Dynamic Estimation of Rigid Motion from Perspective Views via Recursive Identification of Exterior Differential Systems with Parameters on a Topological Manifold

We formulate the problem of estimating the motion of a rigid object viewed under perspective projection as the identification of a dynamic model in Exterior Differential form with parameters on a topological manifold. We first describe a general method for recursive identification of nonlinear implicit systems using prediction error criteria. The parameters are allowed to move slowly on some topological (not necessarily smooth) manifold. The basic recursion is solved in two different ways: one is based on a simple extension of the traditional Kalman Filter to nonlinear and implicit measurement constraints, the other may be regarded as a generalized "Gauss-Newton" iteration, akin to traditional Recursive Prediction Error Method techniques in linear identification. A derivation of the "Implicit Extended Kalman Filter" (IEKF) is reported in the appendix. The ID framework is then applied to solving the visual motion problem: it indeed is possible to characterize it in terms of identification of an Exterior Differential System with parameters living on a C0 topological manifold, called the "essential manifold". We consider two alternative estimation paradigms. The first is in the local coordinates of the essential manifold: we estimate the state of a nonlinear implicit model on a linear space. The second is obtained by a linear update on the (linear) embedding space followed by a projection onto the essential manifold. These schemes proved successful in performing the motion estimation task, as we show in experiments on real and noisy synthetic image sequences

Recursive Motion Estimation on the Essential Manifold

Visual motion estimation can be regarded as estimation of the state of a system of difference equations with unknown inputs defined on a manifold. Such a system happens to be "linear", but it is defined on a space (the so called "Essential manifold") which is not a linear (vector) space. In this paper we will introduce a novel perspective for viewing the motion estimation problem which results in three original schemes for solving it. The first consists in "flattening the space" and solving a nonlinear estimation problem on the flat (euclidean) space. The second approach consists in viewing the system as embedded in a larger euclidean space (the smallest of the embedding spaces), and solving at each step a linear estimation problem on a linear space, followed by a "projection" on the manifold (see fig. 5). A third "algebraic" formulation of motion estimation is inspired by the structure of the problem in local coordinates (flattened space), and consists in a double iteration for solving an "adaptive fixed-point" problem (see fig. 6). Each one of these three schemes outputs motion estimates together with the joint second order statistics of the estimation error, which can be used by any structure from motion module which incorporates motion error [20, 23] in order to estimate 3D scene structure. The original contribution of this paper involves both the problem formulation, which gives new insight into the differential geometric structure of visual motion estimation, and the ideas generating the three schemes. These are viewed within a unified framework. All the schemes have a strong theoretical motivation and exhibit accuracy, speed of convergence, real time operation and flexibility which are superior to other existing schemes [1, 20, 23]. Simulations are presented for real and synthetic image sequences to compare the three schemes against each other and highlight the peculiarities of each one

Recursive Estimation of Camera Motion from Uncalibrated Image Sequences

In This memo we present an extension of the motion estimation scheme presented in a previous CDS technical report [14, 16], in order to deal with image sequences coming from an uncalibrated camera. The scheme is based on some results in epipolar geometry and invariant theory which can be found in [6]. Experiments are performed on noisy synthetic images

Benthic foraminifers and siliceous sponge spicules assemblages in the Quaternary rhodolith rich sediments from Pontine Archipelago shelf

The bottom samples (Quaternary in age) of two cores (CS1 and Caro1) collected at 60 and 122 m water depth in the marine area near Ponza Island (Pontine Archipelago, Tyrrhenian Sea) are investigated. In particular, benthic foraminifers and siliceous sponge spicules are considered. The coralline red algae (pralines, boxworks and unattached branches) are abundant in both samples and, particularly, in the CS1 bottom as well as the benthic foraminifers. The siliceous sponge spicules also are very diversified and abundant in the CS1 bottom sample, while in the Caro1 bottom they are rare and fragmented. Benthic foraminiferal assemblage of two samples is dominated by Asterigerinata mamilla and Lobatula lobatula, typical epiphytic species but also able to live on circalittoral detrital seafloors, adapting to an epifaunal lifestyle. Based on these data the bottom of the studied cores represents the upper circalittoral zone, within the present-day depth limit distribution of coralline red algae in the Pontine Archipelago (shallower than 100 m water depth)

Molecular mechanisms of cell death: recommendations of the Nomenclature Committee on Cell Death 2018.

Over the past decade, the Nomenclature Committee on Cell Death (NCCD) has formulated guidelines for the definition and interpretation of cell death from morphological, biochemical, and functional perspectives. Since the field continues to expand and novel mechanisms that orchestrate multiple cell death pathways are unveiled, we propose an updated classification of cell death subroutines focusing on mechanistic and essential (as opposed to correlative and dispensable) aspects of the process. As we provide molecularly oriented definitions of terms including intrinsic apoptosis, extrinsic apoptosis, mitochondrial permeability transition (MPT)-driven necrosis, necroptosis, ferroptosis, pyroptosis, parthanatos, entotic cell death, NETotic cell death, lysosome-dependent cell death, autophagy-dependent cell death, immunogenic cell death, cellular senescence, and mitotic catastrophe, we discuss the utility of neologisms that refer to highly specialized instances of these processes. The mission of the NCCD is to provide a widely accepted nomenclature on cell death in support of the continued development of the field

Some Inverse Eigenproblems for Jacobi and Arrow Matrices

The first and third authors were supported by direct grant from the Naval Postgraduate School. The third author also acknowledges support from the Interdisciplinary Project Center for Supercomputing at the ETH, Zurich.The article of record as published may be found at DOI: 10.1002/nla.1680020302We consider the problem of reconstruction Jacobi matrices and real symmetric arrow matrices from two eigenpairs. Algorithms for solving these inverse problems are presented. We show that there are reasonable conditions under which this reconstruction is always possible. Moreover, it is seen that in certain cases reconstruction can proceed with little or no cancellation. The algorithm is particularly elegant for the tridiagonal matrix associated with a bidiagonal singular value decomposition

Some inverse problems for Jacobi and arrow matrices

http://archive.org/details/someinverseprobl00borgN

Evidential modeling for pose estimation

International audiencePose estimation involves reconstructing the configura- tion of a moving body from images sequences. In this paper we present a general framework for pose esti- mation of unknown objects based on Shafer's eviden- tial reasoning. During learning an evidential model of the object is built, integrating different image fea- tures to improve both estimation robustness and pre- cision. All the measurements coming from one or more views are expressed as belief functions, and com- bined through Dempster's rule. The best pose esti- mate at each time step is then extracted from the resulting belief function by probabilistic approxima- tion. The choice of a sufficiently dense training set is a critical problem. Experimental results concerning a human tracking system are shown

Motion estimation by vision for mobile mapping with motorcycle

In this paper we present a vision algorithm to estimate the angular velocity of a motorcycle. This estimate, integrated with the measurements provided by other sensors such as a speedometer allows for a complete reconstruction of the trajectory followed by a motorcycle. The proposed scheme is, then, a valid alternative to the use of costly inertial platform to compensate for missing GPS data in order to geo-register information gathered by on-board sensors