The limitations of rigid fingertips in the precise and algorithmic study of manipulation have been discussed in many works, some dating back more than a decade. Despite that fact, much of the work in dexterous manipulation has continued to use the "point-contact" model for finger-object interactions. In fact, most of the existing tactile sensing technologies are not adaptable to deformable fingertips. We report on experimental results obtained with a deformable tactile sensor whose properties are well-suited to manipulation. The results presented here show that the sensor described provides a rich set of tactile data.

We present an analysis of SFM from the point of view of noise. This analysis results in an algorithm that is provably convergent and provably optimal with respect to a chosen norm. In particular, we cast SFM as a nonlinear optimization problem and define a bilinear projection iteration that converges to fixed points of a certain cost-function. We then show that such fixed points are "fundamental", i.e. intrinsic to the problem of SFM and not an artifact introduced by our algorithm. We classify and characterize geometrically local extrema, and we argue that they correspond to phenomena observed in visual psychophysics. Finally, we show under what conditions it is possible-given convergence to a local extremum-to "jump" to the valley containing the optimum; this leads us to suggest a representation of the scene which is invariant with respect to such local extrema.

Several nonlinear partial differential equations that model the scale evolution associated with continuous-space multiscale morphological erosions, dilations, openings, and closings are discussed. These systems relate the infinitesimal evolution of the multiscale signal ensemble in scale space to a nonlinear operator acting on the space of signals. The type of this nonlinear operator is determined by the shape and dimensionality of the structuring element used by the morphological operators, generally taking the form of nonlinear algebraic functions of certain differential operators.>

In the study of mechanisms, there is a significant set of problems for which the solutions require the application of techniques from the fields of both kinematic and elastic issues. Through an emphasis on a geometrical interpretation of these subjects, the authors formulate and solve a number of questions which arise in the design of compliant devices. An important part of this study is the development of an extension of the Frenet-Serret equations which describes the elasto-geometric properties of a thin beam viewed as a nonzero cross-sectional extension of a space curve.>

The authors present an iterative algorithm for the recovery of 2-D motion, i.e., for the determination of a transformation that maps one image onto another. The local ambiguity in measuring the motion of contour segments (the aperture problem) implies a reliance on measurements along the normal direction. Since the measured normal flow does not agree with the actual normal flow, the full flow recovered from this erroneous flow also possesses substantial error, and any attempt to recover the 3-D motion from such full flow fails. The proposed method is based on the observation that a polynomial approximation of the image flow provides sufficient information for 3-D motion computation. The use of an explicit flow model results in improved normal flow estimates through an iterative process. The authors discuss the adequacy and the convergence of the algorithm. The algorithm was tested on some synthetic and some simple natural time-varying images. The image flow recovered from this scheme is sufficiently accurate to be useful in 3-D structure and motion computation.>

The authors present an iterative algorithm for the recovery of 2D motion, i.e. an algorithm for the determination of a transformation which maps one image onto another. The local ambiguity in measuring the motion of contour segments (called the aperture problem) makes it necessary to rely on measurements along the normal direction. Since the measured normal flow itself does not agree with the actual normal flow, the full flow recovered from this erroneous normal flow possesses substantial error too, and any attempt to recover the 3D motion from such full flow is doomed to failure. The present method is based on the observation that a polynomial approximation of image flow provides sufficient information for 3D motion computation. The use of an explicit flow model makes it possible to improve normal flow estimates through an iterative process. The algorithm has been tested on synthetic and simple natural time-varying images. The image flow recovered from this scheme was sufficiently accurate as to be useful in 3D structure and motion computation.>

The theoretical background for an ongoing experiment in motion control is described. The work has as its goal the discovery of efficient ways to distribute the computation and organize the communication needed to manage systems involving many degrees of freedom and unpredictable environments. Formalizing motion control to the extent necessary to be able to investigate correctness of motion-control programs is an important subgoal. A conceptual framework is presented together with some remarks of an existing implementation which uses these ideas.>

This paper deals with the recovery of optical flow, that is to say, with the identification of a vector field, defined on some subset of the image plane, which accounts for the infinitessimal time evolution of the image of a particular object. Our formulation is general in that it allows for the vector field to be expressed as a linear combination of an arbitrary (but chosen in advance) finite collection of vector fields and it allows the measurements to include (a) the velocity of feature points, (b) the velocity normal to an evolving contour and/or (c) the velocity tangent to an intensity gradient. The method is based on least squares and an explicit formula for the generalized inverse of a class of integral operators. It involves a gramian whose invertibility is necessary and sufficient for the identification of a unique best fitting vector field. Various important subcases have been studied earlier and reported in the computer vision literature, the emphasis here is on the systematic development of a general tool.

The purpose of this paper is to analyze, in some depth, the processes involved in the manipulation of solid objects using robotic hands. Such an analysis has implications for design, control, and motion planning. We make a case for the use of finger surfaces which have a distributed compliance and show how such surfaces may be realized by fluid filled pods. The arguments given are based on an analysis of the complexity of the kinematic programming problem, an enumeration of the number of independent feedback control channels necessary for achieving a firm grasp and an examination of frictional forces. We emphasize the necessity of dealing with models which lead to well-posed problems throughout the grasping process and point out some of the ways that earlier models lead to ambiguous situations.

Previous article Full AccessErrata: On the Number of Multiplications Required for Matrix MultiplicationR. W. Brockett and D. DobkinR. W. BrockettSearch for more papers by this author and D. DobkinSearch for more papers by this authorhttps://doi.org/10.1137/0207021PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout"Errata: On the Number of Multiplications Required for Matrix Multiplication." SIAM Journal on Computing, 7(2), p. 238 Previous article FiguresRelatedReferencesCited ByDetails Volume 7, Issue 2| 1978SIAM Journal on Computing History Submitted:24 August 1977Published online:31 July 2006 Article & Publication DataArticle DOI:10.1137/0207021Article page range:pp. 238-238ISSN (print):0097-5397ISSN (online):1095-7111Publisher:Society for Industrial and Applied Mathematics

In this paper we give a new algorithm for matrix multiplication which for n large uses $n^2 + o(n^2 )$ multiplications to multiply $n \times p$ matrices by $p \times n$ matrices provided $p \leqq \log _2 n$. Multiplication and division by 2 is necessary in this algorithm. This is to be compared with $pn^2 $ for the standard algorithm and $ \simeq p^{.58} n^2 + o(n^2 )$ for an algorithm of Hopcroft and Kerr [1] which, however, requires no multiplication and division by 2.

Although general theories are beginning to emerge in the area of automata based complexity theory, there are very few general methods or even general problem formulations in the area of arithmetic complexity. In this paper we propose and defend a general model for studying bilinear multiplication in order to provide a common framework for discussing a wide class of problems.