisting of a smooth variety with a divisor D ∈ Div(X) ⊗ Q whose support has only normal crossings, a canonical Deligne–Mumford stack over X on which D becomes integral. We then reinterpret the Kawamata–Viehweg vanishing theorem as Kodaira vanishing for stacks.

Automatic lane detection is an essential component for autonomous navigation systems. It is a challenging task in unstructured environments where lanes vary significantly in appearance and are not indicated by painted markers. This paper proposes a new method to detect pedestrian lanes that have no painted markers in indoor and outdoor scenes, under different illumination conditions. Our method...

We are concerned with the recovery of the metric structure of the 3D space from the metric structure of a plane, given as the world-plane to image homography. Recent works have pointed out that the metric structure of the 3D space can be defined by a set of three mutually conjugated (vanishing)points with respect to the imaged absolute conic (the vanishingselfpolar triangle) and three additiona...

Using vehicle cameras to automatically assess road weather conditions requires that the road surface first be identified and segmented from the imagery. This is a challenging problem for uncalibrated cameras such as removable dash cams or cell phone cameras, where the location of the road in the image may vary considerably from image to image. Here we show that combining a spatial prior with va...

We present a visionand ladar-based approach to autonomous driving on rural and desert roads that has been tested extensively in a closed-loop system. The vision component uses Gabor wavelet filters for texture analysis to find ruts and tracks from which the road vanishing point can be inferred via Hough-style voting, yielding a direction estimate for steering control. The ladar component projec...

Part 2. Geometric theory 8. Curvature: Introduction 8.1. Three notions of curvature 8.2. Theorems 8.3. Examples 9. Curvature: Some details 9.1. The exponential representation 9.2. Diffeomorphism invariance 9.3. Curvature condition (CY ) 9.4. Two lemmas 9.5. Double fibration formulation 10. Equivalence of curvature conditions 10.1. Invariant submanifolds and deficient Lie algebras 10.2. Vanishin...

The coupling of gravity to dust helps to discover simple quadratic combinations of the gravitational super-Hamiltonian and supermomentum whose Poisson brackets strongly vanish. This leads to a new form of vacuum constraints which generate a true Lie algebra. We show that the coupling of gravity to a massless scalar field leads to yet another set of constraints with the same property, albeit not...