Reducing "Structure From Motion": a General Framework for Dynamic Vision - Part 1: Modeling

The literature on recursive estimation of structure and motion from monocular image sequences comprises a large number of different models and estimation techniques. We propose a framework that allows us to derive and compare all models by following the idea of dynamical system reduction. The "natural" dynamic model, derived by the rigidity constraint and the perspective projection, is first reduced by explicitly decoupling structure (depth) from motion. Then implicit decoupling techniques are explored, which consist of imposing that some function of the unknown parameters is held constant. By appropriately choosing such a function, not only can we account for all models seen so far in the literature, but we can also derive novel ones

Reducing “Structure from Motion”: a general framework for dynamic vision. 1. Modeling

The literature on recursive estimation of structure and motion from monocular image sequences comprises a large number of apparently unrelated models and estimation techniques. We propose a framework that allows us to derive and compare all models by following the idea of dynamical system reduction. The “natural” dynamic model, derived from the rigidity constraint and the projection model, is first reduced by explicitly decoupling structure (depth) from motion. Then, implicit decoupling techniques are explored, which consist of imposing that some function of the unknown parameters is held constant. By appropriately choosing such a function, not only can we account for models seen so far in the literature, but we can also derive novel ones

Volume independence in large Nc QCD-like gauge theories

Volume independence in large \Nc gauge theories may be viewed as a generalized orbifold equivalence. The reduction to zero volume (or Eguchi-Kawai reduction) is a special case of this equivalence. So is temperature independence in confining phases. In pure Yang-Mills theory, the failure of volume independence for sufficiently small volumes (at weak coupling) due to spontaneous breaking of center symmetry, together with its validity above a critical size, nicely illustrate the symmetry realization conditions which are both necessary and sufficient for large \Nc orbifold equivalence. The existence of a minimal size below which volume independence fails also applies to Yang-Mills theory with antisymmetric representation fermions [QCD(AS)]. However, in Yang-Mills theory with adjoint representation fermions [QCD(Adj)], endowed with periodic boundary conditions, volume independence remains valid down to arbitrarily small size. In sufficiently large volumes, QCD(Adj) and QCD(AS) have a large \Nc ``orientifold'' equivalence, provided charge conjugation symmetry is unbroken in the latter theory. Therefore, via a combined orbifold-orientifold mapping, a well-defined large \Nc equivalence exists between QCD(AS) in large, or infinite, volume and QCD(Adj) in arbitrarily small volume. Since asymptotically free gauge theories, such as QCD(Adj), are much easier to study (analytically or numerically) in small volume, this equivalence should allow greater understanding of large \Nc QCD in infinite volume.Comment: 32 pages, 4 figure

Reducing “Structure from Motion”: a general framework for dynamic vision. 2. Implementation and experimental assessment

For pt.1 see ibid., p.933-42 (1998). A number of methods have been proposed in the literature for estimating scene-structure and ego-motion from a sequence of images using dynamical models. Despite the fact that all methods may be derived from a “natural” dynamical model within a unified framework, from an engineering perspective there are a number of trade-offs that lead to different strategies depending upon the applications and the goals one is targeting. We want to characterize and compare the properties of each model such that the engineer may choose the one best suited to the specific application. We analyze the properties of filters derived from each dynamical model under a variety of experimental conditions, assess the accuracy of the estimates, their robustness to measurement noise, sensitivity to initial conditions and visual angle, effects of the bas-relief ambiguity and occlusions, dependence upon the number of image measurements and their sampling rate

Motion control - A SMC approach

Motion control involves many diversified control problems of complex nonlinear systems. In this paper we will be addressing the SMC approach for multi-body mechanical systems control. The main feature of the SMC is constraint of the system motion into manifold in system state space. It will be shown that usage of the SMC methods is a natural way of addressing problems in motion control including constrained systems, redundant systems and functionally related systems to name some. The consistent application of the SMC methods leads to natural decomposition of system motion for redundant tasks and allows simple, straight forward dynamical decoupling of the multiple tasks

A constrained, total-variation minimization algorithm for low-intensity X-ray CT

Purpose: We develop an iterative image-reconstruction algorithm for application to low-intensity computed tomography (CT) projection data, which is based on constrained, total-variation (TV) minimization. The algorithm design focuses on recovering structure on length scales comparable to a detector-bin width. Method: Recovering the resolution on the scale of a detector bin, requires that pixel size be much smaller than the bin width. The resulting image array contains many more pixels than data, and this undersampling is overcome with a combination of Fourier upsampling of each projection and the use of constrained, TV-minimization, as suggested by compressive sensing. The presented pseudo-code for solving constrained, TV-minimization is designed to yield an accurate solution to this optimization problem within 100 iterations. Results: The proposed image-reconstruction algorithm is applied to a low-intensity scan of a rabbit with a thin wire, to test resolution. The proposed algorithm is compared with filtered back-projection (FBP). Conclusion: The algorithm may have some advantage over FBP in that the resulting noise-level is lowered at equivalent contrast levels of the wire.Comment: This article has been submitted to "Medical Physics" on 9/13/201

Sufficient Conditions for Feasibility and Optimality of Real-Time Optimization Schemes - II. Implementation Issues

The idea of iterative process optimization based on collected output measurements, or "real-time optimization" (RTO), has gained much prominence in recent decades, with many RTO algorithms being proposed, researched, and developed. While the essential goal of these schemes is to drive the process to its true optimal conditions without violating any safety-critical, or "hard", constraints, no generalized, unified approach for guaranteeing this behavior exists. In this two-part paper, we propose an implementable set of conditions that can enforce these properties for any RTO algorithm. This second part examines the practical side of the sufficient conditions for feasibility and optimality (SCFO) proposed in the first and focuses on how they may be enforced in real application, where much of the knowledge required for the conceptual SCFO is unavailable. Methods for improving convergence speed are also considered.Comment: 56 pages, 15 figure

Algorithms for envelope estimation

Envelopes were recently proposed as methods for reducing estimative variation in multivariate linear regression. Estimation of an envelope usually involves optimization over Grassmann manifolds. We propose a fast and widely applicable one-dimensional (1D) algorithm for estimating an envelope in general. We reveal an important structural property of envelopes that facilitates our algorithm, and we prove both Fisher consistency and root-n-consistency of the algorithm.Comment: 30 pages, 2 figures, 2 table