Showing papers on "Perspective (geometry) published in 2020"
TL;DR: The results show that the ground plane can be successfully detected, if visible, regardless of camera orientation, ground plane size, and movement speed of the human, and has broad application in conditions where environments are dynamic and cluttered.
Abstract: Identifying the orientation and location of a camera placed arbitrarily in a room is a challenging problem. Existing approaches impose common assumptions (e.g. the ground plane is the largest plane in the scene, the camera roll angle is zero). We present a method for estimating the ground plane and camera orientation in an unknown indoor environment given RGB-D data (colour and depth) from a camera with arbitrary orientation and location assuming that at least one person can be seem smoothly moving within the camera field of view with their body perpendicular to the ground plane. From a set of RGB-D data trials captured using a Kinect sensor, we develop an approach to identify potential ground planes, cluster objects in the scenes and find 2D Scale-Invariant Feature Transform (SIFT) keypoints for those objects, and then build a motion sequence for each object by evaluating the intersection of each object's histogram in three dimensions across frames. After finding the reliable homography for all objects, we identify the moving human object by checking the change in the histogram intersection, object dimensions and the trajectory vector of the homgraphy decomposition. We then estimate the ground plane from the potential planes using the normal vector of the homography decomposition, the trajectory vector, and the spatial relationship of the planes to the other objects in the scene. Our results show that the ground plane can be successfully detected, if visible, regardless of camera orientation, ground plane size, and movement speed of the human. We evaluated our approach on our own data and on three public datasets, robustly estimating the ground plane in all indoor scenarios. Our successful approach substantially reduces restrictions on a prior knowledge of the ground plane, and has broad application in conditions where environments are dynamic and cluttered, as well as fields such as automated robotics, localization and mapping.
6 citations
TL;DR: Geometry Expressions is described in the style used by expositions of semi-synthetic theorem provers such as the area method, and an algorithm is presented for automatically deriving simple forms for angle expressions and is shown to be equivalent to a class of traditional proofs.
Abstract: A symbolic geometry system such as Geometry Expressions can generate symbolic measurements in terms of indeterminate inputs from a geometric figure. It has elements of dynamic geometry system and elements of automated theorem prover. Geometry Expressions is based on the analytical geometry method. We describe the method in the style used by expositions of semi-synthetic theorem provers such as the area method. The analytical geometry method differs in that it considers geometry from a traditional Euclidean/Cartesian perspective. To the extent that theorems are proved, they are only proved for figures sufficiently close to the given figure. This clearly has theoretical disadvantages, however they are balanced by the practical advantage that the geometrical model used is familiar to students and engineers. The method decouples constructions from geometrical measurements, and thus admits a broad variety of measurement types and construction types. An algorithm is presented for automatically deriving simple forms for angle expressions and is shown to be equivalent to a class of traditional proofs. A semi-automated proof system comprises the symbolic geometry system, a CAS and the user. The user’s inclusion in the hybrid system is a key pedagogic advantage. A number of examples are presented to illustrate the breadth of applicability of such a system and the user’s role in proof.
3 citations
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TL;DR: In this article, the authors study cubic surfaces in characteristic two from the perspective of positive characteristic commutative algebra and completely classify those which are Frobenius split, and explicitly describe the finitely many non-F$-pure cubics (up to projective change of coordinates in $\mathbb{P}^3$), exactly one of which is smooth.
Abstract: In this paper, we study cubic surfaces in characteristic two from the perspective of positive characteristic commutative algebra and completely classify those which are Frobenius split. In particular, we explicitly describe the finitely many non-$F$-pure cubics (up to projective change of coordinates in $\mathbb{P}^3$), exactly one of which is smooth. We also describe the configurations of lines on these cubic surfaces; a cubic surface in characteristic two is Frobenius split unless every pair of intersecting lines meets in an Eckardt point, which, in the smooth case, means no three lines form a "triangle".
1 citations
07 May 2020
TL;DR: The results show that the method proposed in this paper can fast complete the three-dimensional reconstruction of the inner and outer feature lines of the shoe sole, which can provide the basis and guarantee for the follow-up shoe sole in-process monitoring and quality inspection.
Abstract: Aiming at the problem of low efficiency of the 3D reconstruction, a fast method based on piecewise quadratic curve is proposed. Firstly, a multi-line structured light binocular vision measurement system is used to obtain the two-dimensional image. Through the two-dimensional image, the center line and feature points of the laser strip are quickly acquired. Then, the acquired feature points are used as the given data points of curve interpolation, and NURBS curves are used to interpolate the feature lines of the image. According to the perspective invariance principle of plane curve, the zero curvature point and cusp point on the curve are detected and used as segmentation points. Using the segmentation results, a number of points on each NURBS curve segment are taken to fit as the quadratic curve. Finally, by constructing the right and left space straight taper surfaces, the three-dimensional reconstruction of the feature lines is completed by the method of surface intersection. Taking the black shoe sole as the experimental object, the results show that the method proposed in this paper can quickly complete the three-dimensional reconstruction of the inner and outer feature lines of the shoe sole, which can provide the basis and guarantee for the follow-up shoe sole process monitoring and quality inspection.