According to the principle of transference, a compact three-dimensional representation of a rigid body kinematics is obtained by substituting dual for real numbers. This representation has recently been applied to robotics where in addition to its compactness, it allows to constitute the Jacobian matrix explicitly from the product of the dual transformation matrices with no additional computati...

We calculate the transformation and inverse transformation, in the form of Taylor expansions, from arbitrary coordinates to Fermi-Walker coordinates in tubular neighborhoods of arbitrary timelike paths for general spacetimes. Explicit formulas for coefficients and the Jacobian matrix are given.

OBJECTIVES To evaluate the accuracy of advanced non-linear registration of serial lung Computed Tomography (CT) images using Large Deformation Diffeomorphic Metric Mapping (LDDMM). METHODS FIFTEEN CASES OF LUNG CANCER WITH SERIAL LUNG CT IMAGES (INTERVAL: 62.2±26.9 days) were used. After affine transformation, three dimensional, non-linear volume registration was conducted using LDDMM with or...

Averaging diffeomorphisms is a challenging problem, and it has great applications in areas like medical image atlases. The simple Euclidean average can neither guarantee the averaged transformation is a diffeomorphism, nor get reasonable result when there is a local rotation. The goal of this paper is to propose a new approach to averaging diffeomorphisms based on the Jacobian determinant and t...

Simulation and analysis of complex, large-scale dynamic systems can be challenging. Complex system structures are difficult for systems engineers to explore and comprehend, and simulating large-scale systems often requires long computation time because of the size of the system equations. This paper introduces the Jacobian pattern for continuous dynamic systems. A Boolean linear fractional tran...

In this paper, we present a linear transformation (LT) to obtain warped features from unwarped features during vocal-tract length normalisation (VTLN). This LT between the warped and unwarped features is obtained within the conventional MFCC framework without any modification in the signal processing steps involved during the feature extraction stage. Further using the proposed LT, we study the...

As in Section 4.3, this objective is minimized using the Gauss-Newton method. Specifically, we start from an initial transformation T and perform optimization iteratively. In each iteration, we locally parameterize T with a 6-vector ξ, evaluate the residual r and Jacobian Jr at T, solve the linear system in (21) to compute ξ, and use ξ to update T. To compute the Jacobian, we need the partial d...

The instantaneous kinematic analysis of a manipulator defines the direction and magnitude (translational and rotational) of impending motion at a specific point in time. This analysis is position dependent, and assumes apriori knowledge of the position information. From the position kinematic analysis, a kinematic transformation between joint space and tool space can be represented as: ( ) x = ...

Let φ be a polynomial over K (a field of characteristic 0) such that the Hessian of φ is a nonzero constant. Let φ̄ be the formal Legendre Transform of φ. Then φ̄ is well-defined as a formal power series over K. The Hessian Conjecture introduced here claims that φ̄ is actually a polynomial. This conjecture is shown to be true when K = R and the Hessian matrix of φ is either positive or negative de...

In this paper, we suggest a new fast transformation for a divisor addition for hyperelliptic curves. The transformation targets the Jacobian of genus-2 curves over odd characteristic fields in projective representation. Compared to previously published results, the modification reduces the computational complexity and makes hyperelliptic curves more attractive for applications.