Lifting symmetric pictures to polyhedral scenes

Scene analysis is concerned with the reconstruction of d-dimensional objects, such as polyhedral surfaces, from (d − 1)-dimensional pictures (i.e., projections of the objects onto a hyperplane). In this paper we study the impact of symmetry on the lifting properties of pictures. We first use methods from group representation theory to show that the lifting matrix of a symmetric picture can be transformed into a block-diagonalized form. Using this result we then derive new symmetry-extended counting conditions for a picture with a non-trivial symmetry group in an arbitrary dimension to be minimally flat (i.e., ‘non-liftable’). These conditions imply very simply stated restrictions on the number of those structural components of the picture that are fixed by the various symmetry operations of the picture. We then also transfer lifting results for symmetric pictures from Euclidean (d − 1)-space to Euclidean d-space via the technique of coning. Finally, we offer some conjectures regarding sufficient conditions for a picture realized generically for a symmetry group to be minimally flat

Characterizing minimally flat symmetric hypergraphs

In Kaszanitzky and Schulze (2017) we gave necessary conditions for a symmetric d-picture (i.e., a symmetric realization of an incidence structure in Rd) to be minimally flat, that is, to be non-liftable to a polyhedral scene without having redundant constraints. These conditions imply very simply stated restrictions on the number of those structural components of the picture that are fixed by the elements of its symmetry group. In this paper we show that these conditions on the fixed structural components, together with the standard non-symmetric counts, are also sufficient for a plane picture which is generic with three-fold rotational symmetry C3 to be minimally flat. This combinatorial characterization of minimally flat C3-generic pictures is obtained via a new inductive construction scheme for symmetric sparse hypergraphs. We also give a sufficient condition for sharpness of pictures with C3 symmetry

Variational Approaches for Motion and Structure from Monocular Video

Motion and structure estimation are elementary problems of computer vision. These are active areas of research, even though the first methods were proposed several decades ago. We develop new approaches for motion and structure estimation for autonomous driving. An autonomous vehicle requires an accurate model of its environment, wrong decisions made by an autonomous car can have severe consequences. We assume the monocular setup, where only a single camera is mounted on the car. Outdoor traffic sequences are challenging for optical flow estimation. The high speed of the car causes large displacements in the optical flow field, the lighting conditions are unstable and there can be strong distortions due to reflections and difficult weather conditions. We propose new discrete methods, which determine optical flow as optimal configuration of probabilistic graphical models. The first approach selects sparse locations in the reference frame, and matches them across the second image. The best correspondences, which match constraints from a multiple view configuration, are considered motion vectors in a graphical model. In a second approach, we solve for dense optical flow by approximating the original infeasible graphical model with a sequence of reduced models. The monocular configuration poses challenges to the estimation of scene structure, camera positions and scene parameters need to be estimated jointly. The geometry of multiple views creates blind spots in the images, and adds a scale ambiguity, which both to not exist in a setup with multiple cameras. We propose two methods for structure estimation. The first approach determines the energy optimal camera track, given optical flow and depth observations. A further approach estimates camera motion and a piecewise planar scene description jointly from a single optical flow field. The scene description contains depth and plane normal information. We evaluate our approaches for motion and structure estimation on different real world and rendered datasets. In addition to evaluation on publicly available evaluation data, we evaluate on a new rendered dataset with ground truth plane normals

Measurements, Models, Systems and Design

531 s.

Rigidity through a Projective Lens

In this paper, we offer an overview of a number of results on the static rigidity and infinitesimal rigidity of discrete structures which are embedded in projective geometric reasoning, representations, and transformations. Part I considers the fundamental case of a bar−joint framework in projective d-space and places particular emphasis on the projective invariance of infinitesimal rigidity, coning between dimensions, transfer to the spherical metric, slide joints and pure conditions for singular configurations. Part II extends the results, tools and concepts from Part I to additional types of rigid structures including body-bar, body−hinge and rod-bar frameworks, all drawing on projective representations, transformations and insights. Part III widens the lens to include the closely related cofactor matroids arising from multivariate splines, which also exhibit the projective invariance. These are another fundamental example of abstract rigidity matroids with deep analogies to rigidity. We conclude in Part IV with commentary on some nearby areas

Connected Attribute Filtering Based on Contour Smoothness

A new attribute measuring the contour smoothness of 2-D objects is presented in the context of morphological attribute filtering. The attribute is based on the ratio of the circularity and non-compactness, and has a maximum of 1 for a perfect circle. It decreases as the object boundary becomes irregular. Computation on hierarchical image representation structures relies on five auxiliary data members and is rapid. Contour smoothness is a suitable descriptor for detecting and discriminating man-made structures from other image features. An example is demonstrated on a very-high-resolution satellite image using connected pattern spectra and the switchboard platform

Object grasping and safe manipulation using friction-based sensing.

This project provides a solution for slippage prevention in industrial robotic grippers for the purpose of safe object manipulation. Slippage sensing is performed using novel friction-based sensors, with customisable slippage sensitivity and complemented by an effective slippage prediction strategy. The outcome is a reliable and affordable slippage prevention technology